EPA/600/3-85/050
POLLUTANT SORPTION TO SOILS AND SEDIMENTS
IN ORGANIC/AQUEOUS .SOLVENT SYSTEMS
by
Jaw-Kwei Fu and Richard 6. Luthy
Department of Civil Engineering
Carnegie-Mellon University
Pittsburgh, Pennsylvania 15213
Cooperative Agreement No. CR810878
Project Officer
Samuel W. Karickhoff
Chemistry Branch
Environmental Research Laboratory
Athens, Georgia 30613
ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
ATHENS, GEORGIA 30613
-------
DISCLAIMER
Although the research described in this report has been funded wholly
or in part by the United States Environmental Protection Agency through
Cooperative Agreement CR810878 to Carnegie-Mellon University, it has not
been subjected to the Agency's required peer and policy review and therefore
does not necessarily reflect the views of the Agency and no official endorse-
ment should be inferred.
11
-------
FOREWORD
Environmental protection efforts are increasingly directed towards
prevention of adverse health and ecological effects associated with specific
compounds of natural or human origin. As part of this Laboratory's research
on the occurrence, movement, transformation, impact, and control of envi-
ronmental contaminants, the Chemistry Branch studies the chemical/biochemical
reactions that control pollutant fate in soil and water ecosystems.
An understanding of the effect of a polar solvent in the aqueous phase
on the physico-chemica-1 properties of aromatic organic compounds is important
in assessing the reactions and fates of these pollutants in heavily comtamin-
ated aquatic and terrestrial systems. In the study reported here, the pres-
ence of a polar solvent in the aqueous phase was shown to have a significant
effect on the solubility and soil sorption characteristics of hydrophobic
aromatic solutes. Chemical thermodynamic models developed in the study
may be used in predicting and assessing near-source transport of hydrophobic
aromatic solutes in soil systems, in estimating aromatic solubility in
heavily contaminated industrial wastewater, in evaluating solute properties
for use in analytical procedures, and in other environmental applications.
Rosemarie C. Russo, Ph.D.
Director
Environmental Research Laboratory
Athens, Georgia
iii
-------
ABSTRACT
This report presents the results of an investigation to evaluate the
solubility of relatively hydrophobic aromatic solutes in an aqueous phase
containing a miscible polar organic solvent and to determine the effect of
a polar solvent in the aqueous phase on the sorption of aromatic solutes
onto soils. The investigation was comprised of both theoretical and experi-
mental developments. The results from the solubility experiments were in-
terpreted by means of chemical thermodynamic models to predict solute solu-
bility in solvent/water systems, and the results of the soil sorption studies
were evaluated by a model that relates reduction in sorption coefficient with
increase in solubility.
The results of the investigation showed that hydrophobic aromatic solutes
generally display a semi-logarithmic increase in solubility with increasing
volume fraction of solvent in solvent/water mixtures-. This results in a
semi-1ogarithmic decrease in the tendency for these solutes to sorb onto soil.
These findings were predicted by theory. However, an important result obtained
from the sorption experiments was that the increase in solute solubility does
not result in a directly proportional decrease in the sorption coefficient.
This is believed to be the result of the solvent swelling the soil organic
carbon material and thereby increasing the accessibility of the solute to this
material. The increase in solute solubility in solvent/water mixtures and the
decrease in sorption partition coefficients may be predicted by chemical
thermodynamic models. This information is useful for assessing near-source
transport of hydrophobic aromatic solutes in soil systems in the event of a
spill or discharge of solutes with a polar solvent. The predictive techniques
developed in this investigation may be useful in other applications in environ-
mental engineering, such as for the estimation of aromatic solute solubility
in heavily contaminated industrial wastewaters, or for evaluation of solute
properties for use in analytical procedures.
The effect of solvent on the increase in solute solubility and the decrease
in soil sorption is much more pronounced for the more hydrophobic solutes. Hence,
the results of the investigation are particularly significant for assessment of
reactions and fates for those aromatic compounds that exhibit lowest aqueous
phase solubility.
This work was submitted in fulfillment of Cooperative Agreement No.
CR810878 by Carnegie-Mellon University under the sponsorship of the U.S.
Environmental Protection Agency. This report covers a period from September
1983 to June 1985, and work was completed as of June 1985.
iv
-------
CONTENTS
FOREWORD iii
ABSTRACT iv
LIST OF FIGURES vii
LIST OF TABLES viii
1. INTRODUCTION 1
2. PREDICTION OF SOLUTE SOLUBILITY IN SOLVENT/WATER MIXTURES 3
Phase Equilibria and Activity 4
Activity Coefficient and Molecular Structure 9
Estimation of Activity Coefficient by the UNIFAC Approach 10
Estimation of Infinite Dilution Activity Coefficient 12
Estimating Solid Solute Solubility from Infinite Dilution 12
Activity Coefficient
Estimating Liquid Solute Solubility from Infinite Dilution 18
Activity Coefficient
Prediction of Solute Solubility in Mixed Solvent Systems by Use of 19
an Excess Free Energy Approach
Prediction of Solute Solubility in Mixed Solvents by Log-Linear 29
Relationships
Molecular Surface Area Approach 34
Intermolecular Forces and Solute Solubility 36
Dispersive Interactions 36
Dipole Moment 37
Hydrogen bonding 39
Hydrophobic Effects and Polarity 41
Solubility Parameters 42
Summary 48
3. EXPERIMENTAL MEASUREMENT OF SOLUTE SOLUBILITY IN 49
SOLVENT/WATER MIXTURES
Introduction 49
Experimental Components 49
Materials 49
Glassware 51
Experimental Instruments 51
Experimental Procedures to Measure Solute Solubility 52
Experimental Results 55
Interferences 64
4. PREDICTION OF AROMATIC SOLUTE SOLUBILITY IN SOLVENT/WATER 65
SYSTEMS
Introduction 65
Activity Coefficient 66
Volumetric Addition Assumption 73
Solute Solubility in Pure Solvent 78
Solute Solubility in Solvent/Water Mixtures 86
Error Analysis for Solute Solubility in Solvent/Water Mixtures 112
Solubility Parameter and Solubility in Co-solvent/Water Mixtures 118
V
-------
Summary 124
5. EFFECT OF ORGANIC SOLVENT ON SORPTION OF AROMATIC SOLUTES 127
ONTO SOILS
Introduction 127
Sorption of Aromatic Solutes onto Soils 128
Sorption and Soil Organic Carbon Content 132
K and Octanol/Water Partition Coefficient 134
OC
K and Solute Solubility 137
OC
Solvent Effect on Solute Sorption 139
Organic Solute Sorption onto Soils in Solvent/Water Mixtures 142
Sorption Isotherm Tests 144
Soil Organic Carbon Content 146
Solvent Effect on Solute Sorption 147
Effect of Organic Carbon Content 160
The Effect of Solvent on Soil Organic Carbon 163
Summary 169
6. SUMMARY AND CONCLUSION 171
Summary 171
Conclusion 175
REFERENCES 177
Appendix A. EXAMPLE CALCULATION OF ACTIVITY COEFFICIENT USING 186
UNIFAC
Appendix B. PREDICTION OF SOLUTE SOLUBILITY BY THE UNIFAC 191
APPROACH, THE LOG-LINEAR APPROACH, AND THE EXCESS FREE
ENERGY APPROACH
Appendix C. ERROR ANALYSIS FOR THE PREDICTION OF SOLUTE 211
SOLUBILITY IN CO-SOLVENT/WATER SYSTEMS
Appendix D. Physical Characteristics of Soils 230
Characteristics of soils 230
Vi
-------
List of Figures
Figure 4-1: Naphthalene Solubility in Methanol/Water Mixtures
Figure 4-2: Naphthalene Solubility in Acetone/Water Mixtures
Figure 4-3: Naphthalene Solubility in Ethanol/Water Mixtures
Figure 4-4: Naphthalene Solubility in Propanol/Water Mixtures
Figure 4-5: Naphthol Solubility in Merhanol/Water Mixtures
Figure 4-6: Naphthol Solubility in Acetone/Water Mixtures
Figure 4-7: Quinoline Solubility in Methanol/Water Mixtures
Figure 4-8: Quinoline Solubility in Acetone/Water Mixtures
Figure 4-9: 3,5-Dichloroaniline Solubility in Methanol/Water Mixtures
Figure 4-10: 3,5-Dichloroaniline Solubility in Acetone/Water
Mixtures
Figure 4-11: Aniline Solubility in Methanol/Water Mixtures
Figure 4-12: Aniline Solubility in Ethanol/Water Mixtures
Figure 4-13: Phenanthrene Solubility in Methanol/Water Mixtures
Figure 4-14: Phenanthrene Solubility in Ethanol/Water Mixtures
Figure 4-15: o-Xylene Solubility in Methanol/Water Mixtures
Figure 4-16: o-Xylene Solubility in Acetone/Water Mixtures
Figure 4-17: o-Xylene Solubility in Ethanol/Water Mixtures
Figure 4-18: o-Xylene Solubility in Propanol/Water Mixtures
Figure 4-19: Linear Regression for Solute Solubility in
Methanol/Water Mixtures
Figure 4-20: Linear Regression for Solute Solubility
Acetone/Water Mixtures
Figure 5-1: Naphthalene Sorption in Methanol/Water Mixtures
Figure 5-2: Naphthalene Sorption in Acetone/Water Mixtures
Figure 5-3: Naphthol Sorption in Methanol/Water Mixtures
Figure 5-4: Quinoline Sorption in Methanol/Water Mixtures
Figure 5-5: 3,5-Dichloroaniline Sorption in Methanol/Water Mixtures
Figure 5-6: Naphthalene Sorption onto Hagerstown Silt Loam in
Methanol/Water and Acetone/Water Mixtures
Figure 5-7: Solvent Effect on Sorption Partition Coefficient for
Naphthalene-Solvent/Water Systems
Figure 5-8: Solvent Effect on Solute Sorption Partition Coefficient
for Methanol/Water Systems
Figure 5-9: Naphthalene Sorption onto Berkeley silt loam in
Methanol/Water Mixtures
Figure 5-10: Naphthalene Sorption onto Tifton silt loam in
Methanol/Water Mixtures
Figure 5-11: Naphthalene Sorption onto Soils in Methanol/Water
Mixtures
Figure 5-12: Sorbent Organic Carbon Content Effect on Naphthalene
Sorption onto Soils in Methanol/Water Mixtures
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
in 107
149
150
151
152
153
154
158
159
164
165
166
167
vn
-------
List of Tables
Table 2-1: Physical Properties of Solutes and Solvents* 38
Table 2-2: Classification of Compounds by Hydrogen Bonding" 40
Table 2-3: Solvent Polarity Using ET as the Indicator 43
Table 2-4: Solubility Parameters of Solvents and Solutes 45
Table 2-5: Partial Solubility Parameters* " 47
Table 3-1: Specifications for HPLC Analysis 53
Table 3-2: Naphthalene Solubility in Methanol/Water Mixtures 56
Table 3-3: Naphthalene Solubility in Acetone/Water Mixtures 57
Table 3-4: Naphthol Solubility in Methanol/Water Mixtures 58
Table 3-5: Naphthol Solubility in Acetone/Water Mixtures 59
Table 3-6: Quinoline Solubility in Methanol/Water Mixtures 60
Table 3-7: Quinoline Solubility in Acetone/Water Mixtures 61
Table 3-8: 3,5-Dichloroaniline Solubility in Methanol/Water Mixtures 62
Table 3-9:" 3,5-Dichloroaniline Solubility in Acetone/Water Mixtures 63
Table 4-1: Predicted Infinite Dilution Activity Coefficients for 68
Aromatic Solutes in Pure Solvent Systems
Table 4-2: Predicted Infinite Dilution Activity Coefficients for 69
Aromatic Solutes in Methanol/Water Mixtures
Table 4-3: Predicted Infinite Dilution Activity Coefficients for 70
Aromatic Solutes in Acetone/Water Mixtures
Table 4-4: Predicted Infinite Dilution Activity Coefficients for 71
Aromatic Solutes in Ethanol/Water and Propanol/Water
Mixtures
Table 4-5: Predicted Activity Coefficients for Solvents in Co- 72
solvent/Water Mixtures
Table 4-6: Error Analysis for the Volume Addition Assumption for 75
Methanol/Water Systems
Table 4-7: Error Analysis for the Volume Addition Assumption for 76
Acetone/Water Systems
Table 4-8: Physical and Chemical Properties of Solutes and 80
Solvents Employed for Solute Solubility Calculations*
Table 4-9: Comparison of Calculation Procedures for Estimation of 82
Solute Solubility in Pure Solvents
Table 4-10: Solute Solubilities in Pure Solvents 83
Table 4-11: Solvent Interaction Parameters for the Binary Solvent 109
Systems
Table 4-12: Naphthalene Solubility in the Methanol/Water System 111
Using the Molecular Surface Area Approach
Table 4-13: Error Analysis of Solute Solubility Prediction in 114
Solvent/Water Mixtures by the UNIFAC Approach
Table 4-14: Error Analysis of Solute Solubility Prediction in 115
Solvent/Water Mixtures by the Excess Free Energy
Approach
viii
-------
Table 4-15:
Table 4-16:
Table 4-17:
Table 4-18:
Table 4-19:
Table 5-1:
Table 5-2:
Table 5-3:
Table 5-4:
Table A-1:
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
A-2:
A-3:
B-1:
B-2:
B-3:
B-4:
B-5:"
B-6:
B-7:
B-8:
B-9:
B-10:
B-11:
B-12:
B-13:
B-14:
B-15:
B-16:
B-17:
B-18:
C-1:
Table C-2:
Table C-3:
Table C-4:
Table C-5:
Table C-6:
Table C-7:
Error Analysis of Solute Solubility Prediction in 116
Solvent/Water Mixtures by the Log-linear Approach
Solubility Parameter and Solubility of Naphthalene in
Methanol/Water Mixtures
Solubility Parameter and Solubility of Naphthalene in
Acetone/Water Mixtures
Solubility Parameter and Solubility of Phenanthrene in
Methanol/Water Mixtures
Solubility Parameter and Solubility of Phenanthrene in
Ethanol/Water Mixtures
Organic Solute Octanol/Water Partition Coefficients*
Sorption Partition Coefficients for Solvent/Water
Mixtures
Calculated a Values
Effect of Solvent on Solute Solubility, and Sorption
Partition Coefficient for Hagerstown Silt Loam
Functional Group Parameters for Methanol, Naphthalene
and Water
Functional Group Interaction Parameters
Functional Group Interaction Energy
Naphthalene Solubility in Methanol/Water Mixtures
Naphthalene Solubility in Acetone/Water Mixtures
Naphthalene Solubility in Ethanol/Water Mixtures
Naphthalene Solubility in Propanol/Water Mixtures
Naphthol Solubility in Methanol/Water Mixtures
Naphthol Solubility in Acetone/Water Mixtures
Quinoline Solubility in Methanol/Water Mixtures
Quinoline Solubility in Acetone/Water Mixtures
3,5-Dichloroaniline Solubility in Methanol/Water Mixtures
3,5-Dichloroanifine Solubility in Acetone/Water Mixtures
Aniline Solubility in Methanol/Water Mixtures
Aniline Solubility in Ethanol/Water Mixtures
Phenanthrene Solubility in Methanol/Water Mixtures
Phenanthrene Solubility in Ethanol/Water Mixtures
Xylene Solubility in Methanol/Water Mixtures
Xylene Solubility in Acetone/Water Mixtures
Xylene Solubility in Ethanol/Water Mixtures
Xylene Solubility in Propanol/Water Mixtures
Error Analysis for
Methanol/Water System
Error Analysis for
Acetone/Water System
Error Analysis for
Ethanol/Water System
Error Analysis for
Propanol/Water System
Error Analysis for Naphthol
System
Error Analysis for Naphthol
System
Error Analysis for
Methanol/Water System
Naphthalene Solubility in
Naphthalene Solubility in
Naphthalene Solubility in
Naphthalene Solubility in
Solubility in Methanol/Water
Solubility in Acetone/Water
Quinoline Solubility in
120
121
122
123
136
157
161
162
187
189
189
192
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
212
213
214
215
216
217
218
ix
-------
Table
C-8:
Error Analysis for Quinoline Solubility in Acetone/Water
System
219
Table
C-9:
Error Analysis for 3,5-Dichloroaniline Solubility in
Methanol/Water System
220
Table
C-10:
Error Analysis for 3,5-Dichloroaniline Solubility in
Acetone/Water System
221
Table
C—11:
Error Analysis for Aniline Solubility in Methanol/Water
System
222
Table
C-12:
Error Analysis for Aniline Solubility in Ethanol/Water
System
223
Table
C-13:
Error Analysis for Phenanthrene Solubility in
Methanol/Water System
224
Table
C-14:
Error Analysis for Phenanthrene Solubility in
Ethanol/Water System
225
Table
C-15:
Error Analysis for Xylene Solubility in MethanoJ/Water
System
226
Table
C-16:
Error Analysis for Xylene Solubility in Acetone/Water
System
227
Table
C-17:
Error Analysis for Xylene Solubility in Ethanol/Water
System
228
Table
C-18:
Error Analysis for Xylene Solubility in Propanol/Water
System
229
Table
D-1:
Sieve Analysis of Soils
231
Table
D-2:
Classification of Soils
233
X
-------
Chapter 1
INTRODUCTION
The purpose of this research is to evaluate the solubility of aromatic
organic compounds in aqueous solutions containing miscible polar solvent,
and to determine the effect of solvent in the aqueous phase on sorption of
aromatic compounds onto soil. This study is comprised of both theoretical
and experimental developments. The investigation was motivated by the need
to understand the effect of polar solvent in the aqueous phase on physico-
chemical properities of aromatics solutes. This is important for assessment
of the reactions and fates of these types of pollutants in heavily
contaminated systems.
It is shown in this investigation that the presence of polar solvent in
the aqueous phase can have significant effect on the solubility and soil
sorption characteristics of hydrophobic aromatic solutes. These phenomena
would be manifested wherever solvents and aromatic solutes are comingled,
such as in wastewaters from chemical manufacturing processes or in
concentrated hazardous/toxic wastes. The effect of solvent on sorption of
aromatic solutes onto soils is related to the evaluation of certain problems
associated with groundwater contamination. This work addresses the
situation for which near-source transport of hydrophobic aromatic solutes
may be accompanied also by the release of water-soluble organic solvents,
as in the case of spill or other discharge of concentrated wastes.
The investigation reports on results of experiments with various
aromatic solutes including unsubstituted polycyclic aromatic compounds as
well as polar, substituted aromatic compounds. This was done in order to
-------
2
represent a range of solute' chemical properties including hydrophobicity,
polarity and hydrogen bonding. The results from the solubility experiments
are interpreted by means of chemical thermodynamic models to predict
solute solubility in solvent/water systems. The results of the soil sorption
studies are evaluated by a model which relates reduction in sorption partition
coefficient to increased solute solubility in these systems.
This report begins with a chapter which provides a synthesis of
available chemical thermodynamic techniques that may be used to estimate
solute activity and solubility for nonelectrolytes in solvent/water systems.
That chapter is followed by a discussion of experimental procedures and
results of experiments which examine aromatic solute solubility in
solvent/water mixtures. The next chapter evaluates and and discusses several
approaches to predict aromatic solute solubility in solvent/water systems.
This evaluation considers a data set comprised of eighteen solute-
solvent/water systems. The next chapter explains the development of a
model to predict aromatic solute sorption onto soil in solvent/water mixtures.
That chapter includes presentation of experimental results and a discussion of
the model's appropriateness. The report concludes with a general summary
of the results of the investigation.
-------
3
Chapter 2
PREDICTION OF SOLUTE SOLUBILITY
IN SOLVENT/WATER MIXTURES
This chapter summarizes several approaches which may be used to
estimate solute solubility in solvent/water mixtures. These various
approaches have a common theoretical basis in thermodynamics of
nonelectrolyte fluid-phase equilibria; however, the approaches differ in the
manner in which non-ideal effects are considered. It would be desired that
the properties of a solution could be calculated from the properties of the
pure components; unfortunately theoretical knowledge has not yet been
developed to where this can be done with a degree of generality (Prausnitz,
1969). Therefore, it is necessary to rely upon experimental data to provide
information on interaction parameters and other characteristics of real
mixtures. Nonetheless, chemical thermodynamic techniques are useful for
correlating data in a logical framework in order that predictions can be made
about systems for which no data exist.
The following section introduces the subject of thermodynamics of
fluids and defines several terms which are employed later. This is followed
by a discussion of a procedure whereby activity coefficient may be predicted
from molecular structure, and this is followed by a discussion of estimation
of activity coefficient in pure solvent. These subjects are then extended to
predict solute solubility in binary solvent mixtures.
-------
4
Phase Equilibria and Activity
This section reviews the concept of chemical potential for ideal and
real solutions. The chemical potential of a real solution component is
expressed in terms of fugacity, which is defined in terms of an activity
coefficient and mole fraction of the solute. Relationships between activity
coefficient and mole fraction are used for predicting solubility.
The solubility of a liquid or a solid solute in aqueous solution can be
addressed by thermodynamics of phase equilibria. The principal
thermodynamic function for describing phase equilibria at constant
temperature was defined by Gibbs as the partial molar free energy, G(, or
chemical potential, fij (Kcal/mole),
where G is the Gibbs free energy, n. is the moles of component i, P is
pressure, T is temperature, and n. is the mole numbers of all other
components except i.
The equilibrium composition depends on various factors including
temperature, pressure, and the chemical characteristics of the constituents of
the system. The mathematical description of phase equilibria begins with the
statement that at equilibrium the chemical potential of each component must
be the same in each phase
where i refers to the ith component and a and /J to the different phases.
For purposes of engineering calculations, it is necessary to relate chemical
potential to temperature, pressure, and mole fraction, X,. This is facilitated
by introducing certain other functions, namely activity and fugacity.
(2-1)
<2-2)
For pure liquids and pure solids, the chemical potential is the partial
molar free energy, 5. (Kcal/mole), and it is a function of temperature and
-------
5
pressure alone. The value of the chemical potential for a pure component at
a pressure of 1 atm is by convention referred to as the standard state
chemical potential, p0. The relationship between chemical potential and
pressure for n moles of pure gas (g) at constant temperature is derived from
the ideal gas law (Prausnitz, 1969)
dP
dG = V dP = nRT — (2-3)
P
Integrating from a standard pressure, P° to P, and recognizing for a one-
component gas phase that the chemical potential is AG/n
G ¦ (3° p
= RT In —— = /j(g) - fi°(g) (2-4)
n P°
where pig) is the chemical potential for the pure gas, V is the volume, R is
the gas constant, T is the system temperature, and P is the pressure. If the
standard pressure is taken as one atmosphere, and for an ideal mixture in
which the chemical potential of each component behaves as if the other
components were not present, then
//.(g) = /i.°(g) + RT In P, (2-5)
where P( is the partial pressure of the component i. The partial pressure is
equal to the total pressure times the mole fraction of the component in the
gas phase (Yj), P( * Y P, and Equation 2-5 can be expressed as
fiig) = //."(g) + RT In P + RT In Y( (2-6)
For an ideal solution, the chemical potential is defined in a manner
similar to Equation 2-5 as for gases
/i,(sol) = /^"(sol) + RT In X, (2-7)
where //.°(sol) is the standard state chemical potential and X( is the mole
fraction of component i in solution. For a solution in equilibrium with a
-------
6
vapor phase, the chemical potential in the liquid phase and gas phase are
equal, and
fiiso\) - (2-8)
If the vapor phase is an ideal gas mixture, then
^."(sol) + RT In X. = /i.°(g) + RT In P. (2-9)
This equation incorporates the relationship between Henry's law and Raoult's
law. Raoult's law states that the ideal gas vapor pressure, P, of an ideal
solution component is equal to the product of the vapor pressure of the pure
liquid component, P,° and the mole fraction of the component in solution, P
« X. P.°. Thus the standard state for a solution component depends on the
ideal gas standard state, and the convention (Raoult's law) that X. « 1 is the
standard state for component i in solution. For real solutions, Raoult's law
is obeyed as X. approaches 1, and
//.°{sol) = («j0(g) + RT In P. (2-10a)
Henry's law states for an ideal component that the mole fraction in
solution is proportional to the ideal gas partial pressure, P( =
Comparison with Equation 2-10a shows that Henry's law constant is
/ fi.°lso!) - p °(g) \
H. ¦ exp \ — / (2-1 Ob)
RT
For real solutions, Henry's law is obeyed as X( -» 0. However, Equations 2-4
and 2-5 are valid only for ideal gas. In order to generalize the expressions,
G. N. Lewis defined a function f, called fugacity, to describe the escaping
tendency for any component in any system, whether solid, liquid, or gas,
pure or mixed, ideal or non-ideal. For a real gas, the chemical potential of a
component is expressed by an idealized pressure, called fugacity, f
f.
= /*,° + RT In —^ (2-11)
-------
7
where f 0 is the standard state fugacity. For a pure, ideal gas, the fugacity
is equal to the pressure, and for a component i in a mixture of ideal gases,
the fugacity is equal to its partial pressure. Since gas systems, pure or
mixed, approach ideal gas behavior at low pressures, it is the convention that
the standard state is taken as one atmosphere, for which the standard state
fugacity of the component i approaches unity, and thus Equation 2-11 can be
expressed as
ft. = * RT In f( (2-12)
The fugacity approaches the partial pressure of the component as the mixture
becomes infinitely dilute (Stumm and Morgan, 1981). The relationship
between fugacity and partial pressure may be expressed by a fugacity
coefficient (Prausnitz, 1969)
f, - r„ P, C-131
The fugacity coefficient is normally equal to unity for real gases at
pressures in the range of one atmosphere.
For the case of real solutions, the chemical potential of a component is
expressed by an idealized concentration called activity, a.
= p* + RT In a. (2-14)
The relationship between actual mole fraction, X(, and activity is given by an
activity coefficient, y
a, • y, X, (2-15)
Hence, the chemical potential in real solutions is
p. = p* + RT In X, + RT In y( (2-16)
The term RT iny. describes the partial molar free energy of interactions that
occur in non-ideal mixtures. The conventional definition of the reference
state for a solvent, identified as component 1, is
-------
8
y, -» 1 as x, -» 1 (2-17)
Thus for pure solvent, /<1 = when ai = y1 X « 1. For a solute, identified
as component 2, the reference state is the infinitely dilute solution. In
general, y2 > 1 for a dilute solution of a given component in a given solvent.
As the solution becomes increasingly dilute, the value of y2 approaches a
limiting value, y2°°> known as the infinite dilution activity coefficient
(Prausnitz, 1969). Knowledge of the infinite dilution activity coefficient can
be used to estimate solute solubility in water and in solvent/water mixtures.
In addition, knowledge of the infinite dilution activity coefficient can be used
to estimate other properties important to the environmental scientist, such as
solvent/water partition coefficient and Henry's law constants (Grain, 1982;
Campbell and Luthy, 1985).
The aqueous solubility of a hydrophobic organic compound in water or
in water/polar solvent mixtures can be expressed in terms of fugacity using
the Raoult's law convention
f - X yfR (2-18)
where X is the mole fraction of the solute in solution, y is the solute
activity coefficient, and fR is the reference fugacity, i.e., the fugacity of the
pure compound at the system temperature. For liquid compounds fR is the
pure liquid compound vapor pressure, fL. For solids, fR is the extrapolated
liquid fugacity below the triple point, f', not the solid fugacity or vapor
pressure (Mackay, 1977; Prausnitz, 1969). Thus for liquids, X = My since fR *
fL, and for solids, X = ( f* I fR )ly. As explained below, the ratio { f* / fR )
can be estimated by several standard procedures.
-------
9
Activity Coefficient and Molecular Structure
Potentially, the most utilitarian approach towards prediction of chemical
properties of mixtures is to base the approach on a description of the
molecular structure of solvent and solute and to employ minimal chemical
data. The following describes an approach of this type which has been
developed in recent years to estimate activity coefficient in liquid mixtures.
The approach was adapted to this investigation in order to estimate solute
infinite dilution activity coefficient in pure solvent and in solvent/water
mixtures.
The UNIFAC approach (UNIQUAC Functional Group Activity Coefficient)
is a group contribution method for the prediction of activity coefficients of
nonelectrolytes in liquid mixtures. The method combines a solution-of-
functional-group concept with a model based on an extension of the quasi
chemical theory (UNIQUAC) of liquid mixtures (Abrams and Prausnitz, 1975).
The method is founded on the principle that group contribution concepts may
be used to estimate thermodynamic properties of a liquid mixture, as first
proposed by Langmuir (1925). Derr and Deal (1969) developed the analytical
solution of groups (ASOG) method for correlating and predicting activity
coefficients, and these concepts were incorporated by Fredenslund et al.
(1975) in the UNIFAC method. Subsequently, the data base of the model has
been extended (Gmehling et al. 1982) and applied to various problems
including: estimating activity coefficients in organic solvent mixtures
(Fredenslund et al. 1975), estimating the solubility of a solid in a solvent
(Gmehling et al. 1978), evaluating the solubility of an aromatic hydrocarbon in
various solvents (Martin et al. 1981), estimation of octanol/water partition
coefficient (Arbuckle, 1983), predicting the solubility of chlorobenzenes in
water (Benerjee, 1984), and estimating aromatic solute distribution coefficients
for both polar and non-polar chemical compounds (Campbell and Luthy, 1985).
-------
10
Estimation of Activity Coefficient by the UNIFAC Approach
The fundamental purpose of a solution-of-groups model is to utilize
existing phase equilibria data for predicting phase equilibria of systems for
which no experimental data are available. The UNIFAC model follows Derr
and Deal's (1969) ASOG model which assumes that the logarithm of the
activity coefficient is the sum of two parts —
• A combinatorial part that provides the contribution due to the
difference of molecular size and shape of the molecule in the
mixture, and
• A residual part that provides the contribution due to molecular
interactions.
The combinatorial part is estimated by using the athermal Flory-Huggins
equation (Flory, 1968), and the residual part is based on functional group
interactions estimated by the Wilson equation (Wilson, 1962). The
computational procedures employed in the UNIFAC model are reviewed below.
In a multicomponent mixture, the activity coefficient of component i
can be expressed as
ln yt s ln 7,° + ln y" (2-19)
where the first term represents the combinatorial contribution and the second
term represents the residual contribution. The combinatorial part of Equation
2-19 can be expressed as
Z TT*
In y" - In — + - q. In — + I ^_X I (2-20)
T' X, 2 1 ' X, j "
with area fraction 6 and segment fraction f are related to mole fraction X
through
r.x« „ q'X<
t 6i = _— {2_21)
Xi ^j-Tl
The pure-component molecular volume r. and surface area q( are given by
group contributions Rk and Qk as
-------
11
'i = I',' 1, = Z',' 1, 12-22)
k k
and
I. = - (r.-q.) - (r.-1) (2-23)
i 2 ' ' i
In these expressions X. is the mole fraction of component i, vk' is the
number of the functional groups of type k in component i, Rk is the van der
Waals volume for functional group k, Qk is the van der Waals surface area
for functional group k, 0. is the area fraction of component i, is the
segment fraction which is similar to volume fraction of component i, and z
is the coordination number, usually taken to be 10. The residual contribution
of the activity coefficient is given by
ln ?iR = [ ln rk " ln rK ] (2_24)
k
where the group residual activity coefficient is related to composition and
temperature through
m r„ ¦ Q,(l - In [ Xoj*. ] - -^=-)) (2-25)
m m l >
> © f
¦ 1 n' nm
n
In this expression ©m is the area fraction of group m over all groups
0 X 2 VmJ XJ
€> = X = '¦ (2-26)
m m _
II-'x
¦ n n r, t JLmm* n j
n j n '
The group interaction parameter y is given by
* = exp (- %=) (2-27)
1 mn ' T
In the above expressions, rfc is the functional group-k residual activity
coefficient, and r 1 is the residual activity coefficient of functional group-k in
a reference solution containing only component i (X, = 1). X is the mole
i m
-------
12
fraction of functional group m, ©m is the surface area fraction of functional
group m, and ^mn is the interaction parameter between functional group m
and n. The parameter amn is a group interaction parameter which is a
measure of the difference in interaction energy between group m and n. In
general, a is independent of temperature (Grain. 1982) and a # a .
mn nm
Considerable effort has been given to collecting and tabulating values of a ,
mn
R, and Q from experimental phase equilibrium data. The most up-to-date
tabulation for amn is given by Gmehling et al. (1982).
Example calculations that demonstrate the use of the UNIFAC approach
for estimating solute infinite dilution activity coefficient are provided in
Appendix A.
Estimation of Infinite Dilution Activity Coefficient
The UNIFAC model can be used to predict infinite dilution solute
activity coefficient (y2°°) in water/co-solvent systems. A convenient
methodology is to treat the solvent system as one component and the solute
as a second component. The solvent system is treated as a single
component in order to allow estimation of solute solubility from appropriate
forms of the two- or three-suffix Margules equation as explained below. In
this approach the solvent system may be envisioned as comprised of a
"molecule" of water and co-solvent in proportion to the mole fraction
water/co-solvent composition of interest. It does not matter if the
"molecule" is comprised of water and co-solvent in non-integer ratios when
using a solution-of-groups approach to estimate activity coefficients.
Estimating Solid Solute Solubility from Infinite Dilution Activity Coefficient
For the case of liquid solutes, mole fraction solubility in a solvent can
be estimated readily as the reciprocal of the activity coefficient, provided the
activity coefficient is sufficiently large. The situation is not as straight
forward for estimation of the solubility of a solid solute (e.g. naphthalene)
-------
13
from knowledge of activity coefficient. This is because solubility depends
not only on the activity coefficient but also on the fugacity of the standard
state to which it is referred and on the fugacity of the pure solid (Prausnitz,
1969). If the solute is designated by the subscript 2, and if there is
negligible solubility of the solvent in the solid, then at equilibrium
f - 4 mm V f O
2 (pure solid) 2(solute in solution) ^2 2 2
where f 0 is the standard state fugacity to which the liquid-phase activity
coefficient, y2, refers. The mole fraction solubility can be calculated from
the activity coefficient and the ratio of the fugacities in the solid phase and
the standard state. For many solids the vapor pressure of the pure solid and
the vapor pressure of the subcooled liquid is not large. Also the pure solute
activity coefficient can be assumed as unity, and thus the vapor pressures of
the pure solid and the subcooled liquid can be substituted for calculating
solute solubility (Prausnitz, 1969)
f P *
^ 2(pure solid) 2 (pure solid) ^
2 yf° P'
' 2 2 2 (pure subcooled liquid)
The standard state fugacity for solids is usually defined by convention
as the fugacity of pure, subcooled liquid at the temperature of the solution
at a specified pressure. Although this is a hypothetical standard state, it is
one for which properties can be calculated provided that the solution
temperature is not very far removed from the triple point of the solute
(Prausnitz, 1969; Mackay and Shiu, 1977).
An expression for the ideal solubility of a solid solute in a liquid
solvent is given by Equation 2-29, but a method still needs to be given for
finding the saturation pressure for the subcooled liquid. This can be achieved
by assuming that the solution is ideal. Then y2 - 1 and the solubility can be
expressed as (Prausnitz, 1969)
-------
14
In
2(pure solid)
/T-T \ AC T
(2-30)
where ACp is the difference of specific heat between solid and liquid, AHf is
the enthalpy of fusion for the solid in units of cal/mole at the triple point
temperature, and T is the triple-point temperature, °K.
Two simplifications in Equation 2-30 are frequently made but these
usually introduce only a slight error (Prausnitz, 1969). First, for most chemical
compounds there is little difference between the triple-point temperature and
the normal melting temperature; also the difference in the heat of fusion,
AH{, at these two temperatures is often negligible. Therefore, in practice the
melting temperature can be used to substitute for the triple-point temperature,
and AHf at the melting temperature can be used for heat of fusion at the
triple-point. Secondly, the three terms on the right hand side of Equation
2-30 are not of equal importance; the first term is the dominant one and the
remaining two, being of opposite sign, have a tendency to cancel each other,
especially if T and T are not far apart (Prausnitz, 1969). Therefore in many
cases it is sufficient to consider only the first term which includes AHf, and
Equation 2-30 becomes
where T is the system temperature in °K, Tm is the melting temperature of
the pure solid in °K, R is the gas constant, 1.987 cal/mole °K, and AHf is the
enthalpy of fusion for the solid in cal/mole, at the melting point.
" 'n y2 x2 s ~,n C
2(pure tolid)
f
(2-31)
Equation 2-31 employs heat of fusion, which is usually close to heat of
-------
15
solution for a solid (Prigogine and Defay, 1973). It may be concluded from
Equation 2-31 that ideal solubility of a solid solute in a liquid solvent
increases with temperature. Also, at a given temperature the solid with the
lower melting temperature will have the greater solubility among solids with
similar enthalpy of fusion, and likewise, among solids with similar melting
temperatures, the solid with the lowest enthalpy of fusion will exhibit the
greater solubility.
Hildebrand (1950) proposed that the heat of fusion at temperature T can
be calculated from the heat of fusion at the melting point, AHfm, and the
molal heat capacity of the solute as liquid (C ,) and as solid (C )
P«l P«t
AH, = AH ¦ (C , - C ) (T ¦ T) (2-32)
f f.m p,l p,« m
This expression can be used to compensate in part for the error introduced
by omission of ACp terms in the simplified fugacity ratio expression given
by Equation 2-31. Heat capacity data are available for only a few solid
solutes; for example, these data were available for two of the aromatic
solutes of interest in this investigation. Fortunately, the AH
-------
16
Various researchers have reported for many moderately-sized organic
molecules, including substituted aromatic hydrocarbons, that entropy of fusion
is nearly constant at about 13 to 13.5 cal/mole °K (Tsonopoulos and Prausnitz.
1971; Yalkowsky, 1979). Thus Equation 2-31 can be reduced to the following
expression by assuming AS( is constant at 13 cal/mole °K
T-T
In y2 x2 = 6.56 Hp> (2-34)
Yalkowsky (1981) has discussed the assumptions in simplification of
Equation 2-30 in which the mole fraction solubility of the crystalline solute
(Xe) and the subcooled liquid Xscl may be given as either
Xc
ln
AS
RT
—(T -T)
or
(2-35)
Xc AS, T
in (jsi) • " -^In (f > (2-3«
Equation 2-35 results from the assumption that ACp 8 0, while Equation 2-36
results from the assumption that ACp « AS,. In an ideal solution, the solute-
solute and solvent-solvent interactions are equivalent to the solute-solvent
interactions, and there is no change in heat or volume on mixing. This
results in infinite miscibility of a solute, or the ideal mole fraction solubility
of the solute can be assumed as unity, X,el « 1. It was demonstrated by
Yalkowsky for polycyclic aromatic hydrocarbons at room temperature (300 °K)
with melting points less than about 100 °C (e.g. naphthalene, acenaphthene,
fluoranthene, flourene, and phenanthrene) that there was little difference
between Equations 2-35 and 2-36, as both equations showed good correlation
for solubility of fourteen polycyclic compounds in benzene. However,
-------
17
Equation 2-35 was recommended because a value of the entropy of fusion
which could be calculated from the data was closer to an expected value of
about 13 cal/mole °K. Also, Equation 2-35 is analogous to Equation 2-31.
In this investigation UNIFAC was used to estimate solute infinite
dilution activity coefficient in various systems, y2°°- For those cases in
which y2°° > 100, Equation 2-31 can be used to estimate solute mole fraction
solubility for solids
™ AHf T
m Y, X, - - (--1) tt-37)
m
However, if y2°° is < 100, then the mole fraction solubility calculation must
recognize that at infinite dilution there is appreciable solubility of solute, and
solvent mole fraction does not approach unity. Lyman (1982) suggests that if
10 < y2°° < 100, the solubility of solute may be described by the two-suffix
Margules equation with X2 being solved by trial and error
_ AH, T
In X2 + (1 - X/ In y2 = - ( 1) (2-38)
m
If y2°° < 10, the recommended procedure is to estimate several values of
y2°° at corresponding values of X2 and to plot y2°° versus X2. Then using
matched values of y2°° and X2, search for a value of In (y2°°) that equals
T „
(AHf/RT) ( 1). UNIFAC can be used to estimate values of y2°° for
m
different values of X2, and thus mole fraction solubility is given by the value
of X2 which satisfies Equation 2-37. If no value of X2 satisfies Equation
2-37, then it may concluded that the solute and solvent are miscible at the
system temperature, T.
-------
18
As discussed later, AH{' was calculated according to Equation 2-32 if
appropriate heat capacity data for the solid and liquid phase were available.
If there was no ACp data available, AH(m was used as AH( in Equation 2-31
without correction. If no data on AH, were available, then the heat of
f,m
fusion of the solute was estimated according to Equation 2-33.
Estimating Liquid Solute Solubility from Infinite Dilution Activity Coefficient
For the case of liquid solutes, mole fraction solubility is estimated
from y2°° as follows. If y2°° > 1000, the solubility of solute can be
estimated by
X2 - <2-39)
If 50 < y2°° < 1000, then X2 is calculated from the following equation by
1
trial and error with X2 = ^ as the initial approximation (Lyman, 1982)
y 2
(1 - 4X2 + 3x22) lny2°° +¦ (2x2 - 3x22) Iny,00 + In X2 - ln(1-x2) = 0 (2-40)
If 7.4 < y2°° < 50, then UNIFAC is used to estimate several values of y1 and
y at corresponding values of X1 and X2< Then the Gibbs free energy of
mixing, (AGM/ RT), is calculated as a function of component mole fraction
(X » X ) and component activity coefficients y2)
AGm
X, In y, + X2 In y2 + X, In X, + X2 In X2 (2-41)
AGm
Values of are then plotted on the ordinate versus X, on the abscissa.
DT *
-------
19
If two phases are predicted, a curve with two minima will result; if only one
minima is obtained, then the two liquids may be assumed to be miscible in
all proportions. In the case of a curve with two minima, a straight line may
be drawn simultaneously tangent to the curve at the two minima. The points
of tangency correspond to the solubility limits for solvent in solute and
solute in solvent (Lyman, 1982).
If y2°° < 7.4, the two liquids can be assumed to be completely miscible
at the system temperature.
Prediction of Solute Solubility in Mixed Solvent Systems by Use of an Excess
Free Energy Approach
The following derivation explains a relationship between solute activity
coefficient, solute Henry's law constant in pure solvent, and solute-free
solvent volume fractions. This relationship (Equation 2-57) is then used with
an expression for the excess Gibbs free energy of mixing to estimate the
solubility of a solute in a mixed solvent system (Equation 2-73). The
theoretical development described below follows the approach of Williams
and Amidon (1984a). In the following, subscript 1 refers to co-solvent,
subscript 2 refers to solute, and subscript 3 refers to water.
For a solute in equilibrium with its solid phase, the fugacity of the
solute in solution is given from Equation 2-18
y, X, f,° = f,, = f,' (2-42)
' 2 2 2 2 (pur* jolid) 2
where f 0 is simplified notation for the fugacity of the hypothetical pure
liquid solute at the same temperature T and pressure P as the solution (f2
.), and f * is a simplified notation for the fugacity of the solute in
subcooled liquid) 2 ¦ r
the liquid solution
f • - f , (2-43)
2 2 (solute in liquid solution)
The solute activity coefficient, y2, has been defined according to the
-------
20
symmetric or Raoult's law convention for which y, 1 as X, 1. As X
*2 2 2
approaches zero, y2 becomes
v 00 = lim y (2-44)
*2-»o
and the mole fraction solubility limit is given as
v
In X = In (—) - lim In y (2-45)
f 0 x„->0
2 2
This condition may be expressed by Henry's law as
V
lim — = H2 (2-46)
x,-»° x.
2 2
where H is Henry's law constant. If the mole fraction solubility of solute in
solution is sufficiently small such that Henry's law holds, then
V " '»». .>» ' HA tt-47)
If Equation 2-46 is expressed in logarithms, and if the expression is written
for solvents, as indicated by subscripts 1 for the organic co-solvent and
subscript 3 for water, and subscript 2 for solute, then for the organic co-
solvent
H2,
lim In y = In (2-48)
x _*0 2-1 - o
2 2
and for solvent 3, water
H2,3
lim In y » In (2-49)
x,-*° f °
2 2
and for a binary mixture of solvents 1 and 3, as indicated by a subscript m
H2m
iim In x. = In — (2-50)
2'm f°
Combining Equations 2-45 and 2-48 to 2-50 gives expressions for mole
fraction solubility, X*, of component 2 in terms of Henry's law constant and
solute fugacity in solution
-------
21
f,s
ln X2 18 = ln ZT"' ln V = ln X2 1S + ln H2, (2_51)
2,1
f,S
In x s = In In f,s = In x,,s + In H (2-52)
2,3 |_| 2 2,3 2,3
2,3
f
In x, * = In ——; In f„s = In x, * + In H (2-53)
2,m |_| 2 2,m 2,m
2,m
The volume fraction, z., of any component in the mixture is computed from
component mole fraction as
X. q,
z. = and y z.= 1 (2-54)
Z*.
V q.
j 1 '
where q. is the molar volume for component i, which is calculated as
component molecular weight divided by component density. It is convenient
to define terms with respect to solute-free volume fraction, i.e. for which X2
0 and thus z2 -» 0, and in this case
z, ~ z3 = 1 (2-55)
where the circumflex denotes solute-free terms. If Equation 2-51 is
multiplied by z? and Equation 2-52 is multiplied by z"3, and the two
resulting equations are combined, then
In f* = F, (In X * + In H,,) + z, (In X,,1 + In H„,) (2-56)
2 I 2,1 2,1 3 2,3 2,3
Substitution of Equation 2-53 into Equation 2-56 results in
ln * r3 " (ln HW " F, ln Hi., " "J (2"57)
For a multicomponent mixture. Equation 2-57 may be expressed as
in v ¦ Z r,in v -
-------
22
which may be called an excess Henry's law constant. Williams and Amidon
(1982a) employed an excess free energy model as proposed by Wohl (1946)
to develop an expression for the excess Henry's law constant. This is
explained below.
In a homogeneous multicomponent system, the total free energy, G, can
be expressed in terms of each component i
(2-59)
where n( is the number of moles for component i, G.° is the free energy per
mole of pure component i, and AG is the excess free energy per mole of
this mixture. The first term in Equation 2-59 represents the contribution of
free energy of each of the pure components, the second term represents the
free energy of ideal mixing, and the third term represents the excess free
energy from nonideal mixing. The partial molar free energy of component j
in the mixture at constant temperature, T, and constant pressure, P, can be
expressed as
( ^ )t,p = Gj + RT ,n Xj + RT ,n {2-60>
where
n. AG/RT]
r, ' Kp.Vj <*•"
a n,
The excess free energy in a three component mixture can be expressed in a
general form as (Wohl, 1946)
AG
-¦ 2a. z.z. + 2a z.z. + 2a„„z z.
2.3RT (q^ + q2x2 + q3x3>
12 1 2 13 1 3 23 2 3
+ 3a z 2z + 3a z z 7 * 3a z 2z
112 1 2 122 1 2 113 1 3
+ 3a z z 1 + 3a z 2z + 3a z z 2
133 1 3 223 2 3 233 2 3
-------
23
6a' z z z
123 1 2 3
(2-62)
x. q.
where z. = —J——, and q values are molar volume, and the "a" terms are
' 5. x. q.
I I
interaction parameters between molecules. For example a12 is the interaction
parameter between one molecule of component 1 and one molecule of
component 2, a1l3 is the interaction parameter for three interacting molecules
comprised of two molecules of component 1 and one molecule of component
3. The numerical coefficient and the volume fraction parameters in each of
the terms in Equation 2-62 relate to the probability of interaction, i.e. (2zi z2)
is the probability that any two molecules consisting of one molecule each of
components 1 and 2 will interact (Prausnitz, 1969). Equation 2-62 is referred
to as a three suffix equation, i.e. a solute or solvent molecule is considered
as interacting with no more than two other bodies. Higher or lower suffix
equations may be written if it is desired to consider fewer or more body
interactions. Wohl (1946) and Wilson and Amidon (1984a) simplified Equation
2-62 by defining
A = q (2a + 3a )
2-1 2 12 112'
A = q (2a + 3a )
3-1 3 13 113'
A2-3 = <*2 (2a23 + 3a233>
A1-2 ~ C'l^ai2 + 3»122^
A1-3 S ^1<2ai3 + 3.,33)
a,, = q,<2a,, + 3
3-2 2 32 s223
C = q [3a + 3a + 3a - 6a 1
1 H1 112 133 223 123
C = ~ [3a + 3a + 3a - 6a ]
2 H2 L 112 133 223 123 ¦*
C = q [3a + 3a + 3a - 6a ]
3 H3 112 133 223 123J
Substitution of these expressions into Equation 2-62
results in an expression for solute activity coefficient in
solvents.
and differentiation
a mixture of binary
-------
24
/8nTAG/RT\
* ' J.P.nyn3 ~ 'n?2,m
a°2
qa . q2
¦ Z3 [A2.3+2z2(A3 —-A2 3)]+zi [Aj 1+2z2(A1 2~-A2 ,)]
3
q2 ^2 ^2 ^2
+ ziZ3tA3-2-+2z2, + z z,[A, — + A - A,
' 2,m 3 2-3 1 2-1 1 3 3-2„ 2-1 l-3_
% qi
* 2F1(A1.3^ - A ^ - cX - CX)1 (2-64)
q, 3 "l
Further simplification of Equation 2-64 is obtained by recognizing that
q q
C = C, —, and C3 = C, — (2-65)
q, q,
It may also be assumed that the following interactions are similar (Williams
and Amidon, 1984a)
— . Ai-* qi
a,22 = aii2' and — = - <2-66)
M2-1 q2
/v A2-3 ^2
a233 = a223' and — = ~ <2-67)
3-2 q3
Substitution of these expressions into Equation 2-64 results in
q2
In r2.m S Z3A2-3 + Z,A2-, + A,-3 Z1 Z3<2 Z ~
q1
q2
+ 2A3-1 Zl' z3 ~ " C2Z1Z3 <2-68)
-------
25
Comparison of the first two terms on the right hand side of Equation 2-68
with Equations 2-48 and 2-49 shows
(2-69)
(2-70)
Hi!.
f2°
lim
In
=
In
A2-1
X -»o
2
2
H,,
2,3
s
f2°
lim
In
2,3
In
A2-3
x2-»o
1
H2.m
f2°
lim
x2-»o
In
?2,m "
In
(2-71)
Therefore
ln H2.m = *, 'n H2,1 + *3 ln H2.3 + A1-3 *1*3 {2f^
~ 2A I,2 z, — - C ,z z (2-72)
3-1 1 3 _ 2 13
3
Substitution of Equation 2-72 into Equation 2-57 results in an expression for
solute solubility in a binary solvent mixture
q2
In X, = z In X * + zln X, * + A, ,z,z, (2z -1) —
2,m 1 2.1 3 2,3 1-313 1
^1
^2
+ 2A J,2z. — - C z z (2-73)
3-11 3 q 2 13
Equation 2-73 expresses the solubility of solute (2) in a binary mixed
solvent (components 1 and 3). The first two terms of Equation 2-73
represent the solubility of solute in pure solvents. The next two terms
represent the contribution of solvent-solvent interactions, and the last term
of Equation 2-73 is due to the interaction between solute and solvent.
Several input data are needed in order to estimate solute solubility in a
multicomponent system through use of Equation 2-73,
• Solute solubility in pure solvents, (X21* and X3*);
• Solvent-solvent interaction constants, A3^ and A13; and
• Solute-solvent interaction constant, C2<
-------
26
Application of Equation 2-73 requires various information as listed
above. Some of these information needs can be estimated by use of the
UNIFAC model. Equation 2-73 was employed in this investigation by using
UNIFAC estimates of solvent activity coefficients to predict solute solubility
in pure solvent and/or to predict the solvent-solvent interaction constants
(At 3 and A3 J. These procedures are discussed below.
Solubility of a solute in a pure organic co-solvent can be obtained
either from literature (Weast, 1983, Stephen and Stephen, 1963), or estimated
from the procedures described in the previous section. It is noted that while
solute solubility in water may be available for various aromatic solutes,
comparatively little information is available on solute solubility in common
organic co-solvents. The solvent-solvent interaction constants (Ai 3 and A )
are independent of solute, and they can be estimated from activity
coefficient, molar volume and solute-free volume fractions of the solvents.
If the mole fraction of the solute is near zero ( X2 -» 0), the volume fraction
of the solute is close to zero ( z2 -» 0), and by applying the definition of
A and A into Equation 2-73, the molar excess free energy is given as
1-3 3-1
(Williams and Amidon, 1984b)
Af5 A, „ A
— =—[z^/IX.q, ~ XA)] ~ XA)] (2-74)
RT q, q3
also
— s In y - X lny + X In y3 (2-75)
RT T 1
and thus
A1-3
x, lny, + x3 lny3 = [z,z32 {x,q, + X3q3)]
^i
\ i
~ — [z(X,q, + X3q3)] (2-76)
^3
Equation 2-73 was used in this investigation to predict solute solubility in
water/co-solvent system. This was done by using Equation 2-76 from which
the constants A^3 and A3>) may be computed from knowledge of solvent
-------
activity coefficients. The solvent activity coefficients (y1 and y3) for
different co-solvent/water compositions can be estimated by UNIFAC method.
z"7, and z~3 can be calculated from Equation 2-54, and hence the constants
A1 3 and A3 can be obtained by statistical regression of two parameters. In
this investigation the two parameter statistical regression procedure was
performed according to the techniques described by Ryan et al. (1981).
Williams and Amidon (1984b) employed Equations 2-73 and 2-76 to
describe the solubility of ten compounds in ethanol/water mixtures. In their
study the solvent-solvent interaction parameters were determined from
estimation of activity coefficient using partial pressure data for ethanol/water
mixtures. The constant C„ accounts for interaction between solute and the
two solvents, and Williams and Amidon (1984b) estimated C2 by linear
regression of the difference between the experimental solubility and
calculated solubility without the C2 term using Equation 2-73. The C2 terms
were obtained in this fashion for ten compounds of interest in pharmaceutical
science, such as acetanilide, barbituric acid, antipyrine, and phenobarbital.
Williams and Amidon (1984b) noted that in principle it is possible to obtain
the constant C2 from only one or two observations on solute solubility in a
dual solvent system. They observed that Equation 2-73 adequately described
the systems investigated except for antipyrine which was not as well
characterized by Equation 2-73. This was attributed to antipyrine having very
high solubility in both solvents which invalidated the assumptions made in
deriving Equation 2-73; that is, the assumption that the solubility of solute
was small. It was noted by these investigators that the solvent-solvent
interaction constants in combination with the ideal mixture solubilities tended
to overpredict for nonpolar compounds and underpredict for polar solutes,
hence C2 was usually of opposite sign to the sum of the solvent-solvent
terms. It was also noted that the C2 term could be related to the polar or
nonpolar nature of the solute by correlation of C2 with solute octanol-water
partition coefficient, Kow. For eight solutes and ethanol-water mixtures C2
was correlated with K as
OW
-------
28
C2 = -3.96 -2.66 log Kow r = 0.95 (2-77)
This correlation suggests that it may be possible to estimate C2 from
octanol-water partition coefficient data, and then use an estimated C2 term in
conjunction with the solvent-solvent terms and pure solvent solubilities to
predict the solute solubility-solvent composition profile.
Williams and Amidon (1984c) refer to Equation 2-73 as a reduced three-
suffix solubility equation, as developed from an excess free energy model
proposed by Wohl (1946). In additional work they obtained experimental
vapor pressure-solvent composition data for ethanol-propylene glycol and
propylene giycol-water systems to estimate binary solvent interaction
constants (the "A" terms) in order to describe phenobarbital solubility in
these solvent mixtures. It was found that the three suffix excess free energy
model predicted solute solubility for the binary solvent systems. It was
concluded that a log-linear solubility relationship is observed when the
solvent interaction constants {the A terms) are small compared to the
interaction between solute and solvent mixture (as estimated by C2). Thus,
the solubility of a solute in propylene glycol-water mixtures showed an
approximate semi-logarithmic relationship between solubility and volume
fraction propylene glycol because solubility may be described from a volume
fraction weighted sum of the pure solvent solubilities and a solute-solvent
interaction term.
It was concluded that the three-suffix equation was ..well suited for the
systems for which it was derived, as for solutes with low solubility in water
or other solvent. It was judged that for pharmaceutical purposes this was
not a restriction, as compounds that demonstrate high solubility in a solvent
such as water do not require a second, or co-solvent, to increase their
solubility for administration of pharmaceutical chemicals.
-------
29
Prediction of Solute Solubility in Mixed Solvents by Long-Linear Relationships
Yalkowsky et al. (1972) reported on the solubility of alkyl p-
aminobenzoates in water-propylene glycol mixtures, and found that the
solubility could be described by a semi-logarithmic relationship
where S is the solute solubility in moles/l, Sw is the solute solubility in
water, z is the volume fraction of co-solvent, and
-------
30
where AHy is the molar enthalpy of vaporization at temperature T. Solubility
parameters at 25 °C may range from low values such as 6 (cal/cm3)1'2 for
neopentane, to high values such as 23.45 (cal/cm3)1'2 for water. Hildebrand
and Scatchard developed the concept of regular solutions, which for binary
mixtures of noninteracting, nonpolar molecules predicts that the activity
coefficient can be given by using only pure component data (Reid et al. 1977)
RT In y, = V,2 z22 (3, - 3/ (2-81)
RT In y3 = V22 z,2 (3, - 3/ (2-82)
where z is the volume fraction of the component in the binary mixtures. For
many systems, an interaction energy density term W [(cal/cm3)1'2] must be
introduced into Equations 2-81 and 2-82. This term is essentially an
empirical parameter which is difficult to predict owing to lack of
understanding of intermolecular forces (Campbell et al. 1983; Reid et al. 1977).
The regular solution theory may be extended to mixtures containing polar
components by dividing the solubility parameter into separate contributions
from nonpolar (dispersion) forces and polar forces. This approach also
requires the use of an empirical correction term (Campbell et al. 1983;
Weimer and Prausnitz, 1965). The activity coefficient for solid solutes can
also be estimated using regular solution theory with empirical constants and
molar volume of the subcooled liquid and solubility parameter of the
subcooled liquid. Procedures for estimating these two parameters are
described by Prausnitz (1969). Weast (1983) tabulates solubility parameters
for various organic compounds, both liquid and solid, at 25°C.
The log-linear solubility relationship (Equation 2-78) is related to the
Hildebrand solubility theory. The activity of a solute (subscript 2) in a binary
solvent mixture (subscript 1) is given as
-------
31
V Z 2
log y2 = ( 2 1 ) U,2 t h* - 2W) (2-83)
V z 2
= A {d 2 + 5.2 - 2W) where A = ——— (2-84)
1 2 2.3RT
where is a volume fraction average of the solubility parameters of the
components in the binary solvent mixture, W is the interaction energy density
of solute and solvent, V2 is the solute molar volume, and z is the total
volume fraction of the two solvents in the solution (Martin et al. 1982). The
relationship between solute activity and mole fraction solubility in pure
water, yw and Xw respectively, and that in a water/co-solvent mixture, y2 and
X2 respectively is
log y2 * log X2 = log Xw + log yw (2-85)
This equation may be combined with Equations 2-83 or 2-84 and
expressed as a power series in terms of co-solvent volume fraction, z,
log y,
— ¦ C + C, z + C, z2 + C, z3 + + C zn (2-86)
A o 1 2 2 n
Regression analysis of experimental data can be used to obtain the
coefficients Co, C1# C2, — etc. Equation 2-86 can be combined with Equation
2-85 to give a form of an extended Hildebrand solubility expression
log X, = log X + log y - C A - C Az - C,Az2 - (2-87)
a 2 w ' w o 1 2
Martin et al. (1982) showed that the solubility of semi-polar drugs in
co-solvent/water systems could be described by Equation 2-87 as a fourth
degree power series, as well as by a simplified expression
log X, ¦ log X + (log y - C A) + C,Az (2-88)
a 2 w ' w o 1
Further, it was noted by Martin et al. (1982) that if regression analysis of
Equation 2-88 was performed with perfect accuracy, then log yw would be
-------
32
equal to CqA in order that X2 = Xw as z -» 0. Hence, with the quantity in
parenthesis of Equation 2-88 being numerically small, it may be neglected
and
log X2 = log Xw + C}Az = log +
-------
33
solutions containing various concentrations of ether, formamide,
methyformamide or dimethylformamide (5 = 12.14). It was found that
methylparaben solubility in the mixed solvent systems could be expressed by
the log-linear relationship approach only up to z = 0.5 owing to the
limitations of the log linear model.
In addition to water/co-solvent systems, Martin et al. (1982b)
investigated systems consisting of nonpolar co-solvent mixtures having
solubility parameters lower than the solubility parameters of the solute. The
systems studied were solubility of testosterone (3 = 10.9) and testosterone
propionate (3=9.5) in cyclohexane (5=8.2) with co-solvents such as chloroform
(5=9.1), ethyloleate (5=8.6) and isopropyl myristate (5=8.9). It was found that
the log-linear relationship could not be applied to these systems. A system
of benzoic acid (5 = 11.5) in various proportions of hexane (5=7.3) and ethyl
acetate (3=8.9) had been investigated by Chertkoff and Martin (1960). A plot
of log solubility of benzoic acid versus volume fraction of ethyl acetate co-
solvent was attempted, and it was found that the plot showed considerable
curvature. The plot was fitted by a quadratic equation of the extended
Hildebrand solubility approach (Chertkoff and Martin 1960).
It is concluded that the log-linear solubility relationship describes
systems of semi-polar solutes with water/co-solvent mixtures when the
solubility parameters of the solute is about 3 solubility parameter units lower
than that of the co-solvent in the water/co-solvent mixture. When the co-
solvent is a strong solvating agent, the solute solubility may be described by
the log-linear relationship up to 100% co-solvent even though the solubility
parameters of solute and solvents are similar. For example a sulfadiazine-
dimethylformamide-water system displayed this behavior (Martin et al. 1982).
However, for systems where the solute solubility parameter is between the
solubility parameters of water and co-solvent, and for systems with solute
solubility parameters higher than both of the solvents, the log-linear solubility
relationship may be applied only over a limited range of solvent mixtures.
-------
34
Molecular Surface Area Approach
Yalkowsky et al, {1976) evaluated the increase in aqueous solubility of
nonpolar drugs upon addition of a co-solvent. These authors surveyed the
pharmaceutical literature and concluded that an exponential increase in
solubility was observed for many classes of drugs as long as the solute was
less polar than the mixed solvent. A molecular and group surface area
approach was developed to describe this phenomena. This approach is based
on correlating the mole fraction solubility of a liquid solute in a water/co-
solvent mixture to the solute hydrophobic surface area (HSA) and polar
surface area (PSA). The total surface area (TSA) of the solute is equal to the
surface area of the polar moiety (PSA) plus the hydrocarbonaceous surface
area (HSA)
TSA = PSA + HSA (2-90)
and the solute solubility in a solvent/water mixture can be expressed as
A«u (HSA) + Af (PSA)
"> ¦ln x« *z. <— — 1 ,2"s"
where X is the mole fraction solute solubility in water/co-solvent mixture,
X is the mole fraction solute solubility in water, z is the solute-free
2,3 1
volume fraction of co-solvent, k is the Boltzman constant, T is the system
temperature, A
-------
35
Af (HSA)
In X, = In X, + z, —- (2-92)
2,m 2,3 1
The molecular surface area model shows that in pure co-solvent, the
solute mole fraction solubility, X21, increases exponentially with increase of
hydrocarbonaceous surface area of the solute. The molecular surface area
model also shows that in binary solvent mixtures, the solute mole fraction
solubility increases log-linearly as the fraction of co-solvent, z , increases.
Yalkowsky et al. (1976) found the mole fraction activity coefficient of alkyl
p-aminobenzoates decreased with increase of molecular surface area in pure
solvents and in propylene glycol-water mixtures, and that the solubilities of
five alkyl p-aminobenzoates gave a linear increase in log mole fraction
solubility. It was also found that mole fraction solubility of hexyl p-
aminobenzoate in six solvent-water systems increased log-linearly with
increase of volume fraction of co-solvent.
Although the molecular surface area approach shows good agreement
with published experimental results and appears attractive, it is limited in
application by lack of information for values of microscopic interfacial
energies, i.e. A < H and A
-------
36
Intermolecular Forces and Solute Solubility
The previous discussion has explained thermodynamic approaches for
estimating solute solubility in mixed solute systems. This chapter concludes
with a brief review of the various intermolecular forces that influence
solubility of aromatic solutes in water and in organic solvents. The purpose
of this discussion is to present the relevant physical and chemical
phenomena that influence organic solute solubility in order that some
intuition may be gained with respect to qualitative aspects of solubilization.
Just as thermodynamic properties of pure substances are determined by
intermolecular interactions, so are thermodynamic properties of mixtures
dependent upon intermolecular forces which are operative between the
molecules of the mixture. These forces include nonspecific dispersive forces,
polar interactions, and hydrogen bonding characteristics.
Dispersive interactions
The intermolecular forces may be divided between chemical forces
which extend over very short distances and which entail merging of electron
clouds, and electrical-type forces which extend over larger distances. Aside
from hydrogen-bonding which is a special case of chemical and electrical-
type forces, the general process of solubilization does not entail the
formation of chemical bonds, and electrical-type forces are the principal
interactions governing this phenomena. Besides electrical forces of attraction
that follow Coulomb's law, there are other electrical-type forces including
those forces between molecules possessing a permanent dipole and those
forces between a molecule which induces a dipole in another molecule.
Dispersive, or London-van der Waals forces, arise between atoms or
molecules constituting systems of oscillating charges that induce
synchronized dipoles that attract each other.
Dispersion forces exist between every pair of adjacent molecules and
those interactions normally account for the major part of the interaction
-------
37
energy that holds molecules together in the liquid phase (Prausnitz, 1969).
Dispersion forces occur as a result of the fact that the electrons associated
with a molecule are in constant random motion and at any instant in time
the electrons of the molecule have a specific configuration. This results in
an instantaneous dipole moment which can then induce an interactive force in
another molecule, and this can result in a net attraction between these two
molecules. Dispersive interactions are independent of the interaction of
permanent molecular dipoles, and are closely related to the refractive index
values of the compound. Dispersive interactions become stronger the greater
the refractive index of a compound. In general, refractive index is greater
for compounds with unsaturated bonds, and for compounds with elements
from the second and third rows of the periodic table. Table 2-1 gives the
refractive index and other physical properties of the solutes and solvents
used in this investigation. London-van der Waals interactions are in the
energy range of 2-10 Kcal/mole.
Dipole Moment
The dipole moment of a molecule may be explained by considering a
particle as having two electric charges of the same magnitude, e, but of
opposite sign, held a distance I apart. Such a particle has a permanent
dipole moment, p, defined by p - e I. The common unit for dipole moment
is the Debye (1 Debye ¦ 10"18 esu-cm). The permanent dipole in one particle
can then induce a dipole in a second particle, just as may occur with
dispersive interactions. The net effect is an increase in the total interaction
between these two particles due to the permanent dipole originally present in
one of the molecules. The potential energy of interaction between two
permanent dipoles i and j is obtained by considering electrostatic forces
between the four Charges and by averaging over all orientations. Prausnitz
(1969) suggests that for a pure polar substance, the potential energy of
interaction varies with the fourth power of the dipole moment. Thus a small
increase of the dipole moment can produce a large change in the potential
-------
38
Table 2-1: Physical Properties of Solutes and Solvents"
Refractive
Index
[-]
Dielectric
Constant
[-h£i£J
Dipole
Moment
[Debye]
Solvents
Water
Methanol
Ethanol
Propanol
Acetone
1.62226
1.3288
1.3611
1.3850
1.4535
78.54
32.63
24.30
20.1
20.7
1.85
1.70
1.69
1.66
2.88
Solutes
Naphthalene 1.5898
Naphthol 1.6224
Quinoline 1.6261
3,5-Dichloroaniline NA
Aniline 1.600
Phenanthrene 1.5943
o-Xylene 1.5055
2.54
NA
9.00
NA
6.89
2.80
2.57
0
NA
2.29
NA
1.53
0
0.62
#: Taken from Weast R.C. (1982).
NA: not available.
-------
39
energy of interaction due t& permanent dipoie forces. Table 2-1 shows
values of the dipoie moment for the solutes and solvents used in this study.
Dipoie interactions are quite short range, and this allows for dipoie
interactions to be determined by the sum of functional group dipoles within a
molecule (Snyder, 1978). For example, in aromatic compounds with para-
isomers of the same substituent, the overall dipoie moment of the para-
compound is zero because of cancellation of group dipoie effects, while
group dipoles are additive in ortho-isomers. Nonetheless, the dipoie
interactions of ortho- or para- isomers with surrounding molecules are in fact
quite similar, because two polar groups exist in each molecule, and the
individual polar groups can undergo dipoie interactions (Snyder, 1978). For
these reasons, dipoie interactions often play an important role in affecting
compound solubility and separation.
Hydrogen bonding
The most common chemical effect encountered in solution
thermodynamics is that due to the hydrogen bonding, H-bonding (Prausnitz,
1969). While the "normal" valence of hydrogen is unity, many hydrogen
bond-containing compounds behave as if hydrogen were bivalent. Hydrogen
bonding is an interaction between a "covalently" bonded H atom (A-H) having
the tendency to be donated, and a region of high electron density on an
electronegative atom or group of atoms, B, which can accept the H atom.
Typical proton donor groups include hydrogen bonded covalently to
electronegative atoms such as O, N, S, halogens and in special cases, carbon.
Table 2-2 classifies H-bonds into four types (A, B, AB and N) in which H-
bond refers to an interaction according to the operational criteria of Pimentel
and McClellan (1960). The H-bond leads to the formation of molecular
aggregates, which in many aspects conform to the criteria of chemical bond.
However, H-bonds differ from chemical bonds in that H-bonds exist in a state
of dynamic equilibrium. This is evident by comparison of differences in
bonding strengths. The bonding strength for ordinary chemical bonds is on
-------
40
Table 2-2: Classification of Compounds by Hydrogen Bonding"
Compound Molecule Contains
Class Proton Proton Examples
Donor Acceptor
(Acid) (Base)
A Yes No
B No Yes
AB Yes Yes
N No No
Haloforms, highly halogenated
compounds, acetylenes
Ketones, aldehydes, ethers,
tertiary amines, olefins,
aromatics, nitriles
Water, alcohols, carboxylic
acids, phenol, primary and
secondary amines
Saturated hydrocarbons, carbon
disulfide, carbon tetrachloride
* After Pimentel and McClellan (1960)
-------
41
the order of 50 to 200 Kcal/mole, while that for H-bonds is on the order of 2
to 10 Kcal/mole.
An unassociated substance which contains an H-bond group (type-A or
type-B) is usually more soluble in a solvent that can supply the other partner
in an H-bonding interaction. There are many examples, such as solubilization
of chloroform or acetylene (type-A) in ethyl ether or acetone (type-B)
(Pimentel and McClellan, 1960). In these mixtures, there is strong H-bonding
between the proton donor and proton acceptor group. Type-A or -B
compounds are usually soluble in type-AB compounds, although this depends
on the strength of the electron donor and acceptor group of the type-A and
-B molecules, and preexisting H-bonding in the type-AB molecule. The
solubility of type-AB compounds is complicated by these compounds being
able to self associate to form dimers or trimers, or to form H-bonds within
a single molecule. The self-associating tendency of type-AB molecules may
be disrupted when those molecules are mixed with a strong donor or
acceptor molecule.
Hydrophobic Effects and Polarity
Hydrophobic compounds are viewed as substances that are readily
soluble in many non-polar solvents but only sparingly soluble in water.
These substances are considered distinct from substances that have generally
low solubility in all solvents owing to the formation of solids with strong
intermolecular cohesion (Tanford, 1973). Hydrophobic effects are said to be
associated with non-polar solutes in polar solvents, in which the non-polar
group plays a minor role compared to the attractive forces between water
molecules. Water "squeezes" out the hydrophobic solute molecules because
the interaction of hydrophobic solute and water ^re much weaker than the
interaction between water molecules. The hydrophobic effect is less
»
pronounced for cyclic aromatic hydrocarbons than for saturated cyclic
hydrocarbons because the electrons in the aromatic compound lead to
stronger van der Waals attraction to water molecules (Tanford, 1973). The
-------
42
aliphatic alcohols ara relatively good solvents for hydrocarbons, because the
local molecular organization segregates the hydrocarbon tails from the OH
group such that no major reorganization is required to accommodate
hydrocarbon molecules.
The concept of polarity has been employed in a somewhat analogous
manner as hydrophobicity to describe solubilization phenomena.
Rohrschneider (1966) has used polarity as a principal means to describe
solvent characteristics, much as solubility parameter is used in regular
solution theory. Rohrschneider's description of overall solvent polarity is
expressed as an ET value in units of Kcal/mole. This value attempts
description of dipole interactions and proton donor/acceptor interactions. It
is obtained through experiments with model solutes, each of which
exemplifies a particular solute-solvent interaction. Solvent ET values reported
for compounds of interest in this investigation are shown in Table 2-3.
These values are examined later during qualitative evaluation of the
experimental solubility data.
Solubility Parameters
Dispersive interactions between nonelectrolytes may be understood in
consideration of the solubility parameter concept developed by Hildebrand
(Hildebrand, 1970). This Concept was discussed briefly under log-linear
solubility relationships. The concept helps to quantify an old rule: "like
dissolve like." This rule refers to various solubility observations such as an
aromatic hydrocarbon like naphthalene dissolving better in aromatic solvents
such as benzene and toluene than in aliphatic solvents such as hexane, and
hardly dissolving at all in water. In this rule, "like" may be characterized by
the solubility parameters for solute and solvent."Vhe solubility parameter is
defined as the square root of the cohesive energy density, C, as given by
Equation 2-79. The values of solubility parameters for the solutes and
solvents used in this study are tabulated in Table 2-4,
-------
43
Table 2-3: Solvent Polarity Using ET as the Indicator
Solvent Solvent Polarity ET
[Kcal/mole]
Water
63.1
Methanol
55.5
Ethanol
51.9
Propanol
50.7
Acetone
42.2
Aniline
44.4
Quinoline
39.4
Reference: Dimroth and Reichardt (1966).
-------
44
For binary mixtures of noninteracting, nonpolar molecules the solubility
parameter concept predicts that the activity coefficient can be given from
pure component data (Reid et al. 1977). If the fugacity of the solute (denoted
by subscript 2) in the pure liquid state is represented by f ° and the fugacity
of the solute in the solution by f , then, the solubility of the solute can be
evaluated by
f2
RT In -2- ¦ RT In a, = -RT In X, ~ V z 2 (5 -a)2 (2-93)
f o 2 2 2 1 1 2
2
where a2 is the activity of the solute, X2 is the solute mole fraction
solubility, and z is the solvent volume fraction in the mixture. The solubility
parameter theory predicts that the solubility of a solute in a solvent will
increase as the absolute difference, A 5, between solubility parameter for the
solute and the solvent decreases. Thus one predicts for the case of five
solvents shown in Table 2-4 that the solubility of naphthalene would be
highest in acetone followed by propanol, ethanol, methanol, and water. The
Hildebrand theory predicts that the solubility parameter of a mixture is the
weighted arithmetic mean of the solubility parameters of the constituent pure
solvents (Hildebrand and Scott, 1970). Thus, the solubility parameter, S13. of
a mixture of solvents 1 and 3 is
5,3 = 21 + 53 Z3 (2"94)
where z1# z3 are the volume fraction of solvents 1 and 3 in the mixture, and
and 53 are the solubility parameters of pure solvents 1 and 3 respectively.
Solubility parameter concepts can be used to interpret relationships
involving: liquid miscibility, polymer solubility, polymer compatibility,
dispersion phenomena, solubility of inorganic compounds, and organic
material in organic solvents (Hansen, 1969; Tijssen et al. 1976, Freeman and
Cheung, 1982). However, it must be recognized that the solubility parameter
concept was developed on the basis that non-specific dispersion forces are
normally the dominant solution interaction forces. Consequently, the
solubility parameter theory does not work as well for strongly polar solvents
-------
45
Table 2-4: Solubility Parameters of Solvents and Solutes
Compound S a & 3 S ^
d p H a b
Solvent
Water
23.50
7.22
15.35
19.07
16.65
10.9
Methanol
15.15
7.18
6.70
13.53
7.18
12.9
Ethanol
13.09
7.46
4.29
10.81
5.17
11.3
Propanol
11.78
7.65
5.54
9.04
4.12
10.0
Acetone
9.93
7.44
6.41
5.47
0.90
16.6
Solute:
Naphthalene
9.9
9.9
9.4
1.0
Naphthol
10.2
Quinoline
10.8
3,5-Dichloroaniline
NA
Aniline
11.81
9.04
2.30
7.88
3.49
8.9
Phenanthrene
9.8
o-Xylene
8.8
8.65
8.5
0.5
b ¦ Solubility parameter (overall)
&d = Solubility parameter due to dispersive force
6^ = Solubility parameter due to dipole induction
3h = Solubility parameter due to hydrogen bonding
&a ¦ Solubility parameter due to proton donor ability
¦ Solubility parameter due to proton acceptor ability
Reference: Snyder, (1979).
-------
46
and solutes. Furthermore, the solubility parameter theory assumes
symmetrical interactions between adjacent molecules in solution, which for
example, does not occur during H-bonding.
More recent work has led to a broader interpretation of the original
Hildebrand solubility parameter approach. An alternative approach is based
on a combination of the original Hildebrand solubility parameter theory plus
an experimentally based solvent classification scheme (Karger et al. 1978,
Snyder, 1980, Hansen, 1967). This alternate approach separates the interaction
between solvent and solute molecules into partial solubility parameters:
dispersive, 5d; dipole, 3p; and H-bonding, SH, 3a, 5b. Partial solubility
parameters are assigned to account for these specific interactions, and these
individual solubility parameters provide a better measure of how a given
solvent will interact with a particular solute. The maximum solubility occurs
when the partial solubility parameters of solvent and solute are matched. In
this approach, hydrogen bonding interactions can be divided into partial
solubility parameters as indicated by 3# (for acid or proton donor) and 3b (for
base or proton acceptor). Maximum solubility occurs when the product of 3a
for the solvent and a for the solute (or vice versa) is a maximum, rather
O
than when these values are equal for both solvent and solute. That is,
maximum solubility is promoted by strong hydrogen bonding between solvent
and solute molecules. For a solvent with a high value of and low value
of 3b, hydrogen bonding with a solute will be strongest when the solute has
a large value of 5b, rather than when the solute is also a strong donor and
weak acceptor. Table 2-5 describes several features of the partial solubility
parameters and the related solvency characteristics.
The partial solubility parameter approach allows for quantitative
%
prediction of solvency for different polar solvent-solute combinations.
However, extended solubility parameter treatment as based on partial
solubility parameters still has some limitations (Snyder, 1980):
• One must know the composition of the sample to be dissolved.
-------
47
Table 2-5:* Partial Solubility Parameters"
Partial Solubility
Parameter
Related to
Maximum Solvency
Polarizability or
refractive index
Equal values of <5d
for solute and solvent
Dipole moment of
groups within solvent
and solute molecule
Equal values of
for both solvent
and solute
Hydrogen bonding
Acidity or proton-donor
strength in
hydrogen bonding
Basicity or proton-
acceptor strength in
hydrogen bonding
Maximum value of
^ ^ ^ Aolute^ ^ Insolvent ^
0f ^AolvnWso.uJ
Minimum value of
^ ^ ^ a^soluta^ ^ Insolvent ^
°r ^.Lvant^bLuJ
* From Snyder (1978)
-------
48
• It requires partial solubility parameter values for solutes as well
as for solvents, and generally solute solubility parameters are not
available.
• The resulting equations for relative solubility are rather
complicated, which discourage their use.
• There is a tendency to underestimate 3 values for strong proton
accepting solvents.
• Solvents which comprise alcohol or water give poor agreement
due to strong self-association, and thus there is deviation from
regular solution behavior.
Thus, the expanded solubility parameter approach is still limited by some of
the other assumptions in the original Hildebrand theory.
Summary
This chapter has assessed several theoretical approaches which may be
used to predict organic solute solubility in water/co-solvent mixtures. The
next chapter describes results of experimental studies to observe aromatic
solute solubility in water/co-solvent systems. These data are then used with
other observations to evaluate the predictive methodologies.
-------
49
Chapter 3
EXPERIMENTAL MEASUREMENT OF SOLUTE SOLUBILITY
IN SOLVENT/WATER MIXTURES
Introduction
The experimental portion of this part of the investigation entailed
measurement of solubility for four aromatic hydrocarbons. Aromatic solute
solubilities were measured in aqueous solution with and without addition of
organic co-solvent. The organic co-solvents which were evaluated were
methanol and acetone. The analytical technique employed was high pressure
liquid chromatography (HPLC) for the analysis of aromatic solutes in water
and in water/co-solvent systems. The results of this experimentation are
discussed in the following chapter in which an evaluation of the co-solvent
effect on solute solubility is presented. That presentation is then followed
by a discussion of results of experiments to evaluate the effect of co-
solvent on solute adsorption onto soil.
Experimental Components
Materials
The solutes used in this study were selected in order to represent
important types of aromatic hydrocarbons having different hydrogen bonding
•w
characteristics. Naphthalene (C1QHB) was selected ^s the principal solute for
this investigation because it is the "building block" for polycyclic aromatic
hydrocarbons. Naphthalene is classified as a N-type compound with respect
to hydrogen bonding characteristics, which means it does not form hydrogen
bonds with hydrogen donors (A- or AB-type compounds) or hydrogen
-------
50
acceptors (B- or AB-type compounds). Two derivatives of naphthalene were
also investigated which were naphthol
-------
51
Glassware
All glassware used in this investigation was carefully cleaned in order
to minimize interferences. Glassware was first cleaned with detergent and
water, and then rinsed with deionized water. After this general cleaning
procedure, the glassware was soaked in a 1:1 nitric acid bath for 24 hours
and then rinsed successively with deionized water, methanol, acetone and
methylene chloride. Following these cleaning procedures, the glassware was
oven dried at 105°C; the glassware was then covered with aluminum foil prior
to use. Solubility and adsorption measurements were performed with use of
50 ml screw top glass centrifuge tubes. These tubes were sealed with a
teflon-lined septum which was held in place by means of a screw cap having
an access hole. This permitted the withdraw of a sample for analysis by
insertion of a microliter syringe through the septum.
Experimental Instruments
Solute solubility determinations were accomplished by high pressure
liquid chromatography (HPLC) techniques. A Perkin-Elmer (Norwalk, Conn.)
Series 3 reverse phase high pressure liquid chromatography system was used
in this investigation. The HPLC was operated by using a constant flow
gradient pumping system with acetonitrile and water, and a reverse phase
column. The acetonitrile and water were used as carrier solvents, and these
solvents were proportionally mixed with the aid of two calibrated HPLC
pumps. Detection was accomplished by either a Perkin-Elmer model LC-15
ultraviolet (UV) detector equipped with a 254 nm filter, or by a Perkin-Elmer
model 204-S fluorescence detector which provided variable excitation and
emission wavelength settings. Samples were injected using a Rheodyne
(Berkeley, CA) Model 7105 injection valve fitted with a 175 /il sample loop.
Injected sample volume ranged between 2 and 8 microliters. Samples were
withdrawn from the centrifuge tube by a Hamilton (Reno, Nevada) 800 series
microliter syringe and injected directly for HPLC analysis.
-------
52
A Perkin-Elmer 2.6 mm x 25 cm PAH/10 column and a Supelco
(Bellefonte, PA) 4.6 mm x 25 cm LC-PAH column were used to provide
resolution of naphthalene and naphthol. The absorbance was then quantified
by using the fluorescence detector. For naphthalene analysis, the
fluorescence detector showed the best resolution at an excitation wavelength
of 280 nm and emission wavelength of 340 nm, while for naphthol the
fluorescence detector showed the best results at the excitation wavelength of
310 nm and emission wavelength of 340 nm. Detail of programs used in
HPLC analysis are described in Table 3-1.
A Supelco 4.6 mm x 15 cm (5 //m packing) LC-8 column was used to
provide resolution of quinoline and 3,5-dichloroaniline. A fixed-wavelength
(254 nm) UV detector was used for quantification purposes. Table 3-1 shows
the parameters used in the HPLC analysis for quinoline and 3,5-dichloroaniline.
Experimental Procedures to Measure Solute Solubility
The solubility of aromatic solutes in pure solvent (i.e. water, methanol
and acetone) and binary solvent mixtures (i.e. methanol/water, and
acetone/water) were determined by batch tests with an aqueous phase
comprised of 0.01 N calcium chloride. The calcium chloride was used to
maintain a background electrolyte concentration, and in this respect the
experimental protocol was consistent with the subsequent sorption tests
described in Chapter 5 in which calcium chloride was used to improve soil
particle coagulation and settling after attaining sorption equilibrium.
The organic solutes, particularly naphthalene, were volatile to some
degree. Therefore, in order to eliminate volatilization loss, all tests were
conducted in sealed 50 ml glass centrifuge tubes ..equipped with a screw-top
and teflon liner septum. Solubility experiments were performed by placing
excess solute in the centrifuge tube and filling with deionized water
containing the electrolyte and co-solvent. Water or co-solvent/water mixture
was added to fill the centrifuge tubes in a manner to leave no head space,
-------
53
Table 3-1: Specifications for HPLC Analysis
Naphthalene Naphthol Quinoline 3,5-Dichloroaniline
Column PAH/10* PAH/10* LC-8" LC-8"
LC-PAH" LC-PAH"
detector
flow rate
[ml/min]
Acetonitrile
[% vol.]
Excitation
wavelength
(nm)
Emission
wavelength
(nm)
UV
wavelength
(nm)
UV aufs
Retention
time (min)
fluor-
escene
1.0
60%
280
340
f luor-
escene
1.0
55%
310
340
UV
2.0
40%
7.8
4.7
254
0.128
4.3
UV
2.0
50%
254
0.128
2.7
* HPLC column obtained from Perkin-Elmer Corp.
" HPLC column obtained from Supelco Co.
-------
54
the centrifuge tubes were then sealed with the teflon-lined septum and
transferred to a wrist-action shaker (Model 74, Burrell Corp., Pittsburgh, PA).
Centrifuge tubes were covered with aluminum foil in order to eliminate
photodegradation. These centrifuge tubes were then shook at room
temperature <23 ± 2°C) for 24 hours to allow equilibrium to be achieved. The
samples were then centrifuged for 1 hour at 8000 rpm using a IEC clinical
centrifuge (International Equipment Co. Needham, MA), after which 2 to 8
microliters of sample solution were withdrawn from the centrifuge tubes and
injected directly with the microliter syringe for HPLC analysis. The septum
port allowed for samples to be withdrawn without concern for loss by
volatilization.
Each experimental setup was run in duplicate, and then the experiment
was repeated. Thus each test was performed in quadriplicate. This allowed
sample-by-sample comparison to ensure correctness of procedure and validity
of the results. Each sample was analyzed by performing at least two, and
usually three, injection determinations. Therefore the number of
determinations exceeded the number of samples analyzed by a factor of two
to three. Analytical standards were measured at the beginning of each series
of analyses. Standards were also measured following every three samples in
order to ensure reproducibility in instrument response factors.
Screening tests were performed to ensure that aqueous phase
equilibrium was achieved within 24 hours. These tests were performed with
naphthalene, the least soluble solute employed in this investigation, and
methanol volume fractions of 0.0, 0.05, 0.1 and 0.5. The duration of these
tests ranged from 24 to 120 hours, and the results showed no increase in
solute solubility beyond that attained after twenty-four hours of equilibration.
-------
55
Experimental Results
Solute solubility was evaluated at least three times for every
combination of solute and water/co-solvent. For the case of naphthalene and
methanol/water mixtures, there were 108 individual samples comprising 12
different solvent volume fractions (0, 0.005, 0.01, 0.05, 0.1, 0.5, 1, 5, 10, 20,
30, 40, 50, and 100%). These results are shown in Table 3-2. Table 3-3
shows the results of measurement of naphthalene solubility in acetone/water
mixtures, for which 48 samples were evaluated. Table 3-4 presents the
results of analysis of 50 samples to measure naphthol solubility in
methanol/water mixtures, and Table 3-5 shows the results of analysis of 57
samples to measure naphthol solubility in acetone/water mixtures. Table 3-6
shows the results of analysis of 40 samples to measure quinoline solubility
in methanol/water mixtures, and Table 3-7 shows the results of analysis of
48 samples to measure quinoline solubility in acetone/water mixtures. Table
3-8 shows the results of analysis of 51 samples to measure 3,5-
dichloroaniline solubility in methanol/water mixtures, and Table 3-9 shows
results of 52 samples that were analyzed for 3,5-dichloroaniline solubility in
acetone/water mixtures.
Tables 3-2 to 3-9 show the number of samples investigated, number of
individual determinations performed, average solute solubility, and standard
deviation for each solvent/water combination. In solvent/water mixtures
containing greater than 50% co-solvent by volume, aqueous solubility for
most solutes was above the instrument detection limit. Solute solubility
measurement for these samples with greater than 50% co-solvent was not
attempted because it was believed that any necessary dilution may alter the
solubility characteristics of the solute at these high concentrations.
-------
56
Table 3-2: Naphthalene Solubility in Methanol/Water Mixtures
Methanol
Number of
Determinations
Average
Solubility
Standard
Deviation
[% vol.]
m
[mg/l]
0 50 30.6 2.65
0.05 19 31.3 1.74
0.1 18 35.1 1.23
0.5 51 38.8 3.18
1 21 39.1 2.16
5 20 46.5 3.55
10 28 58.3 4.95
20 11 104 3.07
30 11 243 19.4
40 11 468 62.9
50 39 1220 189.
100 13 66200 3080.
Total Samples Evaluated: 108
-------
57
Table 3-3: Naphthalene Solubility in Acetone/Water Mixtures
Acetone Number of Average Standard
Determinations Solubility Deviation
[% vol.] [#] tmg/l]
0
50
30.6
2.65
5
9
71.0
2.04
10
10
111.
2.66
20
10
417.
10.8
30
10
1080.
112
40
10
3540
155
50
10
10200
832
Total Samples Evaluated: 48
-------
58
Table 3-4: Naphthol Solubility in Methanol/Water Mixtures
Methanol Number of Average Standard
Determinations Solubility Deviation
[% vol.] [#] tmg/l]
0
24
846
121
0.1
7
938
124
0.5
9
1020
187
1
8
1170
133
5
12
1210
128
10
24
1310
199
20
14
2020
382
30
12
2850
343
40
17
7160
739
50
16
24300
3120
Total Samples Evaluated: 50
-------
59
Table 3-5: Naphthol Solubility in Acetone/Water Mixtures
Acetone Number of Average Standard
Determinations Solubility Deviation
[% vol.] [#] [mg/l]
0
24
846
121
1
8
1210
63.8
5
15
2160
120
10
24
2110
314
20
22
3650
858
30
24
6420
1260
40
16
14900
1570
50
26
28600
3950
Total Samples Evaluated: 57
-------
60
Table 3-6: Guinoline Solubility in Methanol/Water Mixtures
Acetone Number of Average Standard
Determinations Solubility Deviation
[% vol.] [#] [mg/IJ
0 33 6840 236
1 12 7810 299
5 15 9150 1030
10 15 9880 945
20 16 14800 932
30 15 27400 2060
40 15 71200 3210
50 15 106000 6120
Total Samples Evaluated: 40
-------
61
Table 3-7: Quinoline Solubility in Acetone/Water Mixtures
Acetone Number of Average Standard
Determinations Solubility Deviation
[% vol.] [#] [mg/l]
0
33
6840
236
0.5
8
6840
291
1
14
8490
342
5
14
9840
328
10
20
14600
573
20
16
34100
1230
30
12
75900
6900
40
11
127000
20200
50
12
251000
34500
Total Samples Evaluated: 48
-------
62
Table 3-8: 3,5-Dichloroaniline Solubility in Methanol/Water Mixtures
Acetone Number of Average Standard
Determinations Solubility Deviation
[% vol.] [#] [mg/l]
0
40
784
33.5
5
16
1030
15.4
10
21
1090
75.2
20
18
1830
277
30
17
3440
221
40
17
7680
249
50
16
19200
1930
Total Samples Evaluated: 51
-------
63
Table 3-9: 3,5-Dichloroaniline Solubility in Acetone/Water Mixtures
Acetone Number of Average Standard
Determinations Solubility Deviation
[% vol.] [#] [mg/l]
0
40
784
33.5
1
10
837
37.7
5
14
1100
73.2
10
20
1540
117
20
17
2180
163
30
18
3990
315
40
12
10600
1270
50
12
24000
1250
Total Samples Evaluated: 52
-------
64
Interferences
Consideration regarding errors associated with this experimental study
include losses and/or interferences that may occur at several specific points
between sample preparation and analysis. Most of these effects would result
in loss of solute. To the extent that this is true, results of the experimental
study may become unreliable. Effects which may result in loss of solute
include: photodegradation, oxidation, volatilization, adsorption onto an inner
surface of glassware, non-quantitative transfer, and chronic interferences.
Photodegradation of samples in glassware from exposure to light (e.g.
during sample preparation and equilibration) was minimized by covering
glassware with aluminum foil and by using amber glassware whenever
practical. Losses by oxidation were minimized by: degassing the water and
solvent prior to use in making solute solutions, filling the centrifuge tube
with solution with no head space, and sealing the centrifuge tube with a
teflon-lined septum. Volatile losses were minimized by employing excess
solute and by filling the centrifuge tubes with co-solvent/water mixture
without any head space, and by maintaining tight seals during the
equilibration process. Adsorption on inner surface of the glassware was
judged to be inconsequential owing to the fact that the experiments were
performed with excess solute being visibly evident in the sample; adsorptive
losses were also minimized by avoiding contact of sample solutions with
extraneous glassware. Chronic interferences were minimized by carefully
cleaning the glassware and periodically cleaning and calibrating the
instruments. Errors associated with HPLC analysis relate primarily to
uncertainty in measurement of injected volume and peak area calculations.
Measurement of injected volume was taken as the difference of syringe
sample volume before and after each injection, and peak area was measured
by using a planimeter. Standard concentrations of solute were injected after
every three samples in order to minimize the instrument response variation.
-------
65
Chapter 4
PREDICTION OF AROMATIC SOLUTE SOLUBILITY
IN SOLVENT/WATER SYSTEMS
Introduction
This chapter evaluates the applicability of the models described in
Chapter 2 for estimating solute solubility in binary solvent mixtures.
Estimated solute solubilities are compared with experimental solubilities for
eight solute-binary solvent systems: naphthalene-methanol/water, naphthalene-
acetone/water, naphthol-methanol/water, naphthol-acetone/water, quinoline-
methanol/water, quinoline-acetone/water, 3,5-dichloroaniline-methanol/water,
and 3,5-dichloroaniline-acetone/water. Experimental solute solubility data were
obtained from batch equilibrium tests which were presented in the previous
chapter. A limited amount of data for ten additional systems were obtained
from the literature, and these systems were also evaluated. These ten
systems were: naphthalene-ethanol/water, naphthalene-propanol/water, aniline-
methanol/water, aniline-ethanol/water, phenanthrene-methanol/water,
phenanthrene-ethanol/water, xylene-methanol/water, xylene-acetone/water,
xylene-ethanol/water, and xylene-propanol/water. It is evident from the
results of this investigation that the available literature on aromatic solute
solubility in miscible solvent/water mixtures is not extensive. The data for
the ten additional systems evaluated in this study were obtained from
Stephen and Stephen (1963), Dean (1973), and Seidell (1941). In addition,
Stephen and Stephen (1963) provided some data for naphthalene solubility in
methanol/water and acetone/water mixtures. The name xylene refers to the
ortho-substituted compound, 1,2-dimethylbenzene.
-------
66
This chapter begins with a discussion of activity coefficient for solutes
and solvents in the various co-solvent/water mixtures. The UNIFAC group
contribution approach was employed for this task. This discussion is then
used with semi-empirical thermodynamic approaches to predict solute
solubility in pure solvent. The chapter concludes with an evaluation of the
techniques described in Chapter 2 to predict aromatic solute solubility in co-
solvent/water mixtures.
Activity Coefficient
The activity coefficients for the components in the mixed solvent
systems were estimated by a group contribution method using the UNIFAC
approach. The UNIFAC approach computes the activity coefficients from
knowledge of the molecular structure of the solute and solvents through an
equation which contains interaction parameters of the various functional
groups. The UNIFAC approach consists of a two-part calculation to obtain
the component activity coefficient: a combinatorial part, which is essentially
due to difference in size and shape of molecules, and a residual part, which
is essentially due to energy of interactions between functional groups. The
theoretical framework for the UNIFAC model was described in Chapter 2.
The basic steps for estimating activity coefficient are:
1. Draw ^ the molecular structure of every component in the
multicomponent system.
2. Determine the functional group type and number of functional
groups in each molecule.
3. Calculate r and q. using values of Rk and Qk
4. Calculate ljf f. and 0. noting that 1 and X 8 =1
5. Calculate the combinatorial part y.c
6. Calculate & , 0 and X
' nm m m
7. Calculate Tk and rj" for each functional group
8. Calculate the residua! part y*
9. Add the combinatorial part, y.c, and the residual part y* to obtain
activity coefficient, y(.
-------
67
A sample calculation is presented in Appendix A to illustrate the
computational methodology of the UNIFAC approach. This calculation is
performed for prediction of infinite dilution activity coefficient, y00, for
naphthalene solubility in a system consisting of 50% (by volume) methanol
and 50% water. During this investigation, computation of the solute infinite
dilution activity coefficients was facilitated by use of a FORTRAN program
which was developed by Fredenslund et al. (1975) and updated by Anderson
(1983). Solute infinite dilution activity coefficients in pure solvents were
computed using the UNIFAC approach for seven solutes in five pure solvents
as shown in Table 4-1. The data presented in Table 4-1 were used to
evaluate the aromatic solute solubilities in pure solvents. Calculated infinite
dilution activity coefficients for the solutes in eighteen binary solvent
systems are presented in Tables 4-2 to 4-4. Table 4-5 shows the activity
coefficients for the organic co-solvents and water in the binary solvent
mixtures. The activity coefficients presented in Tables 4-2 to 4-5 were
calculated in order to show their dependence on solvent volume fraction and
to allow estimation of mole fraction solute solubility. The results shown in
Tables 4-2 through 4-5 were then used to obtain solute mass concentration
(i.e. mg/l or g/l) solubility in systems with different proportions of solvent.
The data in Tables 4-2 to 4-5 show for the aromatic solutes that the
activity coefficients decrease with increase of organic solvent content. For
example, the activity coefficient for naphthalene in water is 139,000, and this
decreases to 1,540 with an aqueous phase containing 50% by volume of
methanol. The activity coefficient for naphthalene in 100% methanol is 13,
which is 104 times less than the activity coefficient in pure water. It is also
noted that the activity coefficients for the solutes generally increase with
decrease of solute solubility parameter. That is,'the activity coefficients for
phenanthrene (3 » 8.6), naphthalene (5 * 9.9), quinoline (3 ¦ 10.8), and aniline
(3 = 11.8) in water are 7.40 x 10®, 1.39 x 106, 1840 and 90.4; and in methanol
these values are 2,550, 13.0, 1.80, and 2.46 respectively. This trend is only
qualitative at best, as naphthol (3 = 10.2) and xylene (3 - 8.8) are out of
-------
68
Table 4-1: Predicted Infinite Dilution Activity Coefficients
for Aromatic Solutes in Pure Solvent Systems
Water Methanol Acetone Ethanol Propanol
Naphthalene
139,000
13.0
2.53
14.0
9.30
Naphthol
486 "
0.79
0.17
NE
NE
Quinoline
1,840
1.80
2.60
NE
NE
3,5-Dichloroaniline
877
0.39
1.77
NE
NE
Aniline
90.4
2.46
NE
1.45
NE
Phenanthrene
7,410,000
25.5
NE
36.9
NE
Xylene
56,500
9.59
2.17
6.39
4.52
NE: Not Evaluated
-------
69
Table 4-2: Predicted Infinite Dilution Activity Coefficients
for Aromatic Solutes in Methanol/Water Mixtures
Methanol Naphtha- Naph- Quino- 3,5- Ani- Phenan- Xylene
lene thol line Dichloro- line threne
aniline
[% vol.]
0
10
20
30
40
50
70
70
80
90
100
139,000
57,200
23,500
9,590
3,870
1,540
606
235
90
34
13
486 1,840 878
239 786 320
347 129
158
74
120
61
32
17
8.7
4.7
2.5
1.4
0.8
36
18
9.3
5.0
55
25
12
5.5
2.7
1.3
2.9 0.7
1.8 0.4
90 7,410,000 56,500
40 682,000 10,200
21 97,900 2,590
13 19,300 834
8.5 4,800 322
6.1 1,480 143
4.7 525 71
3.8 213 39
3.2 96 23
2.8 48 14
2.5 25 9.6
-------
70
Table 4-3: Predicted Infinite Dilution Activity Coefficients
for Aromatic Solutes in Acetone/Water Mixtures
Acetone Naphthalene Naphthol Quinoline 3,5-Dichloro- Xylene
aniline
[% vol.]
0
139,000
486
1,840
878
56,500
10
64,200
34
162
459
6,090
20
28,800
5.6
31
88
1,280
30
12,400
1.5
9.5
23
394
40
5,160
0.52
3.9
8.9
151
50
2,030
0.24
2.0
4.3
67
60
753
0.13
1.2
2.4
32
70
257
0.08
0.91
1.5
16
80
77
0.07
0.83
1.2
8.3
90
18
0.07
1.07
1.1
4.3
100
2.5
0.17
2.60
1.8
2.2
-------
71
Table 4-4: Predicted Infinite Dilution Activity Coefficients for
Aromatic Solutes in Ethanol/Water and Propanol/Water Mixtures
System Ethanol/Water Propanol/Water
Solute Naphthalene Aniline Phenan- Xylene Naphthalene Xylene
threne
Organic
Co-solvent
[% vol.]
0
139,000
90
7,410,000
56,500
139,000
56500
10
10,900
15.7
249,000
4,280
6,160
2,470
20
2,010
5.1
26,200
792
972
399
30
599
2.4
5,230
241
286
121
40
241
1.4
1,560
99
119
52
50
118
0.98
606
50
61
28
60
66
0.77
283
29
36
16.7
70
41
0.70
150
18
24
11.2
80
27
0.72
88
12
17
7.9
90
19
0.89
55
8.7
12
5.9
100
14
1.45
37
6.4
9.3
4.5
-------
Table 4-5: Predicted Activity Coefficients for Solvents
in Co-solvent/Water Mixtures
System Methanol/Water Acetone/Water Ethanol/Water Propanol/Water
Solute Methanol Water Acetone Water Ethanol Water Propanol Water
Organic
Co-solvent
[% vol.]
0
2.24
1.00
11.47
1.00
7.63
1.00
20.08
1.00
10
1.75
1.01
4.98
1.04
3.43
1.04
5.25
1.07
20
1.47
1.04
3.01
1.14
2.16
1.26
2.64
1.20
30
1.30
1.09
2.17
1.27
1.62
1.34
1.79
1.36
40
1.19
1.14
1.73
1.43
1.35
1.36
1.42
1.54
50
1.12
1.20
1.47
1.63
1.20
1.50
1.24
1.72
60
1.07
1.27
1.30
1.89
1.12
1.64
1.13
1.92
70
1.03
1.34
1.18
2.27
1.06
1.80
1.07
2.13
80
1.01
1.42
1.09
2.88
1.03
1.98
1.03
2.37
90
1.00
1.51
1.03
4.09
1.01
2.22
1.01
2.69
100
1.00
1.56
1.00
7.36
1.00
2.66
1.00
3.25
-------
73
sequence for either water or methanol as the solvent. No specific trend is
evident between activity coefficient in pure solvent and solute refractive
index or dielectric constant. Although, it is noted that among all the
solvents, the largest values of activity coefficients are observed for water as
the solvent, and that water has the highest value of refractive index and
dielectric constant among the various solvents. Further, least values of
activity coefficients for xylene, naphthalene, and naphthol were observed for
acetone as solvent, and that acetone has the largest dipoie moment and least
polarity among the various solvents. Aside from these general observations
and some of the trends with naphthalene and phenanthrene solubility as
discussed in a following section, there does not appear to be an obvious
correlation between estimated value of solute activity coefficient with solute
or solvent physical and chemical properties for the systems considered in
this investigation.
Volumetric Addition Assumption
It is useful for purposes of practical environmental engineering
calculation to be able to express solute concentration in terms of molar
concentration (moles per liter) or mass concentration (mg or g per liter). This
introduces a small difficulty because in computing molar or mass
composition, from activity coefficient and mole fractions, it is necessary to
incorporate a value for the volume of the solute/co-solvent/water mixture. In
using activity coefficient data from Tables 4-1 to 4-5 to compute solute
molar or mass concentration, it was assumed that the separate volumetric
contributions of the solute, co-solvent, and water are conserved. This
assumption means that the molar volume of the solute/co-solvent/water
mixture could be calculated from the volumetric contributions of solute, co-
solvent and water, and density of pure solute, co-solvent, and water.
The validity of the assumption regarding conservation of volume can be
assessed in part by comparing calculated values of the density of the co-
solvent/water mixture with published values. Table 4-6 shows a comparison
-------
74
Table 4-6: Error Analysis for the Volume Addition Assumption
for Methanol/Water Systems
Methanol Methanol Water Mixture" Mixture+ Error+
Density Density
[Wt. %] [Vol.%] [Vol. %] [g/ml] [g/ml] [%]
1.
1.26
98.7
0.9956
0.9964
-0.08
2.
2.51
97.4
0.9930
0.9947
-0.17
4.
4.99
95.0
0.9879
0.9913
-0.34
6.
7.45
92.5
0.9828
0.9880
-0.52
8.
9.88
90.1
0.9778
0.9840
-0.63
10.
12.29
87.7
0.9728
0.9816
-0.90
12.
14.68
85.3
0.9679
0.9875
-1.99
14.
17.04
82.9
0.9630
0.9755
-1.28
16.
19.37
80.6
0.9582
0.9725
-1.47
18.
21.68
78.3
0.9534
0.9695
-1.66
20.
23.97
76.0
0.9486
0.9666
-1.86
24.
28.49
71.5
0.9393
0.9606
-2.22
28.
32.91
67.0
0.9302
0.9545
-2.55
32.
37.25
62.7
0.9212
0.9482
-2.85
36.
41.50
58.5
0.9124
0.9416
-3.10
40.
45.68
54.3
0.9038
0.9347
-3.31
44.
49.78
50.2
0.8953
0.9273
-3.45
48.
53.80
46.2
0.8870
0.9196
-3.55
52.
57.74
42.2
0.8788
0.9114
-3.58
56.
61.62
38.3
0.8708
0.9030
-3.57
60.
65.42
34.5
0.8629
0.8944
-3.52
64.
- 69.16
30.8
0.8552
0.8856
-3.43
68.
72.83
27.1
0.8476
0.8763
-3.28
72.
76.43
23.5
0.8401
0.8667
-3.06
76.
79.98
20.0
0.8328
0.8568
-2.80
80.
83.46
16.5
0.8256
0.8468
-2.50
84.
86.88
13.1
0.8185
0.8365
-2.15
88.
90.24
9.7
0.8116
0.8259
-1.73
92.
93.55
6.4
0.8047
0.8148
-1.23
96.
96.80
3.2
0.7980
0.8034
-0.67
Average Error * -2.1016%
Standard Deviation = 1.1638%
Total data evaluated = 59 (not all data are shown on this table)
* Calculated from volume addition assumption.
+ Observed data from Weast (1983).
.. I calculated value - observed value ^ inna£
++ \ observed value ' 100%
-------
75
of observed densities of various methanol/water mixtures with values of
mixture density calculated according to conservation of volume of the pure
components. This comparison shows that the error in the volume addition
assumption is maximum at about -3.5% for systems in the range of about
50% by weight methanol and water. The error diminishes to less than 1% for
mixtures with large volumetric contribution of either co-solvent or water.
The average error of this assumption for methanol/water mixtures was -2.1%
with a standard deviation of 1.16%. The negative sign means that the
assumption of conservation of volume slightly overestimates the volume of
the co-solvent/water mixture, and therefore the computed density of the
mixture was slightly underestimated by calculation of total mass divided by
total pure component volume.
A similar evaluation was performed for the case of acetone/water
mixtures to check the validity of the volume addition assumption. The
results of the error analysis are shown in Table 4-7 for systems containing
up to 11% by volume acetone. No density data was given in Weast (1983)
for systems with greater than 11% by volume acetone. The largest error
shown in Table 4-7 is about -1.1% for a system with about 11% by volume
acetone. Average error for these data is -0.7% with a standard deviation of
about -0.4%.
The magnitude of error for the volume addition assumption was
evaluated for a system containing 50% volumetric contribution of acetone and
water by conducting an experiment in which 500 ml of acetone and 500 ml
of water were mixed in a one liter volumetric flask. After 24 hours of
equilibration, it was observed that the total volume of the 50% (by volume)
acetone/water mixture was 996.2 ml. This corresponds to about 0.4%
overestimate assuming conservation of volume. This experiment was
performed with a 50% by volume acetone/water mixture because this
represented the largest volumetric contribution of acetone employed in any
of the experiments, and because the methanol density data in Table 4-6
-------
76
Table 4-7: Error Analysis for the Volume Addition Assumption
for Acetone/Water Systems
Acetone Acetone Water Mixture Mixture Error++
Density* Density+
[Wt. %] [Vol.%] [Vol. %] [g/ml] [g/ml] [%]
1.
1.26
98.74
0.9956
0.9968
-0.12
2.
2.51
97.49
0.9930
0.9954
-0.24
3.
3.76
96.24
0.9904
0.9940
-0.36
4.
5.00
95.00
0.9878
0.9926
-0.48
5.
6.24
93.76
0.9852
0.9912
-0.60
6.
7.46
92.54
0.9827
0.9899
-0.73
7.
8.69
91.31
0.9801
0.9866
-0.66
8.
9.90
90.10
0.9776
0.9874
-0.99
9.
11.11
88.89
0.9751
0.9861
-1.12
Average Error = -0.65556%
Standard Deviation = 0.37454%
* Calculated from volume addition assumption.
+ Observed data from Weast (1983).
. . ( calculated value - observed value ) 1rtno/
++ \ observed value ' 10U/fe
-------
77
suggested that largest error in the volume addition assumption may be
observed when co-solvent and water are mixed in approximately equal
proportions.
It was concluded from these evaluations that the assumption of
conservation of volume in co-solvent/water mixtures introduced a small error
when computing system volume. However, as shown later this error is small
in comparison to error introduced in estimation of solute activity coefficient.
Another reason for neglecting volume change upon mixing is the
uncertainity that is introduced when considering co-solvent/water systems
having appreciable concentration of solute. In this investigation all mass
concentration calculations were performed in a manner to account for the
volume of the solute in the co-solvent/water mixture. This consideration is
especially important for those systems which contain a large percentage of
co-solvent which demonstrate strong solute solubilization properties. No
information is available on solution density for the solute/co-solvent/water
systems evaluated in this investigation. For this reason, and also because
only limited density data are available for the solute-free co-solvent/water
systems, it was assumed that volumetric additions were conserved when
computing solute concentration in units of mass per unit volume of solution.
It should be appreciated, however, that thermodynamic calculations which
employ mole fractions require no assumption regarding conservation of
volume of pure components in a solution mixture.
In summary, it is recognized that the volume of a solution of
nonelectrolytes is not strictly equal to the sum of the volume of
components. Nonetheless, the small volume changes that may occur on
mixing were ignored. This assumption is ofteit made in simple theories
pertaining to thermodynamic properties of mixtures of nonelectrolytes
(Hildebrand et al. 1970).
-------
78
Solute Solubility in Pure Solvent
The solubilities of seven aromatic solutes in five pure solvent systems
were evaluated. This included the experimental measurement of the solubility
of naphthalene, naphthol, quinoline and 3,5-dichloroaniline in water, and
naphthalene solubility in 100% (by volume) methanol. Published values for
the following systems were also considered:
• Naphthalene in water: 30 mg/l (Dean, 1973; Stephen and Stephen,
1963; Seidell, 1941), 31.7 mg/l (Mackay and Shiu, 1977),
• Naphthalene in methanol: 78,100 mg/l (Stephen and Stephen, 1963),
86,900 mg/l (Seidell, 1941),
• Naphthalene in ethanol: 95,000 mg/l (Dean, 1973), 83,600 (Stephen
and Stephen, 1963), 95,200 mg/l (Seidell, 1941),
• Naphthalene in propanol: 74,300 mg/l (Stephen and Stephen, 1963),
103,000 mg/l (Seidell. 1941),
• Naphthalene in acetone: 33,4000 mg/l (Stephen and Stephen, 1963),
• Naphthol in water: 866 mg/l (Hassett et. al., 1981), 713 mg/l
(Stephen and Stephen, 1963), 740 mg/l (Seidell, 1941),
• Quinoline in water: 6,100 mg/l (Neely and Mackay, 1982)
• Aniline in water: 36,600 mg/l (Stephen and Stephen, 1963), 36,100
mg/l (Seidell, 1941),
• Phenanthrene in water: 1.29 mg/l (Mackay and Shiu, 1977), 1.6 mg/l
(Stephen and Stephen, 1963),
• Phenanthrene in methanol: 27,600 mg/l (Gmehling et al. 1978),
35,700 mg/l (Stephen and Stephen, 1963); 28,000 mg/l (Seidell,
1941),
• Phenanthrene in ethanol: 36,600 mg/l (Stephen and Stephen, 1963),
Gmehling et al., 1978), 33,000 mg/l (Seidell, 1941), and
• Xylene in water: 196 mg/l (Stephen and Stephen, 1963), 130 mg/l
(Seidell, 1941). Note: 1,2-dimethylbenzene.
Experimental and reported solute solubilities in pure solvents are
compared with predicted values of solute solubility in this section. In order
to estimate the solute solubility in a pure solvent, the required input
parameters are activity coefficient of the solute in the solvent, heat of
-------
79
mixing of the solute, solute molecular weight, and melting point of the
solute. The technique for estimating activity coefficient was the UNIFAC
approach, from which the activity coefficient can be related to solubility by
use of either Equation 2-31 and 2-32 (Hildebrand, 1950) or Equation 2-30
(Prausnitz, 1969). Both of these techniques are discussed below.
If the solute exists as a solid at the system temperature, the heat of
fusion of the solute can be taken as the heat of mixing. The value of the
heat of fusion at the melting point for some of the chemical compounds
used in this work are available (Weast, 1983). If the heat of fusion for a
solid solute is not available, heat of fusion can be estimated by using
entropy of fusion multiplied by melting point temperature. An average value
of entropy of fusion for solid organic compounds has been found to be 13
cal/mole °K (Prausnitz, 1969; Yalkowsky, 1979). If the heat capacities of solid
and liquid phase for the solid solute are available, then the variation of heat
of fusion with temperature should be considered, as provided in Equation
2-32 (Hildebrand, 1950). Alternatively, mole fraction solute solubility can be
computed as given in Equation 2-30 (Prausnitz, 1969). Both of these
approaches will be considered with respect to naphthalene and naphthol
solubility in water, methanol, and acetone. Table 4-8 lists the necessary
physical properties which are required to perform these and other calculations
for the solutes and solvents employed in the investigation. The approach
given by Equations 2-31 and 2-32 will be considered first, for which the heat
of fusion of naphthalene is found from Equation 2-32 to be 4767 cal/mole.
The activity coefficient of naphthalene in water is 139,000, from which the
mole fraction solubility of naphthalene in water can be estimated by Equation
2-37 as 2.04 x 10'®, and from this the solubility of naphthalene in water can
be calculated as 14.5 mg/l. The activity coefficient for naphthalene in
methanol is 13.03, and thus the mole fraction naphthalene solubility in
methanol can be estimated by Equation 2-38 by trial and error as 0.0245, or
77,600 mg/l. The activity coefficient for naphthalene in acetone is 2.53, and
thus the mole fraction solubility of naphthalene in acetone can be estimated
by trial and error by solving Equation 2-38 as 0.178, or 276,000 mg/l.
-------
80
Table 4-8: Physical and Chemical Properties of Solutes and Solvents
Employed for Solute Solubility Calculations*
Molecular
Weight
[g/mole]
Melting
Point
C°C]
Density
[g/ml]
Molar
Volume
Heat of
Fusion
[ml/mole] [cal/mole]
Solutes:
Naphtha-
lene
128.19
80.5
0.9625
133.18
4540
Naphthol
144.19
9.6
1.0989
131.21
5610
Quino-
line
129.16
45.6
1.0929
118.18
-
3,5-Dichloro
aniline
162.02
51-53
(52)**
1.2859
126
3750
Aniline
93.12
-6.3
1.0217
91.49
-
Phenanth-
rene
178.24
96.3
0.9800
181.88
4450
Xylene+
106.17
-25.2
0.880
120.62
-
Solvents:
Water
18.02
0
0.9971
18.07
-
Methanol
32.04
-93.9
0.87914
40.4852
-
Acetone
58.08
-95.4
0.7899
73.5283
-
Ethanol
46.07
-117.3
0.7893
58.37
-
Propanol
58.08
-81
0.8058
72.08
-
* After Weast (1983).
" Melting point
in a range
of 51 and 53°C,
, 52°C was
used in this
study.
+ 1,2-dimethylbezene
Note: ACp for naphthalene
is 5.04 cal/mole
°K
ACp for naphthol is 28.59 cal/mole °K
-------
81
In an analogous manner, Equation 2-30 can be used to estimate
naphthalene and naphthol solubility in water, methanol and acetone. For the
case of naphthalene solubility in pure solvents, the first term of Equation
AH T AC
2-30, [1 ] is calculated as 1.204, the second term, [- (—E)(T-T)],
RT T RT '
t
AC T
is calculated to be -0.473 and the third term. ——In —, is calculated as
R T
+0.433. Note that the second term and the third term tend to cancel each
other. After substitution of these values into Equation 2-30, the naphthalene
mole fraction solubility in water is found as 2.25 x 10"8 (16.1 mg/l).
Similarly, naphthalene mole fraction solubility in methanol is estimated as
0.0239 (82,800 mg/l), and naphthalene mole fraction solubility in acetone is
estimated as 0.123 (187,000 mg/l).
Table 4-9 shows the solubilities of naphthalene and naphthol in different
solvents as calculated by Equation 2-30 and Equation 2-31. The results show
that both approaches give similar results for predicting solubility from an
estimate of activity coefficient. The calculation approach given by Equation
2-31, in conjunction with Equation2-32 if AC dat are available, was selected
P
for estimating solubility from activity coefficient because of the ease of
computation and because of the similarity of the computed results with
Equation 2-30 as shown in Table 4-9.
Table 4-10 shows values of solute solubilities in pure solvents, where
the predicted solute solubilities were calculated from estimation of infinite
dilution activity coefficient via the UNIFAC model with Equations 2-37 to
2-41. For the four solid solutes considered in this study, i.e., naphthalene,
naphthol, 3,5-dichloroaniline, and phenanthrene, the infinite dilution activity
coefficients for these solutes in water are 139,000, 486, 878, and 7,410,000,
respectively. These activity coefficients are greater than 100, thus Equation
2-37 is used to estimate the solid solute solubility in water. The infinite
dilution activity coefficients for naphthalene in methanol and ethanol are 13.0
-------
82
Table 4-9: Comparison of Calculation Procedures for
Estimation of Solute Solubility in Pure Solvents
Solubility of Solute
Solute Solvent Equation 2-30 Equations 2-31, 2-32
X2 [mg/l] X2 [mg/l]
Naphthalene
Water
2.26 x
10"6
16.1
2.04 x
10"6
14.5
Naphthalene
Methanol
0.0278
82.800
0.0245
77.600
Naphthalene
Acetone
0.123
187,000
0.178
271,000
Naphthol
Water
4.73 x
10"4
3,780
1.72 X
10"4
1,370
Naphthol
Methanol
0.127
352,000
0.1265
351,000
Naphthol
Acetone
0.245
792,000
0.218
705,000
Note: X2: mole fraction solute solubility [-]
[mg/l]: solute solubility as mass concentration
-------
83
Table 4-10: Solute Solubilities in Pure Solvents
Solute Solubility
Solute Solvent Prediction Observed
X, (C ,) X, (C ,)
2 s,2 2 s,2
Naphthalene
Water
2.26 x 10"6 (16.1)
4.27
x
10"6 (30.6)+
Naphthalene
Methanol
0.0278 (82,800)
0.0222 (66,900)+
Naphthalene
Acetone
0.178 (271,000)
0.227 (334,000)*
Naphthalene
Ethanol
0.0402 (88,300)
0.0401
(83.600)*
Naphthalene
Propanol
0.0525 (93,400)
0.0434
(74,000)*
Naphthol
Water
1.72 x 10"4 (1,380)
1.06
X
10"4 (846)*
Naphthol
Methanol
0.1265 (351,000)
NA
Naphthol
Acetone
0.218 (365,000)
NA
Quinoline
Water
5.44 x 10"4 (3,900)
9.57
x
10"4 (6,840)
Quinoline
Methanol
1.0 (1,090,000)
NA
Quinoline
Acetone
1.0 (1,090,000)
NA
3,5-Dichloroaniline
Water
8.17 x 10"5 (735)
7.72
x
10*5 (692)+
3,5-Dichloroaniline
Methanol
0.603 (1,060,000)
NA
3,5-Dichloroaniline
Acetone
0.573 (896,000)
NA
Aniline
Water
0.011 (56,900)
6.66
X
10° (34,10C
Aniline
Methanol
1.0 (1,020,000)
NA
Aniline
Ethanol
1.0 (1,020,000)
NA
Phenanthrene
Water
3.156 x 10-8 (0.31)
2.9 >
c 10"7 (1.29)**
Phenanthrene
Methanol
0.0098 (43,100)
0.00751 (35,700)*
Phenanthrene
Ethanol
0.016 (48,900)
0.0130
(38,600)*
Xylene
Water
1.77 x 10"5 (104)
3.33
x
10*5 (196)*
Xylene
Methanol
1.0 (880,000)
NA
Xylene
Acetone
1.0 (880,000)
NA
Xylene
Ethanol
1.0 (880,000)
NA
Xylene
Propanol
1.0 (880,000)
NA
X. = mole fraction solute solubility [-]
C#2 a Mass concentration, [mg/l], as shown in parenthesis
+: experimental data for this study
»: taken from Stephen and Stephen (1963)
#*:taken from Mackay and Shiu (1977)
NA: not available
-------
84
and 14.0 respectively, and that for phenanthrene in methanol and ethanol are
25.5 and 36.9 respectively. Since these activity coefficients are between 10
and 100, Equation 2-38 is then used to calculate the solute (naphthalene and
phenanthrene) solubilities in methanol and ethanol. The infinite dilution
activity coefficients for naphthalene in acetone and propanol are 2.58 and
9.30 respectively, and that for naphthol in methanol and acetone are 0.79 and
0.17 respectively. These activity coefficients are less than 10, therefore
Equation 2-37 was employed with a trial and error calculation to calculate
solute solubility. The heat of fusions for the solid solutes were corrected
for the heat capacity terms if the data were available. The heat capacity of
solid and liquid for naphthalene were known, and ACp was calculated as 5.04
cal/mole °K; the heat of fusion at 25°C was then calculated from Equation
2-32 as 4,767.4 cal/mole. The same procedure was used for naphthol, where
AC is calculated as 28.59 cal/mole °K, and the heat of fusion is determined
p
as 7,645 cal/mole by using Equation 2-32. Heat capacity for phenanthrene are
not available; therefore, the heat of fusion for phenanthrene was taken as
4,450 cal/mole without correction.
The results in Table 4-10 show reasonable agreement between predicted
and experimental solute solubility in pure solvents. The ratio of predicted
aqueous solubility versus observed experimental values are all within a factor
of two except for phenanthrene where aqueous solubility is predicted to be
0.3 mg/l compared to a measured value of about 1.3 mg/l. Solute solubility
in pure co-solvent was predicted to within about ±50% for those solutes for
which experimental data were available. No comparison of liquid solute (e.g.,
quinoline, aniline, and xylene) solubilities in pure methanol, ethanol, acetone
or propanol were made because literature values were not available. Neither
were experimental measurements attempted to measure these solute
solubilities in those solvents owing to difficulties in sample preparation and
because of constraints on the instrument detection limit. The infinite dilution
activity coefficient for quinoline and aniline in pure methanol were estimated
as 1.8, and 2.5 respectively. Therefore, based on the discussion in Chapter 2,
-------
85
it was concluded that quinoline and aniline are infinitely soluble with
methanol. Similar conclusions were made for quinoline in acetone (y2°° =
2.6), xylene in acetone (y2°° a 2.2), aniline in ethanol (y2°° = 1.45), xylene in
ethanol (y2°° = 6.4), and xylene in propanol (y2°° s 4.5). For the case of
xylene solubility in methanol, the infinite dilution activity coefficient is 9.6,
which is greater than 7.4; therefore, Equation 2-41 was used to estimate
solute solubility. The results of this procedure were plotted as AGM/RT
versus solute mole fraction solubility, and only one minimum was observed.
Thus it was concluded that xylene is completely miscible with methanol. For
liquid solutes in pure organic co-solvent, the mole fraction solubility
approaches unity and the concentration of the solute in the mixed solution
can be assumed to approach the pure liquid solute concentration.
The results of solute solubilities in pure solvents show for a non-polar
aromatic solute (i.e., naphthalene and phenanthrene) that solubility increases
with decrease in solvent polarity. For example, naphthalene solubility in
water, methanol, ethanol, and propanol increases as 30.6, 66,900, 83,600, and
103,000 mg/l respectively, and solute polarity (ET value from Table 2-3)
decreases for water, methanol, ethanol, and propanol in the order 63.1, 53.5,
51.9, and 50.7 Kcal/mole respectively. Likewise phenanthrene solubility
increases in the order of water (1.29 mg/l), methanol (35,700 mg/l), and
ethanol (38,600 mg/l).
Solute Solubility in Solvent/Water Mixtures
The solubility of solutes in co-solvent/water mixtures was evaluated by
four approaches: the log-linear approach, the UNIFAC approach, the excess
free energy approach, and the molecular surface area approach. Prediction
and experimental data for the eighteen systems investigated are displayed as
semi-log plots in Figures 4-1 through 4-18. The abscissa of these plots is
the volume fraction of the co-solvent, and the ordinate is the solute
-------
86
Figure 4-1: Naphthalene Solubility in Methanol/Water Mixtures
Naphthalene Solubility in Methanol/Water Mixtures
• Experimental
Log-Linear
UNIPAC
Excess Free Energy
Molecular Surface Area
0.2 0 4 0 6 OS
Methanol Volume Fraction [-]
-------
Figure 4-2:
87
Naphthalene Solubility in Acetone/Water Mixtures
Naphthalene Solubility in Acetone/Water Mixtures
O-
a>
O-
O O-
J=
Experimental
Log-Linear
UNIFAC
Exc.ess Free Energy
04
0.2
0.6
0.0
0.8
t.O
Acetone Volume Fraction [-]
-------
88
Figure 4-3: Naphthalene Solubility in Ethanol/Water Mixtures
Naphthalene Solubility in Ethanol/Water Mixtures
Experimental
Log—Linear
UNIFAC
Excess Free Energy
0.6
1.0
0.2
0.8
o.o
Ethanol Volume Fraction [-]
-------
89
Figure 4-4: Naphthalene Solubility in Propanol/Water Mixtures
Naphthalene Solubility in Propanol/Water Mixtures
'a-
O O-
Experimental
Log-Linear
UNIFAC
Excess Free Energy
~o
0.4
0.6
0.2
0.8
0.0
1.0
Propanol Volume Fraction [—]
-------
90
Figure 4-5: Naphthol Solubility in Methanol/Water Mixtures
Naphthol Solubility in Methanol/Water Mixtures
\°-
Ol —
-O
O
in
o
%
z
Experimental
Log-Linear
UNIFAC
Excess Free Energy
0.000 0.125 0.250 0.375 0.500
Methanol Volume Fraction [-]
-------
91
Figure 4-6: Naphthol Solubility in Acetone/Water Mixtures
Naphthol Solubility in Acetone/Water Mixtures
\'o.
en—
E
J3
_3
O
(/)
o
jC
ar0
o —
/
/i
*
/
/./
4
>
*
,
-------
92
Figure 4-7: Quinoline ;Solubility in Methanol/Water Mixtures
Quinoline Solubility in Methanol/Water Mixtures
o
O -
•=0_
Experimental
Log-Linear
UNIFAC
Excess Free Energy
0.125
0 250
0.000
0.375
0.500
Methanol Volume Fraction [-]
-------
93
Figure 4-8: Quinoline Solubility in Acetone/Water Mixtures
Quinoline Solubility in Acetone/Water Mixtures
in
•¦5 O-
Experimenta!
Log—Linear
UNIFAC
Excess Free Energy
0.125
Acetone Volume Fraction [-]
0.250
0.375
0.000
0.500
-------
Figure 4-9:
94
3,5-Dichloroaniline Solubility in Methanol/Water Mixtures
3,5-Dichlorooniiine Solubility in Methanol/Water Mixtures
'O-
jc"b.
Experimental
Log-Linear
UNIFAC
Excess Free Energy
0.125
0.250
0.000
0.375
0.500
Methanol Volume Fraction [-]
-------
95
Figure 4-10: 3,5-DichloroaiViline Solubility in Acetone/Water Mixtures
3,5-Dichloroaniline Solubility in Acetone/Water Mixtures
X)
Experimental
Log-Linear
UNIFAC
Excess Free Energy
0.125 0.250 0.375
Acetone Volume Fraction [-]
o.ooo
o.soo
-------
96
Figure 4-11: Aniline Solubility in Methanol/Water Mixtures
Aniline Solubility in Methanol/Water Mixtures
O)
Experimental
Log-Linear
UNIFAC
Excess Free Energy
0.325
0.450
0.200
0.575
0.700
Methanol Volume Fraction [—]
-------
97
Figure 4-12: Aniline Solubility in Ethanol/Water Mixtures
Aniline Solubility in Ethanol/Water Mixtures
-OO-
Experimental
Log—Linear
UNIFAC
Excess Free Energy
015 0.30 0.45
Ethanol Volume Fraction [-]
o.oo
0.60
-------
98
Figure 4-13: Phenanthrene Solubility in Methanol/Water Mixtures
Phenanthrene Solubility in Methanol/Water Mixtures
'to
'o.
Experimental
Log-Linear
UNIFAC
Excess Free Energy
a-~o
0.750
0.625
0.875
0.500
1.000
Methanol Volume Fraction [-]
-------
99
Figure 4-14: Phenanthrene Solubility in Ethanol/Water Mixtures
Phenanthrene Solubility in Ethanol/Water Mixtures
'to
E'o-
o"b
Experimental
Log-Linear
UNIFAC
Excess Free Energy
0.625
0.500
0.750
0.875
1.000
Ethanol Volume Fraction [-]
-------
Figure 4-15:
100
Xylene Solubility in Methanol/Water Mixtures
Xylene Solubility in Methanol/Water Mixtures
CTl -
-Q
Experimental
Log—Linear
UNIFAC
Excess Free Energy
0.625 0.750 0.875
Methanol Volume Fraction [-]
o.soo
vooo
-------
101
Figure 4-16: Xylene Solubility in Acetone/Water Mixtures
Xylene Solubility in Acetone/Water Mixtures
O-
Experimental
Log-Linear
UNIFAC
Excess Free Energy
0.525
Acetone Volume Fraction [—]
0.650
0.400
0.775
0.900
-------
Figure 4-17:
102
Xylene Solubility in Ethanol/Water Mixtures
Xylene Solubility in Ethanol/Water Mixtures
Po.
X
Experimental
Log-Linear
UNIFAC
Excess Free Energy
0.6 0.7 0.8
Ethanol Volume Fraction [-]
0.5
0 9
-------
103
Figure 4-18: Xylene Solubility in Propanoi/Water Mixtures
Xylene Solubility in Propanol/Water Mixtures
^2:
u> -
jO
Experimental
Log-Linear
UNIFAC
Excess Free Energy
0.650
0.400
0.525
0.775
0.900
Propanol Volume Fraction [-]
-------
104
solubility in units of mg/l. A'tabulation of these solubility prediction data is
given in Appendix B. The best-fit curves for the log-linear, UNIFAC, excess
free energy and molecular surface area predictions for the co-solvent/water
systems were performed using polynomial curve fitting for predictions
calculated from 0% to 100% by volume co-solvent in 5% by volume
increments. The log-linear approach was plotted as solid line, the UNIFAC
approach as dashed line, the excess free energy approach as chain-dotted
line, and the molecular surface area approach as a chain-dashed line. The
procedures used for these calculations were described in Chapter Two, and
additional information required for the computational procedures is discussed
following some general comments.
A general observation on the results of the solubility of the aromatic
solutes in the various co-solvent/water mixtures is that solute solubility
increases semi-logarithmically with increase of volume fraction of organic
co-solvent. This is illustrated by linear regression of the experimental data
obtained in this investigation. For the case of naphthalene, naphthol,
quinoline, and 3,5-dichloroaniline, Figure 4-19 shows the semi-logarithmic
linear regression results for the four solutes in methanol/water systems, and
Figure 4-20 shows the semi-logarithmic linear regression results for the four
solutes in acetone/water systems. The slopes of the regression lines in
Figures 4-19 and 4-20 show the magnitude of solubility enhancement with
increased solvent content. Figure 4-19 shows the slopes for naphthalene,
naphthol, quinoline, and 3,5-dichloroaniline in methanol/water mixtures are
3.20, 2.67, 2.47, and 2.61 respectively. Figure 4-20 shows the slopes for
naphthalene, naphthol, quinoline. and 3,5-dichloroaniline in acetone/water
mixtures are 5.05, 2.70, 3.14, and 2.47 respectively. The regression coefficient
and r2 values are also shown in Figures 4-19 and 4-20. The eight
experimental systems show excellent r2 values, which range from 92.7% for
naphthol solubility in methanol/water mixtures to 99.7% for naphthalene
solubility in acetone/water mixtures. The linear regression results indicate
that the data conform to the log-linear relationship.
-------
105
Figure 4-19: Linear Regression for Solute Solubility
in Methanol/Water Mixtures
Solubility Enhancement
Solute = Naphthalene, Naphthol,
Qui no line ,3,5 Dichloroaniline
Solvent s Methanol/ Water
0 20 40 60 80 I00
METHANOL CONTENT [% by Volume]
-------
106
Figure 4-20: Linear Regression for Solute Solubility
in Acetone/Water Mixtures
100
Solubility Enhancement
Solute = Naphthalene, Naphthol,
Quinoline,3,5 D ich I oro aniline
Sol vent = Acetone/Water
.0 1
0 10 20 30 40 50
ACETONE CONTENT [% by Volume]
-------
107
The log-linear approadh for predicting solute solubility in co-
solvent/water mixtures was performed for the eighteen systems in this study.
This approach was conducted by taking the difference of the log of solute
solubility in water and the log of solute solubility in pure co-solvent as the
constant a, and then calculating solute solubility according to Equation 2-78.
The magnitude of increase in solubility (corresponding to o in Equation 2-78)
for naphthalene, naphthol, quinoline, and 3.5-dichloroaniline in methanol/water
systems by the log-linear approach was found to be 3.34, 2.65, 2.20, and 2.97
respectively. The magnitude for increase in solubility for naphthalene,
naphthol, quinoline, and 3,5-dichloroaniline in methanol/water systems by the
log-linear approach was found to be 4.04, 2.64, 2.19, and 3.05 respectively.
These values agree with the linear regression coefficients for the eight
experimental systems. The magnitude of increase in phenanthrene solubility
in methanol was found to be 4.44, which is greater than that for naphthalene
(3.34). This suggests that the more hydrophobic the solute the greater the
solubility would be enhanced with increase of fraction co-solvent.
In order to use the excess free energy approach to estimate solute
solubility in solvent/water mixtures, three parameters had to be evaluated:
solvent interaction parameters A13 and A3 ^ and the solute-solvent interaction
parameter, C2. The solvent interaction parameters A%3 and A3 can be
evaluated from estimation of activity coefficients of the co-solvent and
water using the UNIFAC procedure and a two-parameter statistical regression
technique with Equation 2-76. The results of the two-parameter regression
for A13 and A3 ^ showed that these two parameters are constants for any of
the binary solvent systems considered in this investigation. Table 4-11
summarizes the values of A13 and A3 and the standard deviation and r2
values for the four different co-solvent/water systems. It is concluded from
the results shown in Table 4-11 that the A,, and A. terms are co-solvent
1*3 3-1
specific constants. Once the solvent interaction parameters were obtained,
the solute-solvent interaction parameter, C2, can be calculated from Equation
2-73 using the experimental data, other than that data for solute solubility in
-------
108
Table 4-11: Solvent Interaction Parameters for the Binary Solvent Systems
Co-solvent/water System A1 3 A3_, Standard Deviation r2
Methanol - Water 0.771 0.460 0.000738 100%
Ethanol - Water 1.67 0.766 0.001122 100%
Propanol - Water 2.59 0.966 0.001320 100%
Acetone - Water 1.86 1.18 0.000903 99.8%
-------
109
the pure co-solvent and water. The statistical analysis showed that for the
eighteen systems investigated in this study and the eight systems
investigated by Amidon et al. (1982), that C2 can be correlated with solute
K by
OW '
C, = -2.87 - 2.29 log K r2 = 69.1% (4-6)
2 ow
The rather low value of r2 suggests that Kow is not an ideal correlation
parameter.
The values of A1 , A3 ( and C2 were then used to predict solute
solubility in co-solvent/water mixtures. In these predictions the value of C2
was taken as that given by Equation 4-6. The value of C2 was not taken as
an individual, system-specific regression parameter because it was desired to
assess the generality of the approach. The results in Figure 4-1 through 4-18
show that the excess free energy approach accounts for some of the
deviation from the log-linear relationship. This is also demonstrated later
under discussion of error analysis.
In order to calculate solute solubility in solvent/water mixtures by the
molecular surface area approach, several parameters must be known:
hydrophobic and polar surface, HSA and PSA, and microscopic interfacial free
energy densities for water and solvent, A«h and Aep respectively. Of the
eighteen systems evaluated in this investigation, naphthalene solubility in
methanol/water mixtures was the only system for which the four input
parameters were available. It may be assumed for naphthalene that the
compound is relatively nonpolar and that the polar surface area is small
compared to the hydrophobic surface area; therefore, polar surface area may
be neglected and the total surface area may be represented by the
hydrophobic surface area. Yalkowsky et al. (1976) reported that the
O
hydrophobic surface area for naphthalene is 155.8 A and that the
microscopic interfacial free energy density for methanol and water is 23.7
dyne/cm, thus the parameter a in Equation 2-76 can be evaluated as 3.893. It
-------
110
is found that this constant for naphthalene solubility in methanol/water
systems shows reasonable agreement with a values evaluated by the log-
linear approach (
-------
111
Table 4-12: Errof Analysis for Naphthalene Solubility
in the Methanol/Water System Using
the Molecular Surface Area Approach
Methanol Experimental Predicted Error
Solubility Solubility
[% Vol.] [mg/l] [mg/l] [%]
Experimental Values
.010
39.1
32.2
-17.5
.050
46.5
37.7
-19.0
.099
59.0
75.7
28.4
.199
135.
186.
37.6
.299
243.
455.
87.4
.399
463.
1120.
141.
.499
1230.
2740.
123.
1.000
66900.
244000.
265.
Reported Values
.488
986.
2490.
152.
.622
2960.
8240.
179.
.706
6360.
17500.
174.
.749
9960.
25700.
158.
.844
19800.
60300.
204.
.924
36600.
123000.
237.
.996
70600.
237000.
236.
.998
71100.
241000.
239.
Average Molecular Surface Area Approach Error = 139%
Standard Deviation of Molecular Surface Area Error = 60.5%
Number of Points Evaluated a 16
-------
112
Table 4-13 summarizes the results of the error analysis for the UNIFAC
approach. The error by UNIFAC approach ranged from -0.29% for quinoline
solubility in 20% methanol/80% water to 561% for aniline solubility in 23%
ethanol/77% water. The overall average error by UNIFAC approach is +4.95%
with a standard deviation of 107%. The positive sign indicates that on the
average the UNIFAC approach overestimates solute solubility in co-
solvent/water mixtures, although an equal number of systems were
overestimated and underestimated.
Table 4-14 summarizes the results of the error analysis for the excess
free energy approach. The error by the excess free energy approach ranged
from 0.50% for naphthalene solubility in 86.2% ethanol/13.8% water to 804%
for xylene solubility in 66% ethanol/34% water. The overall average error
was +10,2%, and the standard deviation was 97.4%. The excess free energy
approach tended to underestimate solute solubility for ten of the eighteen co-
solvent/water systems.
Table 4-15 summarizes the results of the error analysis for the log-
linear approach. The error by the log-linear approach ranged from 0.08% for
naphthol solubility in 30% acetone/70% water to 998% for xylene solubility in
66% ethanol/34% water. The overall average error for the log-linear approach
is +19.2% with a standard deviation of 111%. The log-linear approach tended
to underestimate solute solubility for eleven of the eighteen co-solvent/water
systems.
Comparison of the average error for the 18 systems investigated in this
study shows that the UNIFAC approach predicted 8 systems within ±50%, and
8 systems between ±50% and ±100%, while 2 systems had greater than 100%
average error. The excess free energy approach predicted 13 systems within
±50%, 3 systems between ±50% and ±100%, while 2 systems had greater
than ±100% average error. The log-linear approach predicted 11 systems
within ±50%, 2 systems between +50% and ±100%, while 4 systems had
greater than ±100% average error. The xylene/acetone system was greater
than 100% overestimated for all three approaches.
-------
113
Table 4-13: Error Analysis of Solute Solubility Prediction
in Solvent/Water Mixtures by the UNIFAC Approach
Solute Solvent Average Standard
Error Deviation
[%] [%]
Naphthalene
Methanol
-14.4
16.9
Naphthalene
Acetone
-91.4
6.1
Naphthalene
Ethanol
-53.0
13.6
Naphthalene
Propanol
77.2
9.26
Naphthol
Methanol
77.4
16.8
Naphthol
Acetone
69.3
33.4
Quinoline
Methanol
-0.238
24.3
Quinoline
Acetone
-42.1
15.8
3,5-Dichloroaniline
Methanol
84.9
46.1
3,5-Dichloroaniline
Acetone
64.5
37.5
Aniline
Methanol
8.06
57.8
Aniline
Ethanol
369
178
Phenanthrene,
Methanol
4.35
61.9
Phenanthrene
Ethanol
-51.8
15.8
Xylene
Methanol
-20.8
39.3
Xylene
Acetone
193
223
Xylene
Ethanol
-12.6
32.9
Xylene
Propanol
-27.0
7.48
Overall
4.95
107
Number of Points Evaluated = 121
-------
114
Table 4-14: Error Analysis of Solute Solubility Prediction
in Solvent/Water Mixtures by the Excess Free Energy Approach
Solute Solvent Average Standard
Error Deviation
[%] [%]
Naphthalene
Methanol
-25.0
15.1
Naphthalene
Acetone
-20.0
22.7
Naphthalene
Ethanol
-21.8
24.0
Naphthalene
Propanol
-54.4
23.8
Naphthol
Methanol
24.6
17.0
Naphthol
Acetone
-4.68
26.6
Quinoline
Methanol
-14.0
13.4
Quinoline
Acetone
-20.1
19.3
3,5-Dichloroaniline
Methanol
27.1
20.9
3,5-Dichloroaniline
Acetone
135
122
Aniline
Methanol
-34.4
30.5
Aniline
Ethanol
20.7
5.4
Phenanthrene
Methanol
-17.3
21.3
Phenanthrene
Ethanol
-6.07
17.0
Xylene
Methanol
66.8
67.1
Xylene
Acetone
222
69.4
Xylene
Ethanol
79.5
231
Xylene
Propanol
0.028
38.9
Overall
10.2
97.4
Number of Points Evaluated * 121
-------
115
Table 4-15: Error Analysis of Solute Solubility Prediction
in Solvent/Water Mixtures by the Log-linear Approach
Solute Solvent Average Standard
Error Deviation
[%] [%]
Naphthalene
Methanol
25.5
19.2
Naphthalene
Acetone
-60.2
13.5
Naphthalene
Ethanol
-8.52
26.8
Naphthalene
Propanol
-60.2
16.4
Naphthol
Methanol
17.3
9.51
Naphthol
Acetone
-19.2
24.9
Quinoline
Methanol
23.4
13.7
Quinoline
Acetone
-36.6
14.3
3,5-Dichloroaniline
Methanol
117
79.5
3,5-Dichloroaniline
Acetone
78.6
40.5
Aniline
Methanol
-8.85
42.0
Aniline
Ethanol
31.4
8.36
Phenanthrene
Methanol
0.963
3.26
Phenanthrene
Ethanol
-13.7
18.2
Xylene
Methanol
126
148
Xylene
Acetone
117
15.4
Xylene
Ethanol
101
285
Xylene
Propanol
-9.71
30.1
Overall
19.2
111
Number of Points
Evaluated = 121
-------
116
The average error for the three approaches showed similar results and
increased in the order: UNfFAC approach (4.95%), the excess free energy
approach (10.2%), and log-linear approach (19.2%). The standard deviation for
these three approaches also showed similar results, and increased in the
order: excess free energy approach (97.4%), UNIFAC approach (107%), and log-
linear approach (111%). Therefore, it may be concluded that these three
approaches gave somewhat similar results for the eighteen systems
investigated. However, the excess free energy approach did show least
standard deviation of error for prediction of solute solubility as a function of
co-solvent volume content in a solvent/water mixture. The UNIFAC approach
performed especially well in consideration that no experimental measurements
are required in order to make the prediction. The log-linear approach is
obviously the simplest technique to apply, and it is attractive if some
experimental co-solvent/water solubility data are available.
Solubility Parameter and Solubility in Co-solvent/Water Mixtures
The solubility parameter, 5, is used as a characteristic parameter to
describe solute and solvent properties, and in certain instances it can be
used to make qualitative predictions on solute solubility. The solubility
parameter was defined in Chapter Two, and Table 2-4 showed the values of
solubility parameters for the solutes and solvents used in this investigation.
The solubility parameter approach for predicting solute solubility was
evaluated for naphthalene and phenanthrene because these compounds are
comparatively non-polar, non-hydrogen bonding. Thus among the various
solutes investigated in this study, they most closely satisfy the basic
requirements for regular solution theory in which the principal solution
interaction consists of dispersion forces.
Hildebrand and Scatchard's (Hildebrand and Scott, 1950) developed
regular solution theory which explains that the solubility of a solid, whose
solution obeys Raoult's law, can be expressed as Equation 2-93. The activity
of the solid solute can be taken as that for the subcooled liquid, which is
-------
117
equal to the ideal solubility of the solid solute, X2', so Equation 2-93
becomes
X ' V z 2
In —— = —LI- (3, - & )2 (4-10)
X2 RT 12
This is the Hildebrand-Scatchard solubility equation for a solid compound,
with solubility parameter 52, dissolved in a solvent with solubility parameter
$ . For purposes of this discussion, the volume fraction of the solvent
mixture (z^ is taken as the sum of the volume fractions of co-solvent and
water. As a first approximation, the solubility of naphthalene and
phenanthrene in water and co-solvents may be assumed small, and thus the
volume contribution of the solute is small compared to the volume fraction
of the co-solvent and water; therefore it was assumed that z; = 1. This
assumption does not introduce appreciable error, because except for
naphthalene solubility in acetone, mole fraction solubility is less than
approximately 2%. The ideal solute solubility can be calculated from the heat
of fusion of the solid solute at the melting point and the heat capacities of
the solid and subcooled liquid (Equation 2-32), and
AH. / T - T \
In X2' = ) (4-11)
m
or
as< Tm
|n x2' - - -y-\n (y) (4-12)
The solubility parameter for the co-solvent/water mixture is calculated from
Equation 2-94. For a multicomponent system, Hildebrand and Scott (1950)
suggest that the solubility parameter is simply the volume fraction weighed
arithmetic mean of solubility parameters of the pure component (Equation
2-94). For example, the solubility parameter for pure water is 23.50 and the
solubility parameter for methanol is 15.15; therefore, the solubility parameter
-------
118
for 50% (by volume) methanol and 50% water mixture can be calculated as
19.4. The evaluation of the solubility parameter approach was performed
using Equations 4-10, 4-11 and 2-94 for naphthalene solubility in
methanol/water and acetone/water systems, and for phenanthrene solubility 'in
methanol/water and ethanol/water systems. Tables 4-16 and 4-17 show the
results of the solubility parameter approach for predicting solubility of
naphthalene in methanol/water and acetone/water mixtures respectively.
Tables 4-18 and 4-19 show the results of the solubility parameter approach
for predicting phenanthrene solubility in methanol/water and ethanol/water
mixtures. The observed naphthalene and phenanthrene solubility data are also
shown in Tables 4-16 through 4-19 for comparison.
The results in Tables 4-16 to 4-19 show that predicted solubility
deviates significantly from the observed solubility. The solubility parameter
approach predicts very poorly for the solute solubility in pure water where
deviations of many orders of magnitude are observed. The predicted
solubility value improves as the water content decreases in the co-
solvent/water mixture. For pure co-solvent, the estimated solute solubilities
are within a factor of two to ten of the observed values.
Hildebrand developed the regular solution theory on the assumption that
dispersive forces are the dominant solution interaction and that symmetrical
interactions occur between adjacent molecules in solution. Clearly these
assumptions are violated with a strongly polar, hydrogen bonding solvent like
water. The assumptions are more applicable for systems comprised of 100%
organic solvent, and this explains the trend toward convergence of observed
and predicted solute solubility as the mixture composition increases in
volume fraction co-solvent. It is concluded that the use of regular solution
theory is not generally suitable for predicting solute solubility for the
solute/co-solvent/water systems investigated in this study.
-------
119
Table 4-16: Solubility Parameter and Solubility of
Naphthalene in Methanol/Water Mixtures
Naphthalene solubility parameter = 9.9
Water solubility parameter = 23.50
Methanol solubility parameter = 15.15
Fraction
Fraction
T
Observed
Predicted
Solubility
solubility
[Wt.]
[vol.]
[-]
[-]
.0000
.0000
23.50
.211E-05
.673E-17
.0472
.1007
22.66
.494E-05
.726E-15
.1003
.2013
21.82
.120E-04
•578E-13
.1604
.3017
20.98
•261E-04
.338E-11
.2292
.4020
20.14
.731E-04
.147E-09
.3084
.5021
19.31
.183E-03
•471E-08
.4008
.6020
18.47
.466E-03
.112E-06
.5099
.7017
17.64
.120E-02
• 197E-05
.6408
.8013
16.81
.323E-02
.258E-04
.8005
.9007
15.98
.878E-02
.251E-03
.2992
.4912
19.40
.731E-04
.328E-08
.4240
.6247
18.28
.578E-03
.221E-06
.5174
.7080
17.59
•193E-02
.234E-05
.5716
.7511
17.23
.265E-02
.731E-05
.7076
.8455
16.44
.502E-02
•736E-04
.8446
.9248
15.78
.112E-01
.417E-03
.9928
.9968
15.18
.237E-01
.172E-02
.9969
.9986
15.16
.242E-01
.178E-02
1.000
1.000
15.15
.246E-01
.183E-02
#: Solubility parameters of methanol/water mixture, calculated from
Equation 2-94
-------
120
Table 4-17: Solubility Parameter and Solubility of
Naphthalene in Acetone/Water Mixtures
Naphthalene solubility parameter = 9.9
Water solubility parameter = 23.50
Acetone solubility parameter = 9.93
Fraction
Fraction "J*
Observed
Predicted
Solubility
solubility
[Wt.]
[vol.]
[-]
[-]
.0000
.0000
23.50
.203E-05
.673E-17
.0266
.1004
22.14
.440E-05
.114E-13
.0578
.2004
20.78
.980E-05
.856E-11
.0952
.3006
19.42
.227E-04
.300E-08
.1406
.4006
18.06
.548E-04
.476E-06
.1971
.5007
16.71
.139E-03
.348E-04
.2691
.6006
15.35
.375E-03
.116E-02
.3642
.7006
13.99
.110E-02
• 179E-01
.4953
.8004
12.64
.377E-02
.126E+00
.6884
.9002
11.28
.169E-01
.411E+00
.2320
.5524
16.00
.230E-03
.236E-03
.2874
.6223
15.06
.465E-03
.225E-02
.3470
.6846
14.21
.919E-03
.122E-01
.3749
.7101
13.86
.122E-02
.223E-01
.4457
.7666
13.10
.239E-02
.711E-01
.4974
.8017
12.62
.384E-02
.129E+00
.5541
.8354
12.16
•610E-02
.209E+00
.6157
.8675
11.73
.984E-02
.304E+00
1.000
1.000
9.93
.227E+00
.615E+00
#: Solubility parameters of acetone/water mixture, calculated from
Equation 2-94
-------
121
Table 4-18: Solubility Parameter and Solubility of
Phenanthrene in Methanol/Water Mixtures
Phenanthrene solubility parameter = 9.8
Water solubility parameter = 23.50
Methanol solubility parameter = 15.15
Fraction Fraction T" Observed Predicted
Solubility solubility
[Wt.] [vol.] [-] [-]
.0000
.0000
23.50
.300E-07
.115E-24
.0472
.1007
22.66
.100E-06
.161E-21
.1003
.2013
21.82
.340E-06
.136E-18
.1604
.3017
20.98
.970E-06
.695E-16
.2292
.4020
20.14
.395E-05
.217E-13
.3084
.5021
19.31
.137E-04
.409E-11
.4008
.6020
18.47
.487E-04
.470E-09
.5099
.7017
17.64
.177E-03
.331E-07
.6408
.8013
16.81
.654E-03
.143E-05
.8005
.9007
15.98 -
.250E-02
.377E-04
.4555
.6542
18.03
.953E-04
.462E-08
.6791
.8271
15.56
.920E-03
.350E-05
.8153
.9089
15.91
.280E-02
•484E-04
.9310
.9683
15,41
.631E-02
•265E-03
1.000
1.000
15.15
.979E-02
.614.E-03
*: Solubility parameters of methanol/water mixture, calculated from
Equation 2-94
-------
122
Table 4-19: Solubility Parameter and Solubility of
Phenanthrene in Ethanol/Water Mixtures
Phenanthrene solubility parameter = 9.8
Water solubility parameter = 23.50
Ethanol solubility parameter = 13.09
Fraction Fraction I*
[Wt.] [vol.]
Observed Predicted
Solubility solubility
[-] C-]
.0000
.0000
23.50
.300E-07
.498E-25
.0419
.1238
22.21
.160E-06
.152E-20
.0716
.1994
21.43
.420E-06
.507E-18
.1167
.2991
20.39
.145E-05
.598E-15
.1705
.3990
19.35
.499E-05
•370E-12
.2357
.4990
18.31
.168E-04
.119E-09
.3163
.5991
17.27
.557E-04
.196E-07
.4185
.6992
16.23
.182E-03
.167E-05
.5523
.7994
15.19
.586E-03
.733E-04
.7351
,-.8996
14.14
.190E-02
.165E-02
.3836
.6678
16.55
. 126E-03
.445E-06
.6101
.8348
14.82
.887E-03
.238E-03
.7864
.9224
13.91
.254E-02
.306E-02
.8946
.9648
13.47
.427E-02
.876E-02
1.000
1.000
13.09
.665E-02
•192E-01
«: Solubility parameters of ethanol/water mixture, calculated from
Equation 2-94
-------
123
Summary
This chapter presented results of interpretation of experimental data to
predict aromatic solute solubility in co-solvent/water systems. Seven
aromatic solutes were selected for evaluation in order to represent different
physical and chemical characteristics with respect to hydrophobicity, polarity,
hydrogen bonding, and functional group substitution. Data for eighteen
aromatic solute/co-solvent/water systems were evaluated, and it was shown
that in general there was a semi-logarithmic increase in solute solubility with
increase volume fraction of co-solvent. This confirmed the trend predicted
by the log-linear approach for estimating solute solubility in co-solvent/water
systems. This approach was the most easily applied of the various
thermodynamic techniques for estimating solubility. However, it requires that
some solubility data be available, preferably solubility in pure water and
solubility in 50% or 100% co-solvent. While aqueous solubility is commonly
available for many aromatic solutes, relatively little information exists on
solubility of aromatic compounds in various co-solvents.
The UNIFAC group contribution model was used to estimate solute
solubility in water and co-solvent/water mixtures. This approach was unique
among the predictive techniques in that it does not require specific
measurements in order to obtain correlation coefficients or other parameters.
The UNIFAC procedure was used to predict infinite dilution activity
coefficients, y00, from which mole fraction or mass solubilities were
estimated. The UNIFAC procedure employs a solution-of-groups concept in
which infinite dilution activity coefficient is given from specification of mole
fraction solvent composition and functional groups comprising the solute, co-
solvent and water. This procedure predicted solute solubility in pure water
and in 100% co-solvent within a factor of approximately two. These
predictions comprised a range of solute solubilities spanning approximately
six orders of magnitude. The standard deviation of the error for prediction
of solute solubility in mixtures for the eighteen co-solvent/water systems
was 109%.
-------
124
An excess free energy approach was also evaluated for predicting
solute solubility. This technique required use of the UNIFAC procedure to
predict co-solvent/water interaction constants. This approach also required
the use of experimental data to obtain a solute-solvent interaction parameter.
The various solute-solvent interaction parameters were correlated with solute
octanol/water partition coefficient, and this correlation was employed as part
of the predictive procedure. It was found that the excess free energy model
provided a reduction in standard deviation of error compared to the UNIFAC
approach; however, this was achieved through use of a more cumbersome
approach requiring an empirical correlation. The excess free energy procedure
may be useful for estimating solute solubility for solutes for which UNIFAC
functional group surface and interaction parameters are unavailable.
A molecular surface area technique was shown to be able to predict
solute solubility with a standard deviation of error of about 60% for the one
solute/co-solvent/water system for which appropriate surface area and
interfacial energy terms were available. The use of standard solubility
parameters and regular solution theory was inappropriate for predicting solute
solubility in the co-solvent/water systems.
-------
125
Chapter 5
EFFECT OF ORGANIC SOLVENT ON SORPTION OF
AROMATIC SOLUTES ONTO SOILS
Introduction
This chapter outlines an approach to investigate procedures for
predicting sorption of certain types of aromatic hydrocarbons onto soils from
an aqueous phase containing polar organic solvent. The work described in
this chapter is comprised of both data base and theoretical developments.
The theoretical developments are used for experimental design and data
interpretation. The motivation for this work is derived from the need to
understand pollutant sorption onto soils for systems containing appreciable
concentration of polar solvent in the aqueous phase. The work is applicable
to understanding near source contaminant transport in the event of spill or
discharge of heavily laden organic wastes to soil systems.
The purpose of this work is to improve understanding of the manner in
which organic chemicals may move through soil or sediments. It is known
that hydrophobic organic solutes can be retarded in movement through soil
relative to the bulk movement of water, and it is also known that sorption
of hydrophobic organic solutes onto soil can play an important role in the
retardation of the transport process. This chapter includes a discussion of
these phenomena. This discussion is then used to develop a model to
describe the sorption of aromatic solutes onto soil for systems containing
miscible, polar organic solvent in the aqueous phase. The chapter begins
with a synthesis of information regarding sorption of aromatic hydrocarbons
onto soil. This includes an evaluation of procedures that enable estimation
-------
126
of sorption characteristics for aromatic hydrocarbons from pure water
systems, and then these procedures are extended to those systems that
contain organic solvent/water mixtures. The procedures incorporate several
physico-chemical properties of the system including: soil organic carbon
content, solute solubility in the solvent/water mixture, and other chemical
characteristics of the aromatic hydrocarbons. The discussion of sorption
phenomena is followed by a description of an experimental methodology and
results of laboratory tests to observe sorption of organic solutes onto soils
from systems containing various proportions of polar solvents. This
information is then used to assess the validity of the sorption model.
Sorption of Aromatic Solutes onto Soils
At present there is much interest in evaluating the nature and extent of
groundwater contamination from toxic/hazardous organic pollutants.
Contamination of groundwater with synthetic organic materials presents major
environmental problems in many areas of the United States and in other
industrialized nations as well. Reports prepared by the U.S. Environmental
Protection Agency (EPA) and the Council on Environmental Quality (CEQ)
describe the magnitude of waste disposal practices in the U.S. and their
effects on groundwater quality. Data presented (EPA, 1977, CEQ, 1980)
indicate that thirty to fifty thousand waste disposal sites in the U.S. may
contain hazardous materials. Although the extent of contamination is
unknown, groundwater systems close to many of these sites are being slowly
degraded and often the contamination involves the presence of synthetic
organic materials (EPA, 1980).
Once groundwater has been contaminated, little can be done to reverse
the damage. Frequently the only remedies for ^groundwater contamination
problems involve extensive pumping or removal of soil, both of which are
expensive and/or impractical propositions. In order to minimize the impact
of man's activity on water quality, factors related to prevention and
contamination need to be better understood. In this study, procedures are
-------
127
developed and evaluated that enable prediction of sorption characteristics for
organic solutes onto soils from an aqueous phase that contains polar solvent.
Organic solutes investigated in this study range from a nonpolar polycyclic
aromatic hydrocarbon to polar, substituted aromatic compounds. Because of
the hydrophobic nature of some of these compounds, sorption is important in
determining the fate of these type of organic pollutants in natural water
systems, and especially in subsurface systems.
Aqueous concentrations of hydrophobic organic solutes in natural water
systems are highly dependent on sorptive/desorptive equilibria with sorbent
present in the system. In subsurface systems, liquid to solid phase
partitioning can play a significant role in the retardation of the transport of
organic solutes (Fu et al. 1983). Sorption may also be involved in pollutant
degradation via chemical reaction or biological degradation through attached
growth biofilms (McCarty et al. 1981). Thus, understanding the fate of
organic solutes in the subsurface environment greatly depends on
understanding several aspects of the sorption process.
The Freundlich sorption model has been found to be useful for
describing sorption characteristics of organic solutes in water/sediment and
water/soil systems (Means et al. 1979, Karickhoff et al. 1978). The Freundlich
sorption isotherm can be expressed as
- » K C "" (5-1)
M
where
S = total mass of solute sorbed [mg]
M = mass of solids [g or kg]
C = equilibrium concentration in the liquid phase [mg/l]
w «v
K = partition coefficient [l/g or t/kg]
K and 1/n are empirical constants which are characteristic of the solute and
solids. If the sorption data are plotted on logarithmic scales with equilibrium
concentration, C#, on the abscissa and sorption capacity, S/M, on the
-------
128
ordinate, then according to Equation 5-1, K is the intercept of the sorption
isotherm plot at C = 1 and 1/n is the slope of the isotherm. K is the
measure of the strength of sorption, or sorption capacity, while 1/n is an
indicator of sorption intensity. It is conventional to express C in units of
mass per volume and S as mass sorbed per mass of dry soil. The units on
K are usually given as l/kg or ml/g.
Many laboratory studies on organic solute sorption onto soils,
sediments, and suspended solids have found that a linear sorption isotherm,
e.g. 1/n = 1 in Equation 5-1, is useful in describing hydrophobic organic solute
sorption onto these materials (Hamaker and Thompson, 1972; Karickhoff et al.
1979). Hamaker and Thompson (1972) summarized available soil Freundlich
sorption isotherm data for a variety of chemicals, and the results show that
the exponent 1/n varied from 0.7 to 1.0. Karickhoff et al. (1979) found that
the sorption isotherms for various polycyclic aromatic hydrocarbon (PAH)
compounds on pond and river sediments were linear (1/n = 1) over a range of
aqueous phase concentrations up to about one half the compound's solubility
in water. Rogers et al. (1980) performed sorption and desorption studies with
benzene at concentration less than 1 mg/l with four soils and obtained
sorption isotherms with 1/n values ranging from 0.9 to 1.1. Schwarzenbach
and Westall (1981) have reported that a linear sorption isotherm can be used
to describe' sorption of non-polar organic solutes by natural sediments.
These experimental results support the concept that a linear sorption isotherm
is appropriate for describing sorption of a relatively hydrophobic organic
solute on soil/sediment at low to moderate equilibrium concentration with
respect to solute solubility.
Schwarzenbach and Westall (1981) and Karickhoff et al. (1979) found that
non-polar organic compounds sorbed independently on soil through the linear
portion of their respective isotherms when studied in a mixture at low to
moderate concentration relative to compound solubility. Thus, in groundwater
contamination problems involving a mixture of sorbable, non-polar, organic
-------
129
solutes at low concentration, it may be reasonable to expect that each
species will sorb independently depending on physico-chemical properties of
the solute. Thus sorption is expected to have significant retardation effect
on transport of strongly sorbing organic solutes. The large degree to which
transport of strongly sorbing contaminants can be retarded has been
illustrated by Pickens and Lennox (1976) who simulated numerically the
movement of a sorbing solute for a range of partition coefficients in simple
two-dimensional groundwater systems.
It is known that organic solutes can be retarded in movement through
soil relative to the bulk movement of water. For the case of hydrophobic
organic solutes, predictive procedures have been developed which correlate a
linear soil sorption partition coefficient with soil organic carbon content and
physical and chemical properties of the solute. Notable among these
approaches are procedures in which the organic solute sorption partition
coefficient is related to the solute octanol-water partition coefficient, (Kqw).
The linear sorption isotherm approach has been used successfully to describe
sorption of hydrophobic organic solutes from an aqueous phase containing
relatively low concentration of organic compounds (Karickhoff et al. 1979;
Schwarzenbach and Westall, 1981; Means et al. 1980; Chiou et al. 1979).
However, except for ongoing work at the University of Florida {Nkedi-Kizza et
al. 1984; Woodburn et al. 1985), no studies have been reported in which the
primary objective was to investigate sorption of relatively hydrophobic
organic solutes from an aqueous phase containing high concentration of polar
organic solvent.
Understanding sorption of organic solutes onto soil from an aqueous
phase containing polar solvent is important for the purpose of evaluating
pollutant transport for hazardous organic materials released to soil and
groundwater systems as a result of accidental spill or improper/inadequate
disposal. In these instances, the release of the hazardous materials may
commonly be accompanied by the release of organic solvents, and these
-------
130
solvents may exert a strong influence on near-source transport. As
discussed in the previous chapter, the presence of miscible organic solvent in
the aqueous phase can significantly enhance organic solute solubility and thus
reduce sorption characteristics. This is because the sorptive behavior of an
organic solute can be related to solute properties, particularly solute
solubility or solute octanol-water partition coefficient. Since organic solute
sorption onto soils and sediments can be inversely correlated with the
organic solute solubility (Means et al. 1980), it is expected that organic solute
sorptive behavior may be altered significantly owing to the effect of
miscible organic solvent on solute solubility enhancement. The following
section outlines an approach to explain these phenomena by encompassing
the relationships between organic solute sorptive behavior, soil and sediment
properties, and organic solute solubility. The development focuses on
mechanisms which may impact solubility and sorption, and this is used to
describe a model to predict organic sorption in miscible organic solvent/water
systems.
Sorption and Soil- Organic Carbon Content
It is known that soils with higher organic material exhibit greater
sorption capacities for hydrophobic organic compounds. The relative
importance . of the organic carbon content of a soil or sediment in the
sorption of organic solutes has been well documented (Karickhoff et al. 1979;
Karickhoff, 1981; Schwarzenbach and Westall, 1981; Rogers et al. 1980;
Lambert et al. 1965). The difference in sorptive behavior between different
types of soils and sediments may be accounted for by normalizing the
partition coefficient on the basis of organic carbon content of the sorbent
(Lambert et al. 1965).
The role of soil organic matter in the sorption of uncharged organic
solutes has been studied extensively and it has been found that the organic
matter in soil/sediments is primarily responsible for sorption (Karickhoff,
1981). In studies with hydrophobic organic solutes at low loadings, a linear
-------
131
correlation is often observed between solute partition coefficient (Kp) and
soil/sediment organic carbon content (OC). The linear dependence of partition
coefficient on organic carbon content can be expressed as
K = K OC (5-2)
p OC
where OC is the fraction organic carbon content, and K is the normalized
OC
organic carbon partition coefficient. Hamaker and Thompson (1972) suggested
that Koc is highly soil or sediment independent and is constant for a
particular organic solute. A similar conclusion is made by Karickhoff (1984),
in his review of sorption of uncharged organic solutes of limited solubility
( < 10'3 M) that are not susceptible to special interactions with soil organic
carbon. For a soil/sediment with a particular particle size distribution having
various organic carbon contents, the partition coefficient can be expressed as
the weighted arithmetic mean of the separate contributions to sorptive
behavior (Karickhoff et al. 1979).
Karickhoff (1984), following Mackay (1979), explains that sorption
equilibrium may be defined as the state in which sorbate fugacities are the
same in the aqueous and sorbed phases. For systems in which sorption to
organic matter dominates over sorption to mineral matter, the organic carbon
normalized partition coefficient may be envisioned as being proportional to
the ratio of the compound's activity coefficient, y, in the aqueous phase (w)
and the organic carbon phase (oc)
K oc — (5-3)
OC
r
oc
in which the proportionality constant contains the reference state fugacities
and appropriate unit conversion factors. Further, Karickhoff (1984) explains
that activity coefficients "contrast" interactions of the solute in a given
''te X.
phase with the cohesive interactions in the reference state (i.e. pure liquid or
subcooled liquid). Thus it may be expected for relatively hydrophobic organic
solutes that yw be highly variable, as are variations in aqueous solubility;
while y , reflecting cohesive interactions in the organic carbon phase, should
-------
132
be similar to that for the reference state and therefore much less variable.
Hence, Koc should be dominated by variations in yw, and as a first
approximation
OC
« (5-4)
K and Octanol/Water Partition Coefficient
OC
The octanol/water partition coefficient. Koy/ like Koc describes the
partitioning of a solute between an aqueous phase and a relatively immiscible
hydrophobic phase. For a solute in equilibrium with octanol and water, the
fugacity is the same in each phase, and Kqw is given as the ratio of the mass
concentration in each phase
K = « JLS- (5-5)
ow C Y
where the proportionality with activity in each phase entails the ratio of the
molar volume of water to octanol, and where the .same standard state is
chosen for the solute in each phase (i.e. pure liquid or subcooled liquid).
Since K and K both describe organic solute partitioning between
OC ow
water and a hydrophobic organic phase, it may be expected that these
parameters would be related
K oc K (5-6)
ow oc
The concept embodied in Equation 5-6 entails correlation of partition
coefficient for a given solvent/water system with that for a reference
solvent/water system. This has been termed linear free energy relationships,
and Leo and Hansch (1971) have shown that octanol is a particularly good
choice of reference solvent. Octanol/water partition coefficient data are
available for a large number of compounds. Current tabulations may be
obtained from Corwin Hansch as part of the MEDCHEM project at Pomona
College, California, as well as from various handbooks and research
-------
133
documents (Lyman et al. 1983; Hansch and Leo, 1979). In addition, various
semi-empirical approaches are available from which Kqw may be estimated
from solute physical, chemical or structural characteristics (Lyman et al.
1982). Reported values of Kow for the organic solutes employed in this
investigation are shown in Table 5-1.
Linear free energy correlations with Kqw have been used to describe
aqueous solubility (Chiou et al. 1982), bioaccumulation (Chiou et al. 1977;
Mackay, 1982), aromatic solute partitioning between immiscible solvent and
water (Campbell et al. 1983), and sorption of organics onto soils (Lambert,
1967; Dzombak and Luthy, 1984).
Various empirical expressions have been developed to describe the
relationship between K and K (Briggs, 1973; Karickhoff etal. 1979; Means et
n p OW *
al. 1980; Karickhoff, 1984). These investigators have reported excellent
correlation between Kqc and Kqw for hydrophobic solute sorption, with a linear
regression equation usually given in the form
log K = a log K + b (5-7)
9 OC OW
where a and b are regression coefficients. Several examples of these
equations are described below.
Karickhoff et al. (1979) found a linear relationship between K and K
OC OW
from linear regression analysis of sorption data for ten compounds, including
eight aromatic solutes:
A linear regression of various sorption data gave a correlation between log
Koc and log Kow for forty-seven organic solutes, including twenty-two
hydrocarbons, for which Karickhoff (1981) summarized as
K = 0.63 K
OC i
r2 = 0.96
(5-8)
OW
log K = 0.989 log K - 0.346 r2 = 0.997
" OC ow
(5-9)
Means et al. (1980) verified a linear relationship between K and K for
r OC OW
-------
134
Table 5-1: Organic Solute Octanol/Water Partition Coefficients*
Compound log Kow
Naphthalene 3.35
Naphthol 2.71
Quinoline 2.04
3,5-Dichloroaniline 2.59
Aniline 0.90
Phenanthrene 4.46
o-Xylene 3.20
» After Hansch and Leo (1979)
-------
135
a variety of nonpolar compounds including various polycyclic aromatic
hydrocarbons. Based on sorption studies for twenty-two compounds on
various soils and sediments, the relationship between Koc and Kow was given
as
log K = log K - 0.317 r2 = 0.98 (5-10)
** oc ow
Schwarzenbach and Westali (1981) investigated the sorption of
halogenated alkanes and benzenes, and for low concentrations they found that
the partitioning between water and sediment could be described as
log K = 0.72 log K + 0.89 r2 = 0.95 (5-11)
° oc ow
Karickhoff (1984) concluded from these and other results that the
correlation between Kqc and Kow was "a somewhat divergent group of
relationships". This was attributed to various factors including hydrophilic
contribution to sorption, as well as kinetic or steric effects. It was
suggested that hydrophilic effects would be evident for solutes containing
polar functional groups which tend to be those with values of log Kow < 3,
while kinetic or steric effects would be more pronounced for those
compounds having values of log Kqw > 5.
Koe and Solute Solubility
As explained in Chapter Two, organic solute solubility in water can be
realted to the solute's infinite dilution activity coefficient, For
hydrophobic liquid solutes having sufficiently large values of mole
fraction solute solubility can be expressed as the reciprocal of the activity
coefficient (Equation 2-39). For hydrophobic solids, a crystal energy term
must be taken into account, and the solute solubility can be expressed as
Equation 2-31. If entropy of fusion, ASf, is substituted for heat of fusion,
AH(, by using Equation 2-33, then the relationship between activity and mole
fraction solubility can be expressed as
-------
136
ASf (Tm-T>
log y ¦ - log X (5-12)
2 2.303 RT
in which Tm is the solute melting point in °K, T is the system temperature in
°K, and R is the gas constant. For hydrophobic liquid solutes, the system
temperature is greater than the melting temperature, and T is set equal to T
rn
and the crystal term vanishes. Yalkowsky and Valvani (1980) have reviewed
AS, data for "rigid" organic solutes which are solids at 25 °C, and it was
found that ASf is not highly variable and is in the range of 12 - 15 cal/mole
°K. "Rigid" solutes include cyclic compounds (alphatic or aromatic) and
molecules with less than five atoms in a flexible chain (Yalkowsky and
Valvani, 1980). Nonrigid molecules typically melt at much lower temperatures
than rigid molecules for molecules of similar molecular weight, and thus are
frequently liquid at room temperature. It has been long recognized by
chemical thermodynamicists that a value of ASf is in the range of 13
cal/mole °K for solid organic compounds (Prausnitz, 1969).
Equation 5-4 suggests that Koc should be proportional to y2. Hence by
combining Equation 5-4 and 5-12, an empirical equation of the following type
may be expected to fit observed sorption data
ASf
log K » - a log X (T - T) ~ B (5-13)
oe 2.303 RT m
in which a and are regression-fitted parameters. Karickhoff (1981)
performed an evaluation of Equation 5-13 for condensed ring aromatic
compounds using Koe data of Hassett et al. (1980) for benzene and polycyclic
aromatic hydrocarbon (PAH) compounds, with ASf assumed to be 13.0
cal/mole °K and system temperature T at 298 °K (25 °C). The empirical
equation was given as
log Koc = 0.921 log X - 0.00953 (Tm - 298) - 1.405 (5-14)
This equation was evaluated for a variety of organic solutes (triazines.
-------
137
carbamates, organophosphates, and chlorinated hydrocarbons), and was found
to estimate K usually within a factor of 2 to 3 of measured values
OC '
(Karickhoff, 1984). It was found that Equation 5-13 worked well for low
molecular weight compounds but tended to overestimate sorption of highly
chlorinated, high molecular weight compounds. It was concluded that a
values for these type of compounds may be in the range of 0.7 to 0.8 which
is considerably less than that for polycyclic aromatic hydrocarbons.
Karickhoff (1984) evaluated the sorption literature values for forty-seven
organic compounds including PAH and chlorinated hydrocarbons, triazines,
carbamates, organophosphates and phenylureas and found that the a value in
Equation 5-13 was 0.83 and the fi value was -0.93
log K = -0.83 log X - 0.01 (T - 298) - 0.93 (5-15)
oc m
Solvent Effect on Solute Sorption
Equations 5-2 through 5-6 and Equation 5-13 may be summarized as
follows. Linear partition coefficients are often observed for hydrophobic
organic solute sorption onto soil or sediments. The sorption partition
coefficient may be normalized for soils and sediments on the basis of
fraction organic carbon, and normalized for various solutes on the basis of
octanol/water partition coefficient or aqueous solubility. Hence for a given
soil or sediment, organic solute sorption is inversely proportional to aqueous
solubility. The following explains a theoretical approach for predicting the
observed effect of miscible organic solvent in the aqueous phase on organic
solute sorption onto soil or sediment. This approach is based on the linkage
between Koe and aqueous solubility, and the effect of solvent on solubility.
It has been demonstrated in Chapter Four ttfat organic solute solubility
in a solvent/water mixture generally increases semi-logarithmically with
increase of volume fraction of solvent. Using the simple log-linear solubility
model, the mole fraction solubility of the solute in the solvent/water mixture
can be expressed as
-------
138
log Xm = log Xw +
-------
139
decrease semi-logarithmically with increase of solvent volume fraction. The
semi-logarithmic relationship predicted by Equation 5-20 can be shown on a
semi-logarithmic plot with volume fraction solvent on the abscissa and Kp on
the ordinate. The slope of this plot represents the combined effect of both
a and a. The a term represents the effect of solvent on increase of solute
solubility, while the a term relates to the dominance of yw in Koe among
various solutes. The a term should approach unity if the fugacity coefficient
for solute in soil/sediment organic carbon is relatively independent of solute
(Karickhoff, 1984). That a may be in the range of 0.7 to 0.8 for certain
solutes may imply kinetic or steric inhibition of sorption, or that the fugacity
coefficient is increased which may imply decreased affinity of the solute for
the organic matter.
Soil sorption partition coefficient data are reported later in this chapter
for various solutes in solvent/water systems. From these data it is possible
to determine experimental values of the coefficient in Equation 5-20, («
-------
140
Soiis The soils used in this study were Hagerstown silt loam, Berkeley
silt loam, and Tifton sand. Hagerstown silt loam was used as the principal
soil, and was obtained from the Department of Agronomy Experimental
Station, The Pennsylvania State University (University Park, PA). The
Hagerstown silt loam was taken from within two feet of the ground surface.
The Berkeley Silt loam and Tifton sand were used for screening tests, and
were obtained from U.S. Department of Agriculture, Agricultural Research
Center (Beltsville, MD). Prtor to storage, the soils were air-dried and
screened to pass a U.S. standard sieve No. 10 (2.0 mm). This procedure
removed any grass and plant root.
Chemicals and Reagents Organic solvents used in this study included
methylene chloride (CH2CI2), methanol (CH3OH), acetone (C3H60), and
acetonitrile (CH3CN). These solvents were HPLC grade and were obtained
from Fisher Scientific Company (Pittsburgh, PA). All organic solvents were
filtered through 0.45 /
-------
141
four hours, followed by rinsing with deionized water, acetone, methanol,
methylene chloride, and water, respectively. Following these procedures, the
glassware was oven dried at 105 °C and covered with aluminum foil until
used.
Experimental Instrumentation Solute analyses were performed with a
high pressure liquid chromatography (HPLC) system made by Perkin-Elmer
Corporation (Norwalk, CT). This system consists of a Series 3 liquid
chromatograph and two detector units. A Perkin-Elmer model 204-S
fluorescence detector equipped with variable excitation and emission
wavelength setting was used for naphthalene and naphthol analysis. A
Perkin-Elmer model LC-15 ultraviolet (UV) detector with a fixed wavelength
(254 nm) was used to measure quinoline and 3,5-dichloroaniline. Sorption
batch tests were performed using a wrist action shaker (Model 74, Burrell
Corp. Pittsburgh, PA). Centrifuging was performed using a IEC clinical
centrifuge from International Equipment Co. (Needham Hts, MA).
A Hamilton (Reno, NV) Series 800 microliter syringe was used to inject
samples of between 2 and 10 microliters into a Rheodyne (Berkeley, CA)
Model 7105 injection valve fitted with a 175 p\ sample loop. Either a 0.26
mm x 25 cm Perkin-Elmer PAH/10 column or a 0.46 mm x 25 cm Supelco
(Bellefonte, PA) LC-PAH column was used to provide resolution for
naphthalene and naphthol. A Supelco 0.46 mm x 15 cm LC-8 column provided
resolution for quinoline and 3,5-dichloroaniline; Results were recorded on a
compatible strip chart recorder, and results were determined using a
planimeter (Kouffel & Esser Co. W. Germany).
-------
142
Sorption Isotherm Tests
Sorption of organic solutes onto soils was investigated by batch tests
with an aqueous phase comprised of 0.01 N CaCI2 inert electrolyte. The
electrolyte assisted in settling and separation of fine particles after the
solute attained sorption equilibrium. Batch sorption shake tests were
performed to obtain isotherm data. Sorption isotherms for a series of
organic solutes were run with a variety of solvent/water ratios with a range
of initial solute concentration. The solvent/water mixture was first prepared
by adding solvent (methanol or acetone) to deionized water, and then
degassed prior to adding a known quantity of solute and CaCI2 into solution
to make up the initial concentration. The soiute and CaCl2 were measured to
10-4 g.
The sorption tests involved equilibration at room temperature <23°C ± 2
°C) with different sets of samples having different values of initial solute
concentration and various quantities of soil. The initial solute concentration
was varied from set to set in order to obtain the complete sorption
isotherm. The shake tests were performed with 50 ml glass centrifuge tubes
fitted with teflon-lined screw caps. The amount of soil added to the
centrifuge tubes was chosen to result in high and low equilibrium
concentrations, and generally this included a range of 0.5 g to 40 g soil. In
order to minimize volatilization loss, the experimental procedures consisted
of placing a calculated amount of soil, weighed to 10'4 g, into a centrifuge
tube, and then adding solution to fill the centrifuge tube without head space.
The solution was measured to 0.1 ml via a calibrated burette. The centrifuge
tube was then sealed with a teflon-lined septum and a screw cap with an
access hole to allow for sample to be withdrawn through the septum. The
centrifuge tubes were then covered with aluminum foil throughout the rest of
the test in order to minimize photodegradation. One set of shake tests
typically involved 16 samples, two of which were blanks and contained no
soil. Each sample was replicated, and two or more tests with this number of
-------
143
samples were performed for each solute. Solute losses in blanks were less
than 2% for those blanks in which the initial concentration was in the range
of solute solubility in water.
After sample preparation, the sealed centrifuge tubes were transferred
to a wrist-action shaker. Centrifuge tubes were shaken at room temperature
for 24 hours to allow equilibrium to be achieved, after which the suspensions
were centrifuged at 8000 rev/min for sixty minutes. Analyses were
performed on liquid phase aliquots withdrawn from the upper portion of the
centrifuge tube. The technique employed 2 to 10 microliter liquid aliquots
withdrawn with a Hamilton series 800 microliter syringe. The sample was
withdrawn from the centrifuge tube directly through the septum in order to
minimize any loss during transfer. Analysis for the organic solutes was
performed by high pressure liquid chromatography. The analytical program
employed in this study was shown in Table 3-1. Results were recorded on a
compatible strip chart recorder.
A planimeter (Kouffel & Esser Co. W. Germany) was used to quantify
the resluts from HPLC analysis. This quantification was accomplished by
measuring the area under the response curve for each sample. First the area
corresponding to known standard concentrations (e.g. 1000 mg/l, 100 mg/l, 10
mg/l) were measured by performing at least triplicate injection of the
standard. This was followed by obtaining the average area from several
injections of sample. The total mass of the solute present in each sample
was calculated by comparing the area under the injection curve with the area
of the standard. Once the total mass of solute in the injected sample was
determined, the concentration in the injected sample was calculated by taking
the total mass of the solute divided by the volume of sample injected for
the HPLC analysis.
-------
144
Characteristics of Soils
In order to understand the influence of soil characteristics on organic
solute sorption onto soil, several soil characteristics were evaluated.
Particle Size Analysis Soil particle size is one of the most apparent
physical characteristics of a soil, and particle size provides a description of
the soil's physical "make-up" or textural composition. This determination
gives the relative proportions of the varying size fractions which comprise
the soil mass. Soil particle sizes greater than 0.074 mm are generally
analyzed by sieving methods, while finer particles, i.e. particle size smaller
than 0.074 mm or particles passing through a U.S. standard sieve No. 200, are
analyzed by gravity sedimentation using a hydrometer. Particle size analysis
was performed according to procedures described by Lambe (1951).
The sieve analysis does not determine individual particle sizes; rather it
determines the percentage of soil particle sizes in a range of diameters.
This is accomplished by adding distilled water to the soil sample
(approximately 500 g) and working it into a slurry, then washing the slurry
through a U.S. No. 200 sieve. This is followed by oven-drying the soil
retained on the No. 200 sieve and performing the sieve analysis. The sieve
analysis is accomplished by passing a quantity of soil (approximately 100 g)
through a series of sieves. The soil is shaken mechanically and sieved for
fifteen minutes. The quantity of soil retained by each sieve is expressed as
percentage of the total mass of soil sample. The results of the sieve
analysis for the three soils are presented in Table 5-2.
Hydrometric techniques are used to determine particle size for particles
passing through the No. 200 sieve. These procedures consist of carefully
washing the suspension into a 1000 ml graduated cylinder, adding dispersant,
filling to the 1000 ml mark with deionized water, and then thoroughly mixing
the suspension for approximately 30 seconds. This is followed by inserting
a calibrated hydrometer in the suspension, and taking hydrometer readings at
-------
145
Table 5-2: Sieve Analysis of Soils
Sieve No.
[#]
Particle
Diameter
[mm]
Percent
Retained
[%]
Percent
Pass.
[%]
Hagerstown
10
2.00
0.0
100.00
20
0.84
2.65
97.35
40
0.42
4.81
90.19
60
0.25
14.01
85.99
100
0.149
18.43
81.57
140
0.015
20.61
79.59
200
0.074
24.97
75.03
bottom
< 0.074
100
0.00
Berkeley
10
2.00
0.00
100.00
20
0.84
1.36
98.64
40
0.42
4.86
95.14
60
0.25
7.84
92.16
100
0.149
11.61
88.39
140
0.105
13.46
80.54
200
0.074
16.99
83.01
bottom
< 0.074
100.00
0.00
Tifton
10
2.00
0.00
100
20
0.84
21.88
78.12
40
0.42
54.00
46.00
60
0.25
72.27
27.73
100
0.149
84.91
15.09
140
0.105
87.30
12.70
200
0.074
92.42
7.58
bottom
< 0.074
100
0.00
-------
146
total elapsed times of 1/4, 1/2 and 1 and 2 minutes. After two minutes, the
hydrometer is removed and the suspension is re-mixed and the test is
performed again, but no readings are taken until two minutes have elapsed.
For this reading and subsequent readings, the hydrometer is inserted just
prior to measurement. Hydrometer readings are taken at increasing time
intervals (e.g. 2, 5, 10, 20, minutes etc.) until the hydrometer reading is close
to 1.001. After the final reading, the suspension is poured into an
evaporating dish and oven-dried, followed by weighing the soil to 0.1 g.
The particle size distribution of an assembly of soil particles is
expressed as percent finer by weight. Lambe (1951) defined sand as
consisting of small rock particles that vary in sire from 0.05 mm to 1.0 mm.
with silt comprising fine particles of size 0.002 to 0.05 mm, and clay
describing fine inorganic particles of less than 0.002 mm in size. Using
these definitions for sand, silt and clay, the composition of the three soils
used in this study is shown in Table 5-3. These compositions may be
compared to the U.S. Department of Agriculture Textural Classification
scheme (Casagrande, 1948), for which Hagerstown soil is classified as silt
loam, Berkeley soil is classified as silt loam, and Tifton soil is classified as
sand.
Specific Gravity Analysis Specific gravity of a soil refers to the mean
density of the soil particles collectively. It is expressed as the ratio of the
weight in air of a given volume of soil to the weight in air of an equal
volume of distilled water at a temperature of 4 °C. A pycnometer is
normally used to measure specific gravity of soil. In this study, a 250 ml
volumetric flask was used for this measurement rather than a customary 1000
ml pycnometer because the soil sample was large enough to compensate for
any decrease in precision in measuring fluid volume.
The specific gravity test gives the dry weight density. This test was
conducted by placing 50 g of oven-dried soil in a 250 ml volumetric flask.
Care was taken to clean the outside and neck of the flask where soil may be
-------
147
Hagerstown
Berkeley
Tifton
Hagerstown
Berkeley
Tifton
Table 5-3: Classification of Soils
Sand Silt Clay
48% 32% 20%
15% 57% 28%
90% 7% 3%
Silt loam
Silt loam
Sand
Sand: 0.05 mm < d < 2.0mm
Silt: 0.002 < d < 0.05 mm
Clay: d < 0.002 mm
-------
148
deposited during transfer, and then the flask was filled approximately one-
half full with deionized water. Entrapped air was removed by gently boiling
the water for several minutes. The flask was then cooled to room
temperature and filled with degassed, deionized water. The flask was then
weighed and the temperature was measured. Lastly, the soil solution was
removed from the flask, and the flask was then filled with degassed,
deionized water at the same temperature and weighed. The specific gravity
of the soil was calculated as follows:
W G,
G = -— (5-21)
» Wt - w, + w2
where W$ is the dry weight of soil, GT is the specific of water at the
temperature, W is the weight of flask, soil and water, and W2 is the weight
of flask and water. The specific gravity for Hagerstown silt loam was
measured as 2.63, Berkeley silt loam was measured as 2.61, and Tifton sand
was measured as 2.60.
Organic Carbon Content Carbon is the principal element of soil organic
matter that can be readily measured quantitatively. Hence, estimation of soil
organic matter is generally based on measuring soil organic carbon. Soil
organic carbon includes (Allison, 1965):
• Fresh plant and animal residues, capable of r&pid decomposition
and loss of identity with simultaneous release of nutrient
elements;
• "Humus", which represents the bulk of resistant organic matter,
having high sorptive capacity for cations and capable of improving
soil structure; and
• Inert forms of nearly elemental carbon such as charcoal, coal or
graphite.
In this study, organic carbon was determined by the Walkley-Black
method (Allison, 1965). A soil sample containing 10 to 25 mg of organic-C
was placed into a 500 ml wide-mouth Erlenmeyer flask, 10 ml of 1.0 N
K Cr O was added and the flask was swirled gently to disperse the soil in
2 2 7
-------
149
the solution. Then 20 ml of concentrated H SO, was added and swirled until
2 4
soil and reagents were mixed, and then vigorously mixed for about one
minute. The mixed solution was allowed to stand for 30 minutes and 200 ml
of deionized water was added, and then the suspension was filtered. Three
or four drops of a phenanthroline indicator were added to the solution, and
the solution was titrated with 0.5 N FeS04. Titration results in a sharp end
point with the color of the solution changing from blue to red. The amount
of FeSO, used in titration was recorded. Blank determinations were made in
the same manner to standardize the K,Cr„0, concentration.
2 2 7
The soil organic carbon content can be calculated according to the
following equation, using a correction factor of f = 1.33 (Allison, 1965).
(meq K Cr O - meq FeSO ) (0.003) (100) (f)
Organic - C [%] = (5-22)
g of dry soil
where meq represents miliequivalent of the chemical used, and the constant
0.003 refers to the number of grams of carbon per miliequivalent carbon at
an average oxidation state of zero. The correction factor, f, adjusts for the
fact that soil organic carbon is typically at an average oxidation state
slightly less than zero. The average organic carbon content of the
Hagerstown silt loam was determined as 1.94%, while that for the Berkeley
silt loam was 2.85%, and that for the Tifton sand was 0.50%.
Solvent Effect on Solute Sorption
Sorption behavior of the organic solutes was evaluated with several
solvent/water mixtures. This included investigation with four solutes
(naphthalene, naphthol, quinoline, and 3,5-dichloroaniline) and two
solvent/water mixtures (methanol/water, and acetone/water). The solvent/water
mixtures ranged from 0% to 50% solvent by volume. Five systems were
evaluated with Hagerstown silt loam as sorbent: naphthalene sorption with
aqueous phase containing 0%, 20%, 30%, and 50% methanol; naphthalene
sorption with aqueous phase containing 0%, 10%, 30%, 40%, and 50% acetone;
-------
150
naphthol sorption with aqueous phase containing 0%, 20%, and 50% methanol;
quinoline sorption with aqueous phase containing 0%, 20%, and 50% methanol;
and 3,5-dichloroaniline sorption with the aqueous phase containing 0%, 20%
and 50% methanol. The results of these five sets of sorption studies are
shown in Figures 5-1 to Figure 5-5. The data shown in Figures 5-1 to 5~5
were obtained from tests in which sorbent and sorbate concentrations were
varied in order that the complete sorption isotherm could be obtained. The
results are characterized by linear sorption isotherms over the range of
sorbate concentration. The sorption data were analyzed by linear-least-square
curve fitting and the regression equations are shown in Figures 5-1 to 5-5.
The regression coefficient and the near zero intercept of the linear regression
equations support the validity of a linear sorption isotherm model. In this
study, the units for Kp are given as l/kg, which is equal to 1000 times the
slope of the linear regression relationships in which equilibrium concentration
is given in units of mg/l and sorption capacity in units of mg/g. Figure 5-6
shows the variation in K for naphthalene sorption onto Hagerstown silt loam
p
with methanol/water and acetone/water mixtures.
The results of organic solute sorption tests with Hagerstown silt loam
with no organic solvent in the aqueous phase showed the following values of
the sorption partition coefficients, Kp: naphthalene, 8.0 l/kg; naphthol, 7.4 l/kg;
quinoline, 4.3 l/kg; and 3,5-dichloroaniline, 2.5 l/kg. The sorption partition
coefficient for naphthalene sorption onto Berkeley silt loam was found to be
8.1 l/kg. and the sorption partition coefficient for naphthalene sorption onto
Tifton sand was found to be 2.0 l/kg. These results show a solute
dependence on the sorption partition coefficient. Linear-least-square
regression of the Kow and Kqc data was performed and the following equation
described the sorption of the the four solutes onto the soils with aqueous
phase containing no solvent
K
log K = log — = 1.45 log K - 0.872 r2 - 96.3% (5-23)
OC QC
This regression equation compares sorptive behavior for four aromatic
solutes representing four different chemical types.
-------
151
Figure 5-1: Naphthalene Sorption in Methanol/Water Mixtures
.35
.30 -
o .25 -
.20 -
Adsorption Isotherm s Naphthalene-
Methanol/Water Systems
Solute: Naphthalene
Solvent: Methanol/Water
Soil: Hagerstown Silty Loam
- 0% Methanol by Volume
- 20%Methanol by Volume
- 30% Methanol by Volume
- 50% Methanol by Volume
A
a
'b
.10 -
.5
A
~
O
0 20 40 60 80 100
SOLUTE EQUILIBRIUM CONCENTRATION, Ceq [mg/i]
a. S = 0.0020 + 0.0080 Ceq R2*98.8%
b. S = 0.0071 +0.0040 Ceq R2=88.3%
c. S s 0.0 I 05 + 0.00 I 8 Ceq R2=95.7%
d. S= 0.0039+0.0007 Ceq R2=87.4%
-------
152
Figure 5-2: Naphthalene Sorption in Acetone/Water Mixtures
.35 "
.30 -
w .25
E
Adsorption Isotherm: Naphthalene
Acetone / Water Systems
Solute s Naphthalene
Solvent5 Acetone/Water
Soil = Hagerstown Silty Loam
a, • — 0% Acetone by Volume
b, a - I 0% Acetone by Volume
c,o - 30% Acetone by Volume
d,0 — 40% Acetone by Volume
e, ~ - 50% Acetone by Volume
'b
.20 -
5 -
H .10 -
.5 -
0 20 40 60 80 100
SOLUTE EQUILIBRIUM CONCENTRATION,Ceq[mg/.£]
a. S = 0.0020 +0.0080 Ceq R2 = 98.8%
b. S = -0.0205 + 0.0047 Ceq R2=93.2%
c. S = -0.0 109 + 0.0018 Ceq R2 = 84,7%
d. S = 0.00 I 2 + 0.00 II Ceq R2*82.0%
e. S s 0.000 I+0.0005 Ceq R2=93.2%
-------
153
Figure 5-3: Naphthol Sorption in Methanol/Water Mixtures
Adsorption Isotherm* Naphthol
Methanol / Water Systerns
Solute = Naphthol
Solvent* Methanol/Water
Soil = Hagerstown Silty Loam
a, • - 0% Methanol by Volume
b, a — 20% Methanol by Volume
c, o — 50% Methanol by Volume
0 1 1 1 1
0 20 40 60 80 I00
SOLUTE EQUILIBRIUM CONCENTRATION,Ceq[mg/i]
a. S = 0.793 + 0.0074 Ceq R2=96.7%
b. S« 0.683 + 0.0047 Ceq R2=98.3%
c. S = 0.496 +0.00 I 4 Ceq R2=83.3%
-------
154
Figure 5-4: Quinoline Sorption in Methanol/Water Mixtures
Adsorption Isotherm: Quinoline
Methanol/Water Systems
Solute: Quinoline
Solvent: Methanol/Water
Soil: Hagerstpwn Silty Loa
a, • - 0%Methanol by
Volume
b, a -20% Methanol
by Volume
c, ~ - 50% Methanol
by Volume
200 400 600 800 1000
SOLUTE EQUILIBRIUM CONCENTRATION,Ceq[mg/j,]
a. S * 0. 3 5 2 + 0.004 3 Ceq R2 s 9 5.8%
b. S s 0. 14 7+ 0.0025 Ceq R2 s 97.3%
c.SsO. Ill +O.OOI4Ceq R*s92.0%
-------
155
Figure 5-5: 3,5-Dichloroaniljne Sorption in Methanol/Water Mixtures
."35
.30
I -25
.20
.15
.10
.5
Adsorption Isotherm : 3.5Dichioroaniline
Methanol / Water Systems
Solute: 3.5 Dichioroaniline
Solvent: Methanol/Water
Soil : Hagerstown Silty Loam
a, • - 0% Methanol by Volume
b, a - 20% Methanol by Volume
c, ° - 50% Methanol by Volume
0 200 400 600 800 1000
SOLUTE EQUILIBRIUM CONCENTRATION, Ceq [ mg/1]
a. S = 0.0921 +0.0025 Ceq R =96.5%
b. S = 0.0151 +0.00 I 3 Ceq
c. S = 0.0094+0.0005 Ceq
R =90.4%
R =93.8%
-------
156
Figure 5-6: Naphthalene'Sorption onto Hagerstown Silt Loam
in Methanol/Water and Acetone/Water Mixtures
tO LU
JO
i
E
o
o
_l
c
>>
a>
¦*—
>
o
CO
C/5
c
k_
5
o
o
*-
o
CO
Q_
i_
0)
cn
o>
c
o
—
X
cz
c
o
o
c
o
c
o
o
'JZ
a;
Q.
(0
k_
o
o
x:
CL
"O
<
V)
3
3
o
cr
.c
<
*—
JO
Cl
a
z
[ i (OS 6/9in|OS Boi ] S 'AllOVdVO NOIldUOSOV
-------
157
Methanol and acetone were used to evaluate the solvent effect on
solute sorption characteristics on Hagerstown silt loam. Sorption isotherms
with methanol/water mixtures were developed for four solutes (naphthalene,
naphthol, quinoline, and 3,5-dichloroaniline), and sorption isotherms with
acetone/water mixtures were developed for naphthalene. Figures 5-1 to 5-5
show sorption partition coefficients obtained at various volume fraction
solvent for the five solute-solvent/water systems investigated in this study,
where the results are plotted as sorption capacity [mg solute sorbed/g soil]
versus equilibrium concentration [mg/l]. These results show that a linear
sorption isotherm can be used to describe the sorption of organic solute
onto soils with the various solvent/water mixtures. In these five systems,
the sorption partition coefficient decreased significantly with increase in
solvent volume content. For example, sorption partition coefficient for the
naphthalene-methanol/water system is 8.0 l/kg for 0% methanol, 4.0 l/kg for
20% methanol, 1.8 l/kg for 40% methanol, and 0.5 l/kg for 50% methanol.
Similar results were observed for the other four solvent/water systems as
summarized in Table 5-4.
Figure 5-7 shows sorption partition coefficient as a function of volume
fraction of solvent for naphthalene sorption onto Hagerstown silt loam where
the aqueous phase contains methanol or acetone as solvent. In general, the
sorption partition coefficient is observed to decrease semi-logarithmically
with increased solvent volume fraction. Similar phenomena were observed
for naphthol, quinoline, and 3,5-dichloroaniline sorption onto Hagerstown silt
loam in methanol/water systems, as illustrated in Figure 5-8.
The effect of solvent on organic solute sorption partitioning may be
explained by invoking Equation 5-20. The a value in this equation was
obtained by regressing solute mole fraction solubility against volume fraction
of solvent. The results of this analysis gave the following a values: 3.79 for
naphthalene-methanol/water systems; 5.14 for naphthalene-acetone/water
systems; 3.01 for naphthol-methanol/water systems; 2.86 for quinoline-
-------
158
Table 5-4: Sorption Partition Coefficients for
Solvent/Water Mixtures
Hagerstown Silt Loam
Berkeley Silt Loam
Naphthalene-Methanol/Water
Methanol
[% vol.]
0
20
40
50
Naphthalene-Acetone/Water
Acetone
[% vol.]
0
10
30
40
50
K
[l/kg]
8.0
4.0
1.8
0.7
K
[f/kg]
8.0
4.7
1.8
1.1
0.5
Naphthalene-Methanol/Water
Methanol K
[% vol.]
0
20
Tifton Sand
[l/kg]
8.1
4.0
Naphthalene-Methanol/Water
Methanol
[% vol.]
0
20
[l/kg]
2.0
1.0
Naphthol-Methanol/Water
Methanol
[% vol.]
0
20
50
Kp
[l/kg]
7.4
4.1
1.4
Quinoline-Methanol/Water
Methanol
[% vol.]
0
20
50
K
[l/kg]
4.3
2.5
1.4
3,5-Dichloroaniline-Methanol/Water
Methanol
[% vol.]
0
20
50
Kp
[f/kg]
2.5
1.3
0.5
-------
159
Solvent Effect on Sorption Partition Coefficient
for Naphthalene-Methanol/Water Systems
X.
Naphthalene Adsorption onto Soil
with Aqueous Phase containing
Polar Solvent
Solute = Naphthalene
Solvent = Methanol /Water,
Acetone / Water
Soil= Hagerstown Silty Loam
l i i i
0 IO 20 30 40 50
SOLVENT CONTENT [% by Volume]
-------
Figure 5-8:
160
Solvent Effect on Solute Sorption Partition Coefficient
for MethanoI/Water Systems
8.0
Organic Solute Adsorption onto Soil with
Aqueous Phase Containing Methanol
5.0
o>
Naphtho
^ 3.0
Quinoline
o
3.5- Dichloroaniline
- Solvent: Methanol/Water
Soil: Hagerstown Silty Loam
0.3
0.2
20
30
fO
40
50
0
SOLVENT CONTENT [% by Volume]
-------
161
methanol/water systems, an'd 2.98 for 3,5-dichloroaniline-methanol/water
systems. These values are slightly different than those which are obtained
from regressing mass concentration solute solubility against volume fraction
solvent as was shown in Figures 2-19 and 2-20. Equation 5-20 was examined
using experimental sorption data for the seven systems investigated in this
study in conjunction with the respective a values. The observed a values for
these seven systems are presented in Table 5-5. This evaluation showed that
the a values are in the range of 0.33 to 0.56. The average a value was 0.44
with a standard deviation of 0.053.
The range of observed a values are significantly less than unity, as
well as uniformly less than the range of 0.7 to 0.9 as found by Karickhoff
(1984) for solute sorption onto soil/sediment for solvent-free systems. This
implies for a given solvent/water mixture, that the decrease of sorption
partition coefficient is not as significant as increase in solute solubility.
Further, the range of a values suggest that the logarithmic decrease in Kp is
less than half the logarithmic increase of solute solubility in a solvent/water
mixture. This is shown also in Table 5-6 by comparison of a and a values
for sorption onto Hagerstown silt loam.
The findings presented herein suggest that organic solute sorption onto
soil can be affected by organic solvent present in the aqueous phase.
Sorption partition coefficients observed in the laboratory isotherm studies are
semi-logarithmically inversely related to the volume fraction of solvent for
the systems reported in this study. The solvent effect can be quantified, and
an estimate of the partition coefficient can be developed from knowledge of
solvent volume fraction, the power-term for the semi-logarithmic solubility
expression and an average value of the regression-fitted parameter a.
-------
162
Table 5-5: Calculated a Values
Solute
Solvent
Solvent
[% vol.]
Kp
[f/mg]
Haqerstown Silt Loam
Naphthalene Methanol
Naphthol
Quinoline
Acetone
Methanol
Methanol
3,5-Oichloroaniline Methanol
Berkeley Silt Loam
Naphthalene Methanol
Tifton Sand
Naphthalene Methanol
Average a ¦ 0.44
0
20
40
50
10
30
40
50
0
20
50
0
20
50
0
20
50
0
20
20
8
4.0
1.8
0.7
4.7
1.8
1.1
0.5
7.4
4.7
1.4
4.3
2.5
1.4
2.5
1.3
0.5
8.1
4.1
2.0
1.0
0.40
0.43
0.56
0.45
0.42
0.42
0.47
0.33
0.48
0.41
0.44
0.48
0.48
0.40
0.40
Standard deviation « 0.053
-------
163
Table 5-6: Effect of Solvent on Solute Solubility and
Sorption Partition Coefficient for
Hagerstown Silt Loam
Solute Solvent a* a aa"
Naphthalene
Naphthalene
Naphthol
Quinoline
3,5-Dichloroaniline
Methanol 3.79
Acetone 5.14
Methanol 3.01
Methanol 2.86
Methanol 2.96
0.47 1.78
0.44 2.26
0.41 1.23
0.39 1.12
0.48 1.42
* Logarithmic increase in mole fraction solute solubility with
volume fraction solvent
## Logarithmic increase in sorption partition coefficient with
volume fraction solvent
-------
164
Effect of Organic Carbon Content
The sorption partition coefficients. K,. fo, naphthalene sorption onto
tnree soils, Hagerstown silt loan, IOC < 1.94%). Berkeley sll. loam (OC •
2 81%), and Tifton sand (OC - 0.5%), were determined. The sorption isotherm
experiments were performed as described previously with the samples being
determined in triplicate and analyzed by HPLC. The liquid phase contained
either 0% methanol or 20% by volume methanol, Figures 5-9 and 5-10 show
the results for naphtha.ene sorption omo Berkeley .lit loam and Tlfton sand
respectively.
Linear least-square regression was performed on the data for these
systems and a trend of increasing sorption partition coefficient with
increasing sorbent organic carbon content was observed for the pure water
systems: K for Tifton sand IOC ¦ 0.5%), Hagerstown silt loam (OC * 1.94*).
and Berkeley silt loam (OC ' 2.85%) were 2.0 l/kg, 8.0 l/kg and 8.1 l/kg
respectively. These data were incorporated in the relationship between K .
and K as shown in Equation 5-23. The trend of increasing values of K
with Increasing OC was also evident in tests with 20% by volume
methanol/water mixtures, where K, values for Tifton sand. Hagerstown .lit
loam and Berkeley silt loam were 1.0 l/kg. 4.0 l/kg and 4.4 llkg respectively.
These results are plotted in Figure 5-11. Linear least-square regression w„
performed for the naphthalene sorption partition coefficients for the three
soils in two different solvent-water combinations (0% and 20% methanol)
vLus the organic carbon content of the sorbents. These results .re shown
e 19 The * values for sorption of naphthalene in Berkeley silt
in Figure 5-12. »no a
loam and Tifton sand are calculated as 0.40 and 0.40 respectively. M
, v.. c c The limited data suggest that sorption partition
reported in Table o a.
in orooortion to the sorbent organic carbon content for
coefficient increases in propom
solvent/water systems.
-------
165
Figure 5-9: Naphthalene Sorption onto Berkeley silt loam
in Methanol/Water Mixtures
.35
.3 0
o .25
.20
.10
Adsorption Isotherm = Naphthalene -
Methanol/Water Systems
Solute = Naphthalene
Solvent2 Methanol/Water
Soil = Berkley Silty Loam
- 0% Methanol by Volume
b, a - 20% Methanol by Volume
0 20 40 60 80 100
SOLUTE EQUILIBRIUM CONCENTRATION, Ceq [mg/i]
a. S * 0.0052 +0.0085 Ceq R2=95.3%
b. S - 0.01 11 + 0.004 4 Ceq R2=94.2%
-------
166
Figure 5-10: Naphthalene Sorption onto Tifton silt loam
in Methanol/Water Mixtures
.35
o
.3 0
a>
3
O
.25
CO
o>
E
CO
.20
«k
>
a
<
.15
CL
<
O
z
.10
o
H
a.
01
o
.5
CO
o
<
Adsorption Isotherm = Naphthalene'
Methanol/ Water Systems
Solute = Naphthalene
Solvent3 Methanol/Water
Soil = Tifton Sandy Loam
a, • - 0% Methanol by Volume
b, a - 20% Methanol by Volume
-q 20 40 60 80 I00
SOLUTE EQUILIBRIUM CONCENTRATION,Ceq[mg/I]
a. S * 0.00I3 + 0.0020 Ceq R2*87.7%
b. S s 0.0049 + O.OOIO Ceq R2=96.0%
-------
167
Figure 5-11: Naphthalene Sorption onto Soils in Methanol/Water Mixtures
o o
CO CO
Vp
E
O"
>s ^
o
o
•*-
&
_l
fs
• —
•
Is
CO
—
0
c
II
in
5
o
CO
CO
o
o
>%
OJ
V)
"—¦
a>
n
E
(J
cn
o
l_
o
o
a>
o
X
_l
aa
o
it
o
CO
•[ MOS 6/a;n|OS 5uj ] s 'AllOVdVO NOIldaOSQV
-------
168
Figure 5-12: Sorbent Organic Carbon Content Effect on
Naphthalene Sorption onto Soils in Methanol/Water Mixtures
o>
X.
Q.
LlJ
O
u.
u_
LlI
O
O
Z
o
ce
<
CL
z
o
I-
Q-
£T
O
to
O
<
Naphthalene Adsorption Coefficients for
Soils of Varying Organic Carbon Content
• Solute = Naphthalene
Solvent = Methanol / Water
Soil = Hagerstown Silty Loam
(O.C. = 1.94%)
Berkley Silty Loam
(O.C. = 2.85%) and .
Tifton Sandy Loam
(O.C. = 0.5%)
• -0% Methanol by Volume
a - 20% Methanol by Volume
_L
0 I 2 •
ORGANIC CARBON CONTENT, O.C. [%]
-------
169
The Effect of Solvent on Soil' Organic Carbon
Results in Chapter Four explained the effect of solvent/water mixtures
on aromatic solute solubility. Results in this chapter have shown how the
presence of solvent in the aqueous phase affects partitioning onto soil. A
conclusion from this investigation is that the semi-logarithmic decrease in
sorption coefficient with increase solvent volume fraction is about half of
that which would be predicted on the basis of semi-logarithmic increase in
mole fraction solubility. An explanation for this phenomena requires
understanding of the effect of polar solvent on natural organic carbon of
soils.
Freeman and Cheung (1981) explain that the organic carbon in
soils/sediments may be envisioned as nonpolar polymeric material, referred
to as humin or kerogen, which is chemically bound to the mineral matter.
The polymeric material is thought to be highly branched and cross linked to
form a three dimensional network. These properties prevent the organic
matter from dissolving into water, although liquid may be absorbed, or
imbibed. The absorption of liquid would be accompanied by the network
swelling to form a gel. The amount of gel swelling depends on the
"network compatibility" with the liquid, and the maximum gel swelling is
dependent on the extent of cross linkage. Solute preference for either the
solution phase or cross linked organic carbon phase depends on competing
attractive effects between solute-liquid and solute-gel interactions. Gel
swelling is expected to increase as the Hildebrand solubility parameter for
the liquid approaches that for the organic carbon gel, which is estimated on
the basis of correlations between K and K to have S ** 10.3. These
P OW
concepts were evaluated by Freeman and Cheung (1981) through liquid
chromatographic experiments with columns packed with sediment and soil.
This type of phenomenon was also studied by Wending and Yen (1980) who
evaluated the swelling of coal with several solvents and solvent/water
mixtures. Freeman and Cheung concluded from their work, and the work of
-------
170
Wending and Yen. that soil cross-linked polymer was not readily soluble in
solvent, but that solvent causes it to swell. It was suggested that solute
diffusion through the swollen gel should be more effective than that through
the more densely entangled structure of an incompletely swollen gel.
The sorption experiments described in this chapter were performed with
liquid phase having solubility parameters that ranged from 23.60 (100% water)
to 19.31 (50% by volume methanol/water) and 16.71 (50% by volume
acetone/water). On the basis of the results reported by Freeman and Cheung,
it is expected that the organic matter In soil would increase in swelling with
decrease in liquid phase solubility parameter. This would result in greater
accessibility of the solute to the humin-kerogen polymers in the presence of
solvent/water mixtures. This phenomenon would then exert a competing
effect that may enhance sorption in contrast to increased solute solubility
effects. It Is concluded from experimental results reported in this chapter
that this phenomenon may account for the observation that decrease in
sorption partition coefficient is less than that predicted from consideration of
only solute solubility effects.
Summary
The sorptive behavior of four aromatic solutes onto three different
soils with solvent/water mixtures was studied. The sorption isotherm data
showed a linear relationship between equilibrium concentration and sorption
capacity for systems containing only solute and water, as well as for
systems containing solute In solvent/water mixtures.
The effect of polar solvent in the aqueous phase on aromatic solute
sorptive behavior was evaluated, and it was observed that the sorption
partition coefficients decreased seml-logarithmically with increase In volume
fraction of solvent in the aqueous phase. The results were interpreted by .
theory which related the relative magnitude of decrease of sorption partition
coefficient to the Increase in solute solubility for misclble solvent/water
-------
171
systems. This entailed estimating or measuring the effect of polar solvent
(methanol or acetone) on solute solubility and sorbent sorptive behavior.
These results were expressed in terms of the parameter a which is the
logarithmic term with which solute solubility increases with volume fraction
solvent in water, and the value of aa which is the logarithmic term with
which sorbent sorption coefficient decreases with volume fraction solvent in
water. It was observed that the parameter a was typically in the range of
0.4 to 0.5. This suggests that the semi-logarithmic manner with which
sorption partition coefficient decreases with solvent volume fraction is less
than the semi-logarithmic manner with which solute solubility increases with
solvent volume fraction. The magnitude of the a values show that the
logarithmic decrease of sorption partition coefficient is about half of that
which could be expected on the basis of the logarithmic increase in solute
solubility in the solvent/water mixtures. This may be a result of the
solvent/water mixture interacting with natural soil organic carbon and swelling
the organic carbon associated with the soil, and thereby increasing solute
accessibility to the organic matter. It was shown that the more hydrophobic
the soulte, the greater the effect of solvent in solvent/water mixtures on
solute solubility enhancement, and hence the less the tendency to sorb onto
soil. Thus the results of this investigation are particularly significant for
those aromatic solutes exhibiting lowest aqueous phase solubility.
-------
172
Chapter 6
SUMMARY AND CONCLUSION
Summary
This report presented results of an Investigation to evaluate the
solubility of relatively hydrophobic aromatic solutes in an aqueous phase
contains mlscible polar organic solvent, and to determine the effect of
polar solvent In the aqueous phase on sorption of aromatic solutes onto
soils. The investigation was comprised of both theoretical and experiment*
developments. The results from the solubility experiments were interpreted
by means of chemical thermodynamic models to predict solute solubility ,n
solvent/water systems, and the results of the soil sorption studies were
evaluated by a model that related reduction in sorption coefficient with
increase in solubility.
The subject of aromatic solute solubilization and sorption in miscible
solvent/water systems is important for understanding pollutant chemical end
physical properties in heavily contaminated industrial wastewaters and in
hazardous wastes. These types of wastewaters and wastes may contain
appreciable quantities of polar organic solvents which can affect physico-
chemical properties of aromatic solutes Including solubility and phase
partitioning.
The phenomenon of aromatic solute solubility in solvent/water systems
was evaluated for eighteen systems. This included four types of
solvent/water mixtures end seven solutes. The phenomenon of ph.„
partitioning in solvent/water systems was evaluated for aromatic solu,.
-------
173
sorption onto soil. This' entailed batch sorption experiments with
methanol/water and acetone/water mixtures with four aromatic solutes and
three soils. The soil sorption studies are useful for understanding some
aspects of near-source groundwater contamination problems, as in situations
for which the release hydrophobic organic contaminant from spill or other
discharge may be accompanied by the release of water-soluble organic
solvents. In these instances, the process of solubilization, sorption and
transport of hydrophobic organic solutes may be influenced strongly by the
presence of comparatively high concentrations of miscible solvent.
The aromatic solutes employed for study of solubility in solvent/water
systems were selected to represent different physico-chemical properties with
respect to hydrophobicity, polarity, hydrogen bonding and functional group
substitution. The solutes ranged in aqueous solubility from about 1 mg/l for
phenanthrene to 34,100 mg/l for aniline. The studies showed that the
presence of appreciable (i.e. percent by volume) concentration of organic
solvent in the aqueous phase can have a very large effect on solubility. In
general it was observed that there was a semi-logarithmic increase in
solubility with increasing solvent volume fraction. This confirmed a trend
predicted from adaptation of regular solution theory wherein logarithmic mole
fraction solubility is proportional to solvent volume fraction. The prediction
holds for systems for which the solubility parameter of the solute is
approximately three units less than that for the solvent. This log-linear
approach was the most easily applied of the various techniques which were
developed to predict solubility. However, application of the log-linear model
requires at least two data points, preferably solubility in pure water and
solubility in 50% or 100% pure solvent. While aqueous solubility is
commonly available for many aromatic solutes, relatively little information
exists on solubility of aromatic compounds in various solvents. If solvent
solubility data are lacking, then solubility in solvent may be estimated from
prediction of solute infinite dilution activity coefficient as discussed below.
-------
174
The UNIFAC solution-of-groups model was shown to be useful for
predicting solute Infinite dilution activity coefficients in solvent/water
mixtures. The Infinite dilution activity coefficient could then be related to
solute solubility through several techniques depending on the value of the
activity coefficient and on whether the solute exists as a solid or liquid at
the system temperature. This approach was unique among the various
predictive techniques in that it did not require specific measurements to
obtain correlation coefficients or other parameters. The procedure employs a
solution-of-groups concept for which the activity coefficient is estimated
from surface area and interection parameters available in the literature, plus
specification of the mole fraction solvent composition and the functional
groups comprising the solute, solvent and water. This procedure predicted
solute solubility in pure water and in 100% solvent within a factor of two
for a range of solute solubilities spanning approximately six orders of
magnitude. The standard deviation of the error for prediction of solute
solubility in the various eighteen solvent/water systems was 109%. It was
concluded that this approach is a versatile and generally applicable technique
for predicting solute solubility in solvent/water systems. However. It needs
to be evaluated for systems containing functional groups not considered In
this study; also, it is limited In that interaction parameters are available for
only certain systems.
If the solute functional group interaction parameters are not available In
the UNIFAC data base, then an excess free energy approach is useful for
estimating solute solubility. This technique requires knowledge of solvent-
water Interaction constants, which may be estimated from prediction of
solute free-solvent/water activity coefficients. The technique also requires
knowledge of a solute interaction constant which may be obtained from
correlation of experimental data with solute octanol/water partition
coefficient. The excess free energy model accounted for some of the
variation in the experimental data from a log-linear relationship. The standard
deviation of the error for prediction with the eighteen solute-solventfwater
-------
175
systems was 97.6%. The excess free energy approach was computationally
more cumbersome than either the log-linear approach or the approach based
on estimation of infinite dilution activity coefficient. Also, it required the
use of an empirical correlation. For these reasons it is not preferred if
either of the other two approaches may be employed.
A molecular surface area technique was shown to predict solute
solubility with a standard deviation of error of about 60% for one solute-
solvent/water system. This technique is based on consideration of
hydrophobic surface area (HSA) and polar surface area (PSA) of the solute,
and interfacial free energy terms for water and solvent. At present, this
approach is limited because in the absence of experimental data, the
proportion of solute total surface area attributable to HSA and PSA is not
generally known, and because of the lack of information on the interfacial
energy terms for all but a few solvents.
The sorptive behavior of four aromatic solutes onto three different
soils with miscible solvent/water mixtures was studied. The sorption
isotherm data showed a linear relationship between equilibrium concentration
and sorption capacity for systems containing solvent/water mixtures in the
liquid phase. It was observed that the sorption partition coefficients
decreased semi-logarithmically with increase of volume fraction of solvent in
the aqueous phase. These results were interpreted by a theory which related
the relative magnitude of decrease of sorption partition coefficient to
increase in solute solubility. This entailed estimating or measuring the effect
of polar solvent (methanol or acetone) on solute solubility and solute
sorptive behavior. The results were expressed in terms of the parameter «r
which is the logarithmic term with which solute solubility increases with
volume fraction solvent in water, and the value of aa which is the
logarithmic term with which solute sorption partition coefficient decreases
with volume fraction solvent in water. It was observed that the parameter a
was typically in the range of 0.4 to 0.5. This suggests that the semi-
-------
176
logarithmic manner with which sorption partition coefficient decreases is less
of a consequence than the semi-logarithmic manner with which solute
solubility increases with solvent volume fraction. The magnitude of the «
values shows that the logarithmic change of sorption partition coefficient
decrease is about half of that which would be expected on the basis of the
logarithmic increase in solute solubility in the solvent/water mixtures. This
may be a result of the solvent/water mixture interacting with natural soil
organic carbon and swelling the organic carbon associated with the soil,
thereby increasing solute accessibility to the organic matter.
It was shown that the more hydrophobic the solute, the greater the
effect of the solvent in water on solubility enhancement with concomitant
decrease in soil sorption partition coefficient. Hence, the results of this
investigation are particularly significant for predicting physico-chemical and
soil sorption characteristics for those aromatic pollutants that exhibit lowest
aqueous solubility.
Conclusion
Hydrophobic aromatic solutes display a semi-logarithmic increase in
solubility with Increasing volume fraction o( solvent in solvent/water
mixtures. This results in a semi-logarithmic decrease in tendency for these
solutes to sorb onto soil. The increase in solubility does not result in a
directly proportional decrease In sorption coefficient for the solutes studied
in this Investigation. The increase in solubility In solvent/water mixtures end
the decrease in sorption partitioning coefficients may be predicted by
thermodynamic models. This information is useful for accessing near-source
transport of hydrophobic aromatic solutes in soil systems in the event of
spill or discharge of hydrophobic solutes with polar solvent. The predictive
techniques developed in this investigation may be useful in other applications
in environmental engineering, such as for estimation of aromatic solute
solubility in heavily contaminated Industrial wastewaters, or fo, evaluation of
solute properties for use in analytical procedures.
-------
177
REFERENCES
Abrams D.S., and J.M. Prausnitz, 1975, "Statistical Thermodynamics of Liquid
Mixtures: A New Expression for the Excess Free Energy of Partly or
Completely Miscible Systems," AlChE Journal, Vol. 21, No. 1, P. 116-128.
Allison, L.E., 1965, "Organic Carbon," in "Methods of Soi/ Analysis, Part II:
Chemical and Microbiological Properties," Editor-in-Chief, C.A. Black,
American Society of Agronomy, Inc., Madison, Wl.
Anderson, F.E., 1983, "Supplement to Program UNIFAC," 3rd revision, Dept. of
Chemical Engineering, Univ. of California, Berkeley, CA.
Arbuckle, W.B., 1983, "Estimating Activity Coefficients for Use in Calculating
Environmental Parameters," Environ. Sci. & Techno!., Vol. 17, No. 9, p.
537-542.
Banerjee, S., 1984, "Solubility of Organic Mixtures in Water," Environ. Sci. &
Techno/., Vol. 18, p. 587-591.
Briggs, G.G., 1973, "A Simple Relationship Between Soils Adsorption of
Organic Chemicals and Their Octanol/Water Partition Coefficients."
proceedings 7th British Insecticide and Fungicide Conference, Nov. 1973,
p. 83-86.
Campbell, J.R. and R.G. Luthy, 1985, "Prediction of Aromatic Solute Partition
Coefficients Using the UNIFAC Group Contribution Model," to appear in
Environ. Sci. & Technol.
Campbell, J.R., R.G. Luthy, and Carrondo, M.J.T., 1983, "Measurement and
Prediction of Distribution Coefficients for Wastewater Aromatic Solutes,"
Environ. Sci. & Technol., Vol. 17, No. 10, p. 582-590.
Casagrande, A., 1948, "Classification and Identification of Soils," ASCE Trans.,
Vol. 113, p. 401.
-------
178
Chertkoff M.J., and A.N. Martin, 1960, "The Solubility of Benzoic Acid in
Mixed Solvents," J. Am. Pharma. Assoc., Sci. Ed., Vol. 49, No. 7,
p. 444-447.
Chiou, C.T., I I. Peters and V.H. Freed, 1979, "A Physical Concept of Soil-
Water Equilibria for Nonionic Organic Compounds," Science, Vol. 206, p.
831-832.
Chiou, C.T., D.W. Schmedding, and M. Manes, 1982, " Partitioning of Organic
Compounds in Octanol-Water Systems," Environ. Sci. & Techno!., Vol. 16,
No. 1, p. 4-10.
Chiou, C.T., P.E. Porter, and D.W. Schmedding, 1983, "Partition Equilibria of
Nonionic Organic Compounds Between Soil Organic Matter and Water,"
Enviorn. Sci. & Techno!., Vol. 17, p. 227-231.
Council on Environmental Quality, 1980, "Environmental Quality - 1980."
Eleventh Annual Report of the Council on Environmental Quality,
- - m
Washington, D.C.
Di Tore D M. and L.M. Hor2empa. 1982, "Reversible and Resistant Components
of PCB Adsorption - Desorption: Isotherms," Environ. So,. * Techno,.. Vol.
16, p. 594-602.
Dean, J. . . ... r p
Aromatic Hydrocarbons on Soils." So,I Sc., Vol. 137. No. 5, P. 308.
a nonrv 1977 "Waste Disposal Practices and Their
Environmental to Congress, U.S. EPA, Washington, D.C.
Effects on Groundwater,
-------
179
Environmental Protection Agency, 1980, "Proposed Groundwater Protection
Strategy," U.S. EPA, Office of Drinking Water, Washington, D.C.
Flory, P.J., 1965, "Statistical Thermodynamics of Liquid Mixtures," J. Amer.
Chem. Soc., Vol. 87, No. 9, p. 1833-1965.
Fredenslund, A., R.L. Jones and J.M. Prausnitz, 1975, "Group Contribution
Estimation of Activity Coefficients in Nonideal Liquid Mixtures," AlChE
Journal, Vol. 21, No. 6, p. 1086-1099.
Freeman, D.H. and L.S. Cheung, 1981, "A Gel Partition Model for Organic
Desorption from a Pond Sediment," Science, Vol. 214, p. 790-792.
Fu, J.K, R.G. Luthy, and D.A. Dzombak, 1983, "Adsorption of Polycyclic
Aromatic Hydrocarbon Compounds onto Soil and Transport of Naphthalene
in Unsaturated Porous Media," Report to U.S. Dept. of Energy, Morgantown
Energy Technology Center, West Virginia.
Gmehling, J.G., P. Rasmussen and A. Fredenslund, 1982, "Vapor-Liquid
Equilibria by UNIFAC Group Contribution, Revision and Extension 2," Ind.
Eng. Chem. Process., Des. Dev., Vol. 21, p. 118-127.
Gmehling, J.G., T.F. Anderson and J.M. Prausnitz, 1978, "Solid-Liquid Equilibria
Using UNIFAC," Ind. Eng. Chem., Fundam., Vol. 17, No. 4, p. 269-273.
Grain, C.F., 1982, "Activity Coefficients" in "Handbook of Chemical Property
Estimation Methods," Eds. W.J. Lyman, W.F. Reehl and D.H. Rosenblatt,
McGraw-Hill Book Company, New York, NY.
Hansch, C. and A.J. Leo, 1979, "Substituent Constants for Correlation Analysis
in Chemistry and Biology," John Wiley & Sons, New York, NY.
Hansen, C.M. 1967 a,b, "Three Dimensional Solubility Parameter - Key to Paint
Component Affinities: I and II," J. of Paint Techno!., Vol. 59, p. 105 and
p. 505-510.
Hansen, C.M. and K. Skaarup, 1967, "Three Dimensional Solubility Parameter -
Key to Paint Component Affinities: III, Independent Calculation of the
Parameter Components," J. of Paint Technol., Vol. 59, p. 511-514.
Hansen, C.M., 1969, "The Universality of the Solubility Parameter," Ind. Eng.
Chem., Res. and Dev., Vol. 8, No.1, p. 2-11.
-------
180
Hassett. J.J.. W.L. Banwart. S.G. Wood and J.C. Means, 1981. "Sorption of
a-Naphthol: Implications Concerning in the Limits of Hydrophobic
Sorption," Soif Sci. Soc. Am. J., Vol.45, p. 38-42.
Hamaker, J.W. and J.M. Thompson, 1972, "Adsorption" in "Organic Chemicals
in the Soil Environment." Vol.1, edited by C.A.I. Goring and J.W. Hamaker,
Marcel-Dekker. New York, NY.
Hildebrand, J.H.. 1936, "Solubility of Non-electrolytes." Reinhold Publishing
Company, New York, NY.
Hildebrand. J.H.. J.M. Prausnitz. and R.L. Scott. 1970. "Regular and Related
Solutions." Von Nostrand Reinhold Company. New York. NY.
Hildebrand. J.H. and R.L. Scott, 1950. "The Solubility of Nonelectrolytes." 3rd
ed., Reinhold Publishing Company, New York. NY.
Johnson. A.I. and C.J. Huang, 1955, "Estimation of Heat Capacities of Organic
Liquids," Canadian Journal of Technology. Vol. 53. p. 421-425.
Karger. B.L., L.R. Snyder and C. Eon, 1976, "An Expanded Solubility Parameter
Treatment for Classification and Use of Chromatographic Solvents and
Adsorbents: Parameters for Dispersion, Dipole and Hydrogen Bonding
Interactions," J. of Chromatography. Vol. 125, p. 71-88.
Karger, B.L., L.R. Snyder and C. Eon. 1978. "Expanded Solubility Parameter
Treatment for Classification and Use of Chromatographic Solvents and
Adsorbents," Analytical Chemistry, Vol. 50, No. 18. p. 2126-2136.
Karickhoff, S.W., D.S. Brown, and T.A. Scott, 1979, "Sorption of Hydrophobic
Pollutants on Natural Sediments." Water Research. Vol. 13. p. 241-248.
Karickhoff. S.W., 1981. "Semi-Empirical Estimation of Sorption of Hydrophobic
Pollutants on Natural Sediments and Soils," Chemosphere. Vol. 10. No. 8. p.
833-846.
Karickhoff, S.W., 1984, "Organic Pollutant Sorption in Aquatic Systems." J. of
hydraulic Engineering, ASCC, Vol. 110. No. 6. p. 707-735.
Lambe, T.W., 1951. "So" Testing tor engineers." John Wiley & Sons. Inc..
New York, NY.
-------
181
Lambert, S.M., P.E. Porter and H Schieferstein, 1965, "Movement and Sorption
of Chemicals Applied to the Soil," Weeds, Vol. 13, p. 185-190.
Lambert, S.M., 1967, "Functional Relationship Between Sorption in Soil and
Chemical Structure," J. Agri. Food Chem., Vol. 15, No. 4, p. 572-576.
Langmuir, I., 1925, "The Distribution and Orientation of Molecules," Third
Colloid Symposium Monograph, The Chemical Catalog Company, Inc., New
York. NY.
Lindstrom, R.E., 1979, "Solubility in Amide-Water Cosolvent Systems II:
Cosolvent Excess at Solvent Surface," J. Pharma. Sci., Vol. 68, No.9, p.
1141-1143.
Lyman. W.J., 1982 "Solubility in Various Solvents," in "Handbook of Chemical
Property Estimation Methods," Eds. W.J. Lyman, W.F. Reehl, and D.H.
Rosenblatt, McGraw-Hill Book Company, New York, NY.
MacKay, D., 1977, correspondence, Environ. Sci. & Techno/., Vol. 11, No. 13,
p. 1219.
MacKay, D., and W.Y. Shiu, 1977, "Aqueous Solubility of Polynuclear Aromatic
Hydrocarbons," J. of Chemical and Engineering Data, Vol. 22, No. 4, p.
399-402.
MacKay, D., 1979, "Finding Fugacity Feasible," Environ. Sci. & Techno!., Vol. 3,
No. 10, p. 1218-1223.
Mackay, D., W.Y. Shiu, A. Bobra, J. Billington, E.Chau, A. Yeun, C.Ng, and
F. Szeto, "Volatilization of Organic Pollutants from Water," Report to U.S.
EPS, Report No.600/3-82-019.
Martin, A., P.L. Wu, A. Adjei, A. Beerbower and J.M. Prausnitz, 1981,
"Extended Hasen Solubility Approach: Naphthalene in Individual Solvents,"
J. of Pharma. Sci., Vol. 70, No. 11, p. 1260-1264.
Martin, A., P.L. Wu, A. Adjei, R.E. Lindstrom and P.H. Elworthy, 1982a, ,"
Extended Hildebrand Solubility Approach and the Log-linear Solubility
Equation," J. of Pharma. Sci., Vol. 71, No 8, p. 849-856.
Martin, A., P.L. Wu, A.Adjei, M. Mehdizadeh, K.C. James, and C. Metzler,
-------
182
1982b "Extended Hildebrand Solubility Approach: Testosterone and
Testosterone Propionate in Binary Solvents," J. Pharma. Set.. Vol. 71. No.
12, p. 1334-1340.
Mccarty. P.L., M. Reinhard, and B.E. Rittmann, 1981. "Trace Organics in
Groundwater," Emiorn. Sci. & Techno!.. Vol. 15, No. 1, p. 40-51.
Means J.C.. J.I. Hasselt, S.G. Wood, and W.L. Banwart. 1979. "Sorption
Properties of Energy-Related Pollutants and Sediments," in "Polynuclear
Aromatic Hydrocarbons." edited by P.W. Jones and D. Leber. Ann Arbo,
Science, Ann Arbor, Michigan.
Means. J.C., S.G. Wood. J.J. Hassett and W.L. Banwart, 1980. "Sorption of
Polynuclear Aromatic Hydrocarbons by Sediments and Soils." Environ.
Sci. & Techno!., Vol. 14. No. 12, p. 1524-1528.
Neely WB. and D. MacKay. 1982. "Evaluative Model for Estimating
Environmental Fate." in "Modelling the Fate of Chemicals In the Aquatic
Environment," Eds. K.L. Dickson, A.W. Maki and J. Cairns. Jr., Ann Arbor
Science, Ann Arbor, Ml.
Nkedi-Kizza, P.. P.S.C. Rao and A.G. Hornsby. 1984. "Influence of Organic Co-
solvent on Sorption of Hydrophobic Organic Chemicals by Soils," paper
submitted to Environ. Sci. & Techno!.
Pickens JF. and W.C. Lennox, 1976, "Numerical Simulation of Waste
Movement in Steady Groundwater Flow Systems." Water Resource Research.
Vol. 12, No. 2, p. 171-180.
Pimentel, G.C. and A.L. McClellan. 1960. "The Hydrogen Bond." W.H. Freeman
and Company, San Francisco, CA.
Prausniu, J.M.. 1989- "Molecular Thermodynamics of Fluid-Phase Equilibria."
Prentice-Hall, Inc. Englewood Cliffs, N.J.
Prlgogine, I., and R. Defay. 1973, "Chemical Thermodynamics." Translated by
D.H. Everett, Longman Group limited, London.
Reid RC JM Prausnitz and T.K. Sherwood, 1977, "The Properties of Gas and
liquids." 3rd ed.. McGraw-Hill Book Company. New York. NY.
-------
183
Rogers, R.D., J.C. McFarlane, and AJ. Cross, 1980, "Adsorption and Desorption
of Benzene in Two Soils and Montmorillonite Clay," Environ. Sci.
Techno!., Vol. 14, p. 457-460,
Rohrschnieder, L., 1973, "Solvent Characterization by Gas-Liquid Partition
Coefficients of Selected Solutes," Analytical Chemistry, Vol. 45, p.
1241-1247.
Rohrschneider, L., 1966, "Eine Methods zur Charakterisierung von
Gaschromatographischen Trennflussigkeiten," J. of Chromatography, Vol.
22, p. 6-22.
Ryan, T.A., Jr., B.L. Joiner, and B.F. Ryan, "Minitab Student Handbook," Duxbury
Press, Boston, MA.
Schwarzenbach, R.D., and J. Westall, 1981, "Transport of Nonpolar Organic
Compounds from Surface Water to Groundwater. Laboratory Sorption
Studies," Environ. Sci. & Techno/., Vol. 15, No. 11. p. 1360-1367.
Seidell, A., 1941, "Solubilities of Organic Compounds," 3rd ed. Vol II, D. Van
Nostrand Company, Inc., New York, NY.
Snyder L.R., 1978, "Solvent Selection for Separation Processes," in
"Separation and Purification," 3rd ed. Eds. E.S. Perry and A. Weissberger,
John Wiley & Sons, New York, NY.
Snyder, L.R., 1979, "Solutions to Solution Problems - 1," CHEMTECH, p.
750-755.
Snyder, L.R., 1980, "Solutions to Solution Problems - 2," CHEMTECH. p.
188-193.
Stephen, H. and T. Stephen (eds.), 1963, "Solubility of Inorganic and Organic
Compounds," Macmillan Co., New York, NY.
Stumm, W. and J.J. Morgan, 1981, "Aquatic Chemistry," 2nd ed., John Wiley &
Sons, New York, NY.
Tanford, C., 1973, "The Hydrophobic Effect: Formation of Micelles and
Biological Membrane," John Wiley & Sons, New York, NY.
-------
184
Tijssen, P., H.A.H. Billiet and P.J. Schoenmakers, 1976, "Use of Solubility
Parameter for Predicting Selectivity and Retention Chromatography," J. of
Chromatography, Vol. 122, p. 185-203.
Tsonopoulos, C. and J.M. Prausnitz, 1971, "Activity Coefficients of Aromatic
Solutes in Dilute Aqueous Solutions," Ind. Eng. Chem., Fundam.. Vol. 10,
No. 4, p. 593-600.
Weast, R.C. (ed.), 1983, "CRC Handbook of Chemistry and Physics." 3rd ed..
Chemical Rubber Publishing Company, Boca Raton, FL.
Weimer, R.F. and J.M. Prausnitz, 1965, "Screen Extraction Solvents This Way."
Hydrocarbon Processing, Vol. 44, No. 9, p. 237-242.
Wending, V.L., and T.F. Yen, 1980, '"Solubility Parameters' in Coal and Coal
Liquefaction Products," Fuel, Vol. 59, No. 5, p. 287.
Wilson, G.M.. and C.H. Deal. 1962, "Activity Coefficient and Molecular
Structure." Ind. Eng. Chem., Fundam., Vol.1, No. 1, p. 20-23.
Williams, N.A. and G.L. Amidon, 1984a, "Excess Free Energy Approach to the
Estimation of Solubility in Mixed Solvent Systems I: Theory," J. of
Pharma. ScL. Vol. 73. No. 1. p. 9-13.
Williams. N.A.. and G.L. Amidon, 1984b, "Excess Free Energy Approach to the
Estimation of Solubility in Mixed Solvent Systems II: Ethanol-Water
Mixtures," J. of Pharma. ScL. Vol. 73, No. 1, p. 14-18.
Williams, N.A., and G.L. Amidon, 1984c. "Excess Free Energy Approach to the
Estimation of Solubility in Mixed Solvent Systems III: Ethanol-Propylene
Glycol-Water Mixtures," J. Pharama. Sci.. Vol. 73. No. 1. p. 18-23.
Woodburn. K.B.. P.S.C. Rao. M. Fukui and P. Nkedi-Kizza, 1985, "Solvophoblc
Approach for Predicting Sorption of Hydrophobic Organic Chemicals on
Synthetic solvents and Soils." Contamination Hydrology. Pre-publication
draft.
Wohl K, 1946, "Thermodynamic Evaluation of Binary and Ternary Liquid
Systems," Trans. Am. Inst. Chem. Bngrs.. Vol. 42. No. 5. p. 215-249.
Yalkowsky, S.H., G.L. Flynn and G.L. Amidon, 1972. "Solubiity of
-------
185
Nonelectrolytes in Polar Solvents," J. of Pharma. Sci., Vol. 61, No. 6, p.
983-984.
Yalkowsky, S.H. and G.L. Flynn, 1974, "Correlation and Prediction of Mass
Transport Across Membranes II: Influence of Vehicle Polarity on Flux from
Solutions and Suspensions," J. Pharma. Sci., Vol. 63, No.8, p. 1276-1280.
Yalkowsky, S.H., S.C. Valvani, and G.L Amidon, 1976, "Solubility of
Nonelectrolytes in Polar Solvents IV: Nonpolar Drugs in Mixed Solvents,"
J. of Pharma. Sci., Vol. 65, No. 10, p. 1488-1494.
Yalkowsky, S.H., 1979, "Estimation of Entropies of Fusion of Organic
Compounds," Ind. Eng. Chem., Fundam., Vol. 18, No.2, p. 108-111.
Yalkowsky, S.H. and S.C. Valvani, 1980, "Solubility and Partitioning I:
Solubility of Non-electrolytes in Water," J. Pharma. Sci., Vol. 69, No. 8,
p. 912-922.
Yalkowsky, S.H., 1981, "Solubility and Partitioning V: Dependence of Solubility
on Melting Point," Technical Note, J. Pharma. Sci., Vol. 70, No. 8, p.
971-973.
Yalkowsky, S.H., 1985, Personal communication.
-------
186
Appendix A
EXAMPLE CALCULATION OF ACTIVITY COEFFICIENT USING UNIFAC
The behavior of an organic solute in a multicomponent mixture can be
determined by the solute and solvent physical and chemical properties. This
Appendix presents the use of the UNIFAC group contribution model for
prediction of the solute infinite dilution activity coefficient. Some of the
available functional group data are used in the sample calculation. A
complete listing of the available functional group interaction data can be
found in Gmehling et at. (1982).
The following example shows the steps for calculating the solute
infinite dilution activity coefficient. This example considers a three
component system: methanol (1, co-solvent), naphthalene (2, solute), and water
{3). Using the functional group classification data base (Gmehling et. al,
1982), methanol (CH3OH) can be considered as one CH3OH group, end
naphthalene (C10Hs) may be divided into 8 ACH groups and 2 AC groups, and
water can be considered as one H20 group. The solute activity coefficient
can be estimated by Equation 2-19. The functional group parameters shown
in Table A-1 are required to perform the calculation for obtaining the
combinatorial of solute infinite dilution coefficient From Equation 2-20
* i 9,
where r and q terms cab be calculated by Equation 2-22
r e V 2 R = V 2 R + V 2 R + V * R ~ V 2 R
e J' "k *10 10 11 11 IS 1« 17 17
8 8 (0.5313) + 2 (0.3652) + 0 (0.3682) + 0 (0.920) = 4.9808
-------
187
Table A-1: Functional Group Parameters for
Methanol, Naphthalene and Water
Group
Main
Sub-group
v,
Component
group No.
No.
ch3oh
1
6
16
1
1.4311
1.432
ACH
2
3
10
8
0.5313
0.400
AC
2
3
11
2
0.3652
0.120
h2o
3
7
17
1
0.920
1.40
r1 = 1 (1.4311) + 0 (0.5313) + 0 (0.3632) + 1 (0.920) = 1.4311
r3 = 0 (1.4311) + 0 (0.5313) + 0 (0.3632) + 1 (0.920) = 0.920
q = / V 2 Q = V 2 Q + V 2 Q + V 2 Q + V 2 Q
2 -4—' *k k 10 10 *11 11 16 16 17 17
k
= 8 (0.400) + 2 (0.120) + 0 (4.432) + 0 (1.40) = 3.44
qi = 1 (1.432) + 0 (0.400) + 0 (0.120) + 0 (1.40) = 1.432
q3 = 0 (1.432) + 0 (0.400) + 0 (0.120) + 1 (1.40) = 1.40
z 10
l2 = —(r2-q2) - (r2 - 1) = — (4.9808 - 3.44) - (4.9808-1) = 3.7232
10
I, = (1.4311 - 1.432) - (1.4311 - 1) = 0.4356
1 2
10
I, = (0.920 - 1.40) - (0.920 - 1) = 2.32
3 2
-------
For computation of the infinite dilution activity coefficient of naphthalene in
50% (by volume) methanol and 50% (by volume) water mixture, the mole
fraction of methanol is X1 = 0.3085, the mole fraction of naphthalene is X2 =
0, and the mole fraction of water is X3 = 0.6915.
«L r, 4.9808
Li 1 = — = 4.6218
X r X +r X +r X 1.4311(0.3085)+4.9808(0)+0.920(0.6915)
2 1 1 2 2 3 3
q, X,
~2 2
tl - qiX1+q2X2+C|3X3 . % r,X1+raVr3X3
fi ^ X2 'J
riX,+rjX2+r3X3
3.44 ( 1.4311 (0.3085) + 4.9808 (0) + 0.92 (0.6915)\
s ^ ———_) q 5079
4.9808 1.432 {0.3085) + 3.44 (0) + 1.40 (0.6915}
10
In y2c = In 4.6218 + — (3.44) In (1.687) ~ 3.7232
- 4.6218 £0.3085(0.4356) + 0(3.7232) + 0.69t5(-2.32)]
In y3c * 2.3016
Table A-2 shows the functional group interaction parameters which are used
to calculate the residua! contribution of the solute infinite dilution activity
coefficient. The functional group interaction energy, y, is calculated using
Equation 2-27 The residual part of the infinite dilution activity coefficient can
be calculated using Equation 2-24
In r>» = ]
. y,,' imr„ - m rie1. y„> (mr); - miy)
where In rk can be calculated using Equation 2-25. In TK2 can be calculated
using Equation 2-25 assuming pure naphthalene for which X2 = 1, thus mole
fractions of methanol and water are zero {Xt = 0 and X$ * 0). For
-------
189
Table A-2: Functional Group Interaction Parameters
Main Group No. 6 3 3 7
ch3oh ACH AC h2o
6 CH2OH 0
3 ACH 637.3
2 AC 637.3
7 H20 362.3
-50 -50 -181
0 0 903.8
0 0 903.8
362.3 289.6 0
Table A-3: Functional Group Interaction Energy
Subgroup No. 16 10 11 17
CH OH ACH AC H„0
3 2
16 CH3OH 0 1.1827 1.1827 1.8356
10 ACH 0.1178 0 0 0.04817
11 AC 0.1178 0 0 0.04817
17 H20 0.2965 0.295 0.3784 0
naphthalene at infinite dilution in 50% by volume methanol/water mixture, ©
and X can be calculated using Equation 2-26.
For naphthalene in infinite dilution (X2 = 0)
X1(J = 0 Xn s 0 x16 = 0.3085 X„ = 0.6915
01O = 0 = 0 016 = 0.3133 ©17 = 0.6867
-------
190
let A = 0 V + © ¥ +' © ¥ +©¥
10 10,10 11 11,10 16 16,10 17 17,10
B = 0 ¥ +© ¥ +0 ¥ +0 ¥
10 10,11 11 11,11 16 16,11 17 17,11
C = 0 ¥ + © ¥ + © ¥ + © V
10 10,16 11 11,16 16 16,16 17 17,16
D = © ¥ + © ¥ + © ¥ + © ¥
10 10,17 11 11,17 16 16, 17 17 17,17
0 ¥ © ¥ © ¥ AM/
In r =0 [1 - In A — U !°dl _ is 10,16 _ 13 Yiq,i7 ..
10 10 ABC D ]
= 0.4 (1+0.5549 -0 -0 - 0.06439 - 0.0262) = 0.585)
In rn = 0.1757
For pure naphthalene (X2 = 1)
X,Q = 0.8 X„ = 0.2 X„ = 0 X,7 = 0
01O = 0.5714 ©„ = 0.4286 ©1(J = 0 ©i? = 0.
using Equation 2-25, and
mr10» = 0
lnr„z - 0
ln y* ¦ ^102 I|nr,0 - 'nr102] * *„2 [inrn - mrn2]
= 8 (0.5857-0) + 2 (0.1757-0) = 5.037
The combinatorial and residual contributions to the infinite dilution activity
coefficient are added as in Equation 2-19
R
2
In y2°° = In y2c ~ lny.
In y2°° « 2.3061 + 5.037 * 7.3386
y2°° « 1538.56
This value of y2°° was obtained by hand calculation, and it agrees with
computer calculation as shown in Table 4-2 to three significant figures.
a
-------
191
Appendix B
PREDICTION OF SOLUTE SOLUBILITY BY THE UNIFAC APPROACH,
THE LOG-LINEAR APPROACH, AND THE EXCESS FREE ENERGY APPROACH
-------
192
Table B-1: Naphthalene Solubility in Methanol/Water Mixtures
Mole
Frac.
Volume
Frac.
[-3 t-3
UNIFAC
Excess
Mole
Free
Frac.
Energy
Sol.
Mole
Frac.
Sol.
t-3
t-3
Log-linear UNIFAC
Mole Sol.
Frac.
Sol.
Excess Log-linear
Free Sol.
Energy
Sol.
C-l
[mg/l] [mg/1] [mg/1]
.0000
.0000 .1
.0500
.1055 .
.1000
.1993 .
.1500
.2833 .
.2000
.3590 .
.2500
.4275 .
.3000
.4898 .
.3500
.5468 .
.4000
.5990 .
.4500
.6470 .
.5000
.6914 .
.5500
.7325 .
.6000
.7707 .
.6500
.8062 .
.7000
.8394 .
.7500
.8705
.8000
.8996
.8500
.9270
.9000
.9528
.9500
.9770
1.0000
1.0000
.0472
.0999
.1003
.1999
.1604
.2948
.2292
.3998
.3084
.4998
.4008
.5998
.5099
.6998
.6408
.7999
.8005
.8999
.2992
.4889
.4240
.6225
.5174
.7061
.5716
.7493
.7076
.8443
.8446
.9241
.9928
.9968
.9969
.9986
0000021
0000052
0000120
0000254
0000504
0000942
0001672
,0002839
,0004629
.0007286
.0011105
.0016443
.0023717
.0034430
.0065300
.0087590
.0115700
.0150650
.0193550
.0245600
.0000049
.0000120
.0000287
.0000731
.0001833
.0004664
.0012029
.0031413
.0082578
.0001658
.0005779
.0012770
.0019322
.0048223
.0104364
.0210242
.0213987
.0000043
.0000073
.0000129
.0000232
.0000415
.0000731
.0001262
.0002128
.0003498
.0005604
.0008755
.0013346
.0019877
.0028954
.0041309
.0057793
.0079391
.0107209
.0142482
.0186560
.0240900
.0000071
.0000130
.0000252
.0000579
.0001380
.0003525
.0009535
.0027061
.0079636
.0001251
.0004400
.0010166
.0015897
.0043525
.0103869
.0232384
.0237204
.0000043
.0000107
.0000241
.0000497
.0000955
.0001724
.0002952
.0004824
.0007570
.0011459
.0016804
.0023957
.0033303
.0045261
.0060272
.0078798
.0101313
.0128300
.0160242
.0197618
.0240900
.0000102
.0000242
.0000549
.0001358
.0003216
.0007622
.0018065
.0042845
.0101560
.0002928
.0009275
.0019069
.0027701
.0062850
.0125155
.0234286
.0238036
14.97
34.67
75.48
152.02
286.40
509.80
864.01
1402.42
2190.97
3307.89
4842.99
6895.72
9572.53
13380.15
17920.00
23564.28
30467.15
38791.30
48676.40
60250.20
73625.24
33.07
75.83
167.28
403.64
939.96
2206.02
5205.05
12295.68
28752.97
857.05
2680.84
5493.30
7969.14
17965.06
35201.04
63749.82
64694.72
30.57
48.78
81.55
138.70
235.66
395.66
652.19
1051.71
1656.33
2546.22
3821.43
5602.91
8032.39
11271.01
15496.49
20898.88
27674.95
36021.43
46127.48
58166.82
72289.93
47.45
81.81
146.91
319.56
707.83
1668.08
4129.77
10606.48
27750.31
647.10
2042.20
4377.16
6563.93
16236.98
35038.51
70122.80
71351.28
30.57
71.53
151.87
297.14
542.39
932.89
1524.23
2381.59
3578.44
5194.60
7313.86
10021.35
13400.72
17531.47
22486.40
28329.38
35113.55
42880.00
51656.98
61459.58
72289.93
68.39
152.51
319.18
749.46
1647.77
3600.78
7800.55
16711.59
35186.29
1512.86
4296.77
8185.01
11394.02
23315.86
41992.95
70667.29
71588.69
-------
193
Table B-1: continued
Solvent Solvent Molecular Molecular
Mole Volume Surface Surface
Fraction Fraction Area Area
Solubility Solubility
[-]
C-]
[-]
[mg/1]
.0000
.0000
.0000043700
31.00
.0472
.0999
.0000107442
72.00
.1003
.1999
.0000263150
166.00
.1604
.2999
.0000697873
406.00
.2292
.3999
.0001581667
873.00
.3084
.4999
.0003880909
1988.00
1.0000
1.0000
.0373488100
108943.00
-------
194
Table B-2: Naphthalene Solubility in Acetone/Water Mixtures
Mole
Frac.
Volume
Frac.
[-] [-3
UNIFAC
Excess
Log-linear
Mole
Free
Mole
Frac.
Energy
Frac.
Sol.
Mole
Sol.
Frac.
Sol.
[-]
[-]
[-]
Sol.
[mg/1]
Excess Log-linear
Free Sol.
Energy
Sol.
[mg/1]
[mg/1]
.0000
.0000 .
.0500
.1764 .
.1000
.3114 .
.1500
.4180 .
.2000
.5043 .
.2500
.5756 .
.3000
.6356 .
.3500
.6866 .
.4000
.7307 ,
.4500
.7690
.5000
.8027
.5500
.8326
.6000
.8592
.6500
.8831
.7000
.9047
.7500
.9243
.8000
.9421
.8500
.9584
.9000
.9734
.9500
.9872
1.0000
1.0000
.0266
.1001
.0578
.1998
.0952
.2998
.1406
.3997
.1971
.4997
.2691
.5997
.3642
.6998
.4953
.7997
.6884
.8999
.2320
.5514
.2874
.6214
.3470
.6838
.3749
.7093
.4457
.7659
.4974
.8011
.5541
.8349
.6157
.8670
.0009486
.0015658
.0024780
.0039205
.0059080
.0087350
.0127350
.0183800
.0263500
.0453100
.0670200
.0975800
.1403650
.1781000
.0000044
.0000098
.0000227
.0000548
.0001391
.0003751
.0010990
.0037680
.0168940
.0002303
.0004650
.0009190
.0012246
.0023855
.0038355
.0061040
i .0098450
.0000043
.0000213
.0001212
.0005573
.0019507
.0053156
.0117544
.0219728
.0359485
.0529336
.0717154
.0909520
.1094414
.1262700
.1408538
.1529083
.1623847
.1694001
.1741736
.1769773
.1781000
.0000095
.0000281
.0001033
.0004271
.0018271
.0073604
.0255804
.0699101
.1376896
.0038041
.0097923
.0212497
.0284949
.0513832
.0707161
.0925108
.1149385
0000043
0000281
0001180
, 0003663
,0009169
,0019572
.0037010
.0063688
.0101700
.0152892
.0218780
.0300513
.0398867
.0514271
.0646841
.0796425
.0962646
.1144952
.1342653
.1554957
.1781000
.0000125
.0000360
.0001043
.0003016
.0008736
.0025282
.0073245
.0211927
.0614560
.0015132
.0031830
.0061787
.0081079
.0147931
.0214972
.0307944
.0433257
14.40
69.80
136.18
327.37
638.56
1176.86
2010.66
3236.38
4968.46
7344.59
10891.85
15433.40
21508.72
29614.64
40418.78
54833.75
88484.31
123146.30
168254.40
226281.80
271301.50
28.86
59.04
124.67
271.46
614.63
1455.63
3671.29
10530.48
37632.45
953.56
1750.25
3149.76
4027.69
7110.94
10690.71
15866.97
23806.16
30.57
131.14
657.42
2700.94
8515.76
20983.94
42013.13
71158.82
105708.20
141961.90
176569.20
207209.80
232653.90
252516.10
266957.40
276444.80
281586.80
283033.50
281419.60
277333.20
271301.50
62.25
169.44
566.70
2112.66
8023.55
27972.13
80577.16
173457.50
264068.80
15567.29
35885.73
69222.79
87914.76
138867.30
174852.10
209501.70
239492.50
30.57
172.80
639.95
1776.71
4017.49
7807.97
13527.22
21433.90
31644.23
44137.81
58782.13
75365.42
93630.52
113303.70
134117.10
155823.60
178205.70
201079.30
224293.90
247731.30
271301.50
81.88
217.01
572,41
1492.53
3849.30
9747.96
24097.90
57319.27
129200.30
6238.82
11887.59
20895.00
26228.99
42976.34
57970.76
76803.55
99669.19
-------
195
Table B-3: Naphthalene Solubility in Ethanol/Water Mixtures
Solvent Solvent UNIFAC Excess Log-linear UNIFAC Excess Log-linear
Mole Volume Mole
Frac. Frac. Frac.
Sol.
Free
Energy
Mole
Frac.
Sol.
Mole
Frac.
Sol.
Sol.
Free
Energy
Sol.
Sol.
[-] [-]
[-]
[-]
[-]
[mg/1] [mg/1]
[mg/1]
.0000 .
.0500 ' .
.1000 .
.1500 .
.2000 .
.2500 .
.3000 .
.3500 .
.4000 .
.4500 .
.5000 .
.5500 .
.6000 .
.6500 .
.7000 .
.7500 .
.8000 .
.8500 .
.9000 .
.9500 .
1.0000 1.
.0419 .
.0716 .
.1167 .
.1705 ,
.2357 ,
.3163 .
.4185 .
.5523 .
.7351 .
.1419 .
.1686 .
.2012 .
.2172 .
.2646 .
.3589 .
.4192 .
.5402 .
.6591 .
.9480 .
1.0000 1.
0000
1453
2641
3631
4468
5185
5806
6349
6829
7255
7636
7979
8289
8571
8829
9065
9282
9482
9667
9840
0000
1238
1994
3115
3990
4990
5991
6992
7994
8996
3482
3929
4486
4428
5375
6439
6998
7914
8620
9833
0000
.0000020
.0000084
.0000259
.0000652
.0001406
.0002695
.0004712
.0007655
.0011717
.0017081
.0023915
.0033350
.0044190
.0057200
.0072590
.0090550
.0111300
.0135080
.0162080
.0192480
.0226350
.0000068
.0000140
.0000360
.0000908
.0002261
.0005560
.0013541
.0033800
.0084920
.0000568
.0000881
.0001430
.0001779
.0003200
.0008291
.0013613
.0031460
.0059820
.0191200
.0226350
.0000043
.0000123
.0000339
.0000857
.0001957
.0004051
.0007668
.0013423
.0021961
.0033899
.0049782
.0070038
.0094967
.0124729
.0159356
.0198762
.0242765
.0291104
.0343463
.0399487
.0450800
.0000103
.0000192
.0000524
.0001217
.0003322
.0009278
.0025951
.0071080
.0186529
.0000742
.0001146
.0001994
.0001881
.0004923
.0014721
.0026111
.0065707
.0130670
.0397181
.0458800
.0000043
.0000166
.0000499
.0001249
.0002714
.0005277
.0009389
.0015541
.0024241
.0035985
.0051240
.0070423
.0093897
.0121960
.0154843
.0192715
.0235682
.0283796
.0337056
.0395419
.0458800
.0000136
.0000274
.0000774
.0001743
.0004407
.0011146
.0028206
.0071406
.0180900
.0001088
.0001648
.0002761
.0002617
.0006297
.0016889
.0028364
.0066336
.0127580
.0392987
.0458800
14.40
53.48
150.21
346.28
689.23
1226.39
1999.74
3042.61
4378.31
6020.34
7973.77
10544.44
13281.63
16377.20
19836.71
23658.91
27849.49
32417.27
37357.86
42664.95
48310.11
44.18
85.94
210.75
466.35
1050.34
2308.76
4949.71
10661.33
22482.62
305.84
450.86
699.65
796.21
1426.09
3258.43
4972.19
10048.80
16980.26
42446.46
48310.11
30.57
78.27
196.45
455.30
959.45
1842.22
3250.69
5325.61
8181.97
11894.93
16493.17
21959.53
28237.23
35239.17
42858.45
50978.23
59479.75
68248.88
77180.29
86180.03
95166.72
67.12
117.35
307.08
625.28
1542.57
3847.62
9453.38
22231.07
48513.26
399.87
586.51
975.62
841.76
2192.58
5774.13
9503.83
20821.92
36583.27
85819.80
95166.72
30.57
105.82
289.37
663.62
1330.08
2398.99
3977.98
6161.88
9025.55
12619.76
16970.13
22078.46
27925.65
34475.51
41678.93
49477.92
57809.23
66607.52
75807.80
85347.24
95166.72
88.11
167.54
453.58
895.33
2045.75
4619.38
10268.36
22331.43
47095.23
586.00
842.72
1350.57
1170.48
2802.79
6620.10
10317.38
21018.14
35739.49
84959.86
95166.72
-------
196
Table B-4: Naphthalene Solubility in Propanol/Water Mixtures
Solvent Solvent UNIFAC Excess Log-linear UNIFAC Excess Log-linear
Mole Volume Mole
Frac. Frac. Frac.
Sol.
Free
Energy
Mole
Frac.
Sol.
Mole
Frac.
Sol.
Sol.
Free
Energy
Sol.
Sol.
[-] [-]
[-]
[-]
[-]
[mg/l] tmg/1] [mg/1]
.0000
.0000
.0000020
.0000043
.0000043
14.40
30.57
30.57
.0500
.1735
.0000121
.0000189
.0000224
74.98
116.82
138.30
.1000
.3071
.0000459
.0000709
.0000797
250.58
386.99
435.37
.1500
.4131
.0001282
.0002153
.0002184
627.56
1053.46
1068.61
.2000
.4993
.0002907
.0005396
.0004952
1289.18
2391.33
2194.96
.2500
.5707
.0005671
.0011525
.0009764
2298.34
4662.21
3951.99
.3000
.6309
.0009894
.0021619
.0017297
3690.13
8036.18
6437.60
.3500
.6823
.0015851
.0036543
.0028187
5473.16
12550.54
9701.69
.4000
.7267
.0023763
.0056811
.0042978
7635.36
18113.94
13747.76
.4500
.7655
.0034850
.0082556
.0062101
10464.85
24541.08
18540.52
.5000
.7996
.0047922
.0113568
.0085862
13502.58
31597.53
24016.14
.5500
.8298
.0063710
.0149378
.0114444
16902.51
39039.40
30092.64
.6000
.8568
.0082380
.0189346
.0147923
20643.40
46641.13
36678.88
.6500
.8811
.0104110
.0232749
.0186276
24711.01
54210.95
43681.74
.7000
.9030
.0129050
.0278844
.0229404
29087.58
61596.63
51011.22
.7500
.9229
.0157380
.0326918
.0277144
33765.11
68684.72
58583.85
.8000
.9410
.0189250
.0376315
.0329287
38731.21
75396.25
66324.44
.8500
.9576
.0224870
.0426454
.0385587
43987.48
81681.11
74167.07
.9000
.9729
.0264350
.0476833
.0445778
49517.34
87511.99
82055.27
.9500
.9870
.0307750
.0527030
.0509578
55298.79
92879.18
89941.30
1.0000
1.0000
.0360000
.0576700
.0576700
62130.05
97785.74
97785.74
.0270
.0997
.0000057
.0000097
.0000111
37.61
63.61
72.92
.0588
.1995
.0000158
.0000242
.0000287
95.26
146.19
173.04
.0967
.2992
.0000425
.0000654
.0000740
233.74
359.73
407.14
.1427
.3990
.0001120
.0001854
.0001910
556.57
921.12
949.06
.1998
.4990
.0002898
.0005378
.0004938
1285.90
2384.28
2189.28
.2725
.5991
.0007373
.0015518
.0012777
2876.19
6038.52
4976.24
.3682
.6992
.0018496
.0043286
.0033094
6217.94
14462.37
11085.07
.4997
.7994
.0047840
.0113368
.0085705
13484.46
31553.80
23981.41
.6921
.8997
.0124900
.0271411
.0222278
28378.42
60447.00
49834.95
.0880
.2779
.0000345
.0000526
.0000604
193.47
295.49
339.36
.1051
.3190
.0000516
.0000801
.0000893
278.33
432.49
481.90
.1407
.3951
.0001078
.0001778
.0001840
538.16
887.24
918.09
.2064
.5092
.0003190
.0005996
.0005440
1397.98
2625.20
2382.16
.3191
.6515
.0011951
.0026713
.0021029
4325.33
9628.46
7591.44
.4476
.7637
.0034290
.0081197
.0061080
10329.17
24216.22
18294.27
.6440
.8783
.0101340
.0227384
.0181418
24207.25
53309.67
42822.42
.7993
.9408
.0188880
.0375617
.0328527
38680.04
75305.15
66215.20
-------
197
Table B-5: Naphthol Solubility in Methanol/Water Mixtures
Solvent Solvent UNIFAC Excess Log-linear UNIFAC Excess Log-linear
Mole Volume Mole
Frac. Frac. Frac.
Sol.
Free
Energy
Mole
Frac.
Sol.
Mole
Frac.
Sol.
Sol.
Free
Energy
Sol.
Sol.
[-] [-]
[-]
[-]
[-3
[mg/1] [mg/1] [mg/1]
.0000
.0500
.1000
.1500
.2000
.2500
.3000
.3500
.4000
.4500
.5000
.5500
.6000
.6500
.7000
.7500
.8000
.8500
.9000
.9500
1.0000
.0472
.1003
.1604
.2292
.3084
.4008
.5099
.6408
.8005
.0000
.1055
.1993
.2833
.3590
.4275
.4898
.5468
.5990
.6470
.6914
.7325
.7707
.8062
.8394
.8705
.8996
.9270
.9528
.9770
1.0000
.0999
.1999
.2997
.3998
.4998
.5998
.6998
.7999
.8999
.0001716
.0003621
.0006911
.0012307
.0020435
.0032200
.0048560
.0070500
.0124550
.0179350
.0251600
.0342300
.0449260
.0566300
.0686000
.0802100
.0911200
.1012000
.1104200
.1188400
.1265300
.0003483
.0006936
.0012205
.0026804
.0051830
.0125300
.0268100
.0544400
.0912400
.0001060
.0001638
.0002631
.0004279
.0006938
.0011110
.0017474
.0026919
.0040570
.0059801
.0086249
.0121812
.0168634
.0229088
.0305745
.0401337
.0518718
.0660819
.0830605
.1031031
.1265000
.0001596
.0002638
.0004735
.0009151
.0018818
.0040830
.0092502
.0216826
.0520012
.0001060
.0002238
.0004351
.0007891
.0013488
.0021914
.0034077
.0051005
.0073831
.0103772
.0142103
.0190133
.0249183
.0320564
.0405552
.0505377
.0621204
.0754122
.0905136
.1075156
.1265000
.0002151
.0004367
.0008862
.0018010
.0036558
.0074251
.0150800
.0306445
.0622447
1367.50
2715.20
4887.63
8227.92
12937.49
19329.33
27662.99
38133.13
63383.70
86186.95
113931.10
145812.40
179951.90
213633.50
244561.00
271439.70
294076.30
312834.70
328216.50
340806.60
351092.10
2620.27
4903.62
8072.99
16448.31
29268.96
63708.00
119955.60
207603.50
294321.20
845.27
1229.58
1864.92
2872.47
4420.96
6732.54
10086.03
14815.65
21303.94
29967.89
41238.74
55536.01
73238.26
94653.50
119992.40
149348.80
182688.30
219849.30
260553.90
304427.90
351027.20
1202.34
1869.71
3143.46
5661.64
10774.56
21424.29
43816.53
90423.29
183041.30
845.27
1679.28
3081.32
5287.13
8567.55
13215.83
19531.48
27802.37
38286.74
51196.74
66685.25
84837.20
105665.60
129113.00
155057.80
183323.20
213690.00
245909.50
279717.10
314843.80
351027.20
1619.56
3091.91
5871.45
11096.72
20776.85
38473.71
70066.41
124606.80
214003.40
-------
198
Table B-6: Naphthal Solubility in Acetone/Water Mixtures
Solvent
Solvent
UNIFAC
Excess
Log-linear
UNIFAC
Excess
Log-linear
Mole
Volume
Mole
Free
Mole
Sol.
Free
Sol.
Frac.
Frac.
Frac.
Energy
Frac.
Energy
Sol.
Mole
Sol.
Sol.
Frac.
Sol.
[-]
[-]
[-]
[-]
[-]
[mg/1]
[mg/1]
[mg/1]
.0000 .0000 .0001716 .0001060 .0001060 1367.50 845.27 845.27
.0500 .1764 .0007386 .0003423 .0004071 5089.96 2363.41 2810.24
.1000 .3114 .0024665 .0013533 .0011399 14892.24 8212.15 6923.79
.1500 .4180 .0067370 .0045821 .0025707 35852.03 24589.42 13904.33
.2000 .5043 .0217000 .0123746 .0049667 99723.11 58646.53 24138.11
.2500 .5756 .0480000 .0270204 .0085588 188587.40 112547.90 37642.70
.3000 .6356 .0795000 .0493761 .0135205 270487.40 180367.40 54134.93
.3500 .6866 .1060000 .0782150 .0199614 322343.20 251672.60 73141.91
.4000 .7307 .1279000 .1107015 .0279305 355426.50 317196.10 94109.36
.4500 .7690 .1453000 .1434581 .0374250 375198.00 371522.60 116484.30
.5000 .8027 .1595000 .1735263 .0484013 387032.30 412746.40 139766.50
.5500 .8326 .1715000 .1988796 .0607853 394115.80 441128.10 163533.80
.6000 .8592 .1814000 .2185065 .0744824 397312.40 457969.10 187449.10
.6500 .8831 .1898700 .2322353 .0893850 398185.00 464945.30 211255.20
.7000 .9047 .1970600 .2404677 .1053789 397198.90 463777.80 234765.20
.7500 .9243 .2030500 .2439258 .1223483 394626.10 456089.40 257850.00
.8000 .9421 .2080300 .2434589 .1401789 390858.20 443347.90 280426.90
.8500 .9584 .2120000 .2399151 .1587604 385955.10 426846.30 302448.40
.9000 .9734 .2149500 .2340675 .1779884 379948.70 407699.70 323894.00
.9500 .9872 .2169000 .2265802 .1977651 372905.30 386848.50 344762.90
1.0000 1.0000 .2177000 .2180000 .2180000 364638.90 365068.00 365068.00
.0266 .1001 .0003880 .0001845 .0002274 2855.90 1359.75 1675.63
.0578 .1998 .0009106 .0004248 .0004866 6142.49 2872.76 3289.25
.0952 .2998 .0022190 .0011910 .0010436 13563.86 7314.78 6413.70
.1406 .3997 .0056470 .0037053 .0022358 30769.84 20347.10 12350.15
.1971 .4997 .0204900 .0117531 .0047970 95013.48 56111.40 23453.76
.2691 .5997 .0393953 .0346715 .0102851 154094.80 137346.30 43612.83
.3642 .6998 .1138248 .0872167 .0220685 335995.80 271181.60 78921.97
.4953 .7997 .3430000 .1708770 .0473082 660099.40 409432.70 137551.40
-------
199
Table B-7: Quinoline Solubility in Methanol/Water Mixtures
Solvent Solvent UNIFAC Excess Log-linear UNIFAC Excess Log-linear
Mole
Frac.
Volume
Frac.
Mole
Frac.
Sol.
Free
Energy
Mole
Frac.
Sol.
Mole
Frac.
Sol.
Sol.
Free
Energy
Sol.
Sol.
[-] [-]
[-]
[-]
[-]
[mg/l] [mg/1] [mg/1]
0000
.0000
.0005437
.0009610
0500
.1055
.0013743
.0015410
1000
.1993
.0030470
.0025266
1500
.2833
.0062050
.0041480
2000
.3590
.0119330
.0067350
2500
.4275
.0223150
.0107395
3000
.4898
.0259952
.0167562
3500
.5468
.0388383
.0255386
4000
.5990
.0555880
.0380094
4500
.6470
.0766466
.0552633
5000
.6914
.1022798
.0785618
0472
.0999
.0013103
.0014995
1003
.1999
.0030610
.0025342
1604
.2997
.0063030
.0045935
2292
.3998
.0172150
.0088668
3084
.4998
.0261200
.0180154
0009610 3874.71 6832.62 6832.62
0019998 9184.38 10289.57 13321.95
0038382 19095.38 15873.44 23963.94
0068811 36375.09 24538.22 40219.40
0116411 65048.37 37500.12 63531.81
0187372 91788.30 56184.30 95112.49
0288888 123338.60 82105.11 135720.60
0429034 170053.30 116674.30 185493.70
0616613 223650.10 160958.40 243879.90
0860982 282389.50 215436.60 309695.50
1171859 344286.70 279826.20 381293.90
0019238 8788.05 10047.33 12861.90
0038524 19175.61 15915.14 24043.24
0077108 36549.58 26835.63 44442.00
0154574 89503.40 47619.57 80909.25
0309501 123049.20 87273.59 143448.40
-------
200
Table B-8: Quinoline Solubility in Acetone/Water Mixtures
Solvent
Solvent
UNIFAC
Excess
Log-linear
UNIFAC
Excess
Log-linear
Mole
Volume
Mole
Free
Mole
Sol.
Free
Sol.
Frac.
Frac.
Frac.
Energy
Frac.
Energy
Sol.
Mole
Sol.
Sol.
Frac.
Sol.
[-]
[-]
[-]
[-]
[-]
tmg/i]
[mg/1]
[rag/1]
.0000 .0000 .0005437 .0009610 .0009610 3874.71 6832.62 6832.62
.0266 .1001 .0011842 .0016284 .0019260 7779.03 10673.41 12605.04
.0500 .1764 .0021775 .0028937 .0032729 13357.76 17692.49 19976.21
.0578 .1998 .0026388 .0035334 .0038499 15829.47 21111.05 22969.19
.0952 .2998 .0062430 .0091146 .0077137 33679.62 48618.28 41372.56
.1000 .3114 .0059320 .0102453 .0083591 36888.65 53825.43 44236.82
.1406 .3997 .0162550 .0257021 .0154382 76713.59 117552.30 73060.05
.1500 .4180 .0197200 .0311879 .0175308 90324.02 137710.00 80873.15
.1971 .4997 .0552200 .0734219 .0309407 210232.90 266766.90 125827.90
.2000 .5043 .0595300 .0769360 .0319358 223119.30 275949.80 128882.60
.2500 .5756 .1545000 .1561027 .0524226 440906.80 444124.20 185729.10
.2691 .5997 .1810000 .1955771 .0619712 482890.80 508732.30 209135.00
.3000 .6356 .5105000 .2691330 .0794998 852767.80 608003.90 248362.90
.0266 .1001 .0011842 .0016284 .0019260 7779.03 10673.41 12605.04
.0578 .1998 .0026388 .0035334 .0038499 15829.47 21111.05 22969.19
.0952 .2998 .0062430 .0091146 .0077137 33679.62 48618.28 41372.56
.1406 .3997 .0162550 .0257021 .0154382 76713.59 117552.30 73060.05
.1971 .4997 .0552200 .0734219 .0309407 210232.90 266766.90 125827.90
-------
201
Table B-9: 3,5-Dichloroahiline Solubility in Methanol/Water Mixtures
Solvent Solvent UNIFAC Excess Log-linear UNIFAC Excess Log-linear
Mole Volume Mole Free Mole Sol. Free Sol.
Frac. Frac. Frac. Energy Frac. Energy
Sol. Mole Sol. sol.
Frac.
Sol.
[-] [-] [-] [-] [-] [mg/l] [mg/1] [mg/1]
.0000
.0000
.0000817
.0500
.1055
.0002266
.1000
.1993
.0005101
.1500
.2833
.0010035
.2000
.3590
.0017922
.2500
.4275
.0029719
.3000
.4898
.0046448
.3500
.5468
.0073730
.4000
.5990
.0107650
.4500
.6470
.0152320
.5000
.6914
.0209870
.5500
.7325
.0282500
.6000
.7707
.0372700
.6500
.8062
.0483000
.7000
.8394
.0615600
.7500
.8705
.0772800
.8000
.8996
.2970000
.8500
.9270
.3147000
.9000
.9528
.3282000
.9500
.9770
.3391000
1.0000
1.0000
.3481500
.0472
.0999
.0002154
.1003
.1999
.0005122
.1604
.2948
.0010156
.2292
.3998
.0024272
.3084
.4998
.0049816
0000872
.0000872
732
0001508
.0002091
1910
0002684
.0004552
4057
0004795
.0009137
7549
0008477
.0017114
12769
0014700
.0030205
20081
0024894
.0050642
29786
0041076
.0081193
44819
0065992
.0125180
62066
0103258
.0186460
83241
0157487
.0269392
108610
0234396
.0378792
138283
0340888
.0519865
172329
0485098
.0698133
210652
0676406
.0919358
252896
0925407
.1189457
298664
1243853
.1514426
767077
1644554
.1900262
783310
2141261
.2352892
793119
2748517
.2878104
799228
3481500
.3481500
802868
0001461
.0001996
1822
0002693
.0004572
4073
0005213
.0010049
7434
0011723
.0024007
16764
0027130
.0054984
31669
.27 781.19 781.19
.52 1271.93 1762.88
.93 2137.62 3622.48
.20 3616.36 6876.79
.82 6065.94 12198.88
.42 9997.20 20405.61
.96 16103.65 32421.55
.07 25279.36 49217.93
.08 38614.60 71730.45
.91 57358.85 100763.70
.20 82842.23 136896.00
.60 116353.50 180401.20
.10 158983.70 231201.10
.50 211456.20 288862.00
.30 273979.90 352632.00
.00 346160.50 421517.20
.60 426999.40 494376.60
.90 514987.70 570023.40
.90 608274.90 647315.20
.10 704875.60 725221.40
.40 802868.40 802868.40
.23 1236.28 1688.77
.73 2144.37 3637.25
.55 3825.04 7356.62
.61 8141.77 16583.75
.08 17403.34 34882.83
-------
202
Table B-10: S^-Dichlorcaniline Solubility in Acetone/Water Mixtures
Solvent
Solvent
UNIFAC
Excess
Log-linear
UNIFAC
Mole
Volume
Mole
Free
Mole
Sol.
Frac.
Frac.
Frac.
Energy
Frac.
Sol.
Mole
Sol.
Frac.
Sol.
[-]
[-]
[-]
[-3
[-]
tmg/l]
Energy
Sol.
[mg/1] tmg/i] tmg/l]
.0000 .0000 .0000817 .0000872 .0000872 732.27 781.19 781.19
.0500 .1764 .0003692 .0003342 .0004109 2864.52 2593.81 3187.59
.1000 .3114 .0012044 .0014962 .0013459 8219.71 10198.83 9179.88
.1500 .4180 .0031378 .0055975 .0034353 19039.52 33655.87 20821.66
.2000 .5043 .0074060 .0164600 .0073372 40159.52 86711.16 39795.24
.2500 .5756 .0151940 .0387417 .0137361 73784.51 176423.00 66980.15
.3000 .6356 .0288900 .0757249 .0232639 125338.50 294780.60 102337.50
.3500 .6866 .0520800 .1275040 .0364456 200472.80 423610.20 145060.50
.4000 .7307 .5025500 .1908076 .0536718 976937.40 546055.90 193864.80
.4500 .7690 .5143000 .2602438 .0751934 972313.20 652505.90 247290.40
.5000 .8027 .5242000 .3299749 .1011305 966876.90 739828.50 303936.10
.5500 .8326 .5325800 .3950132 .1314890 960805.40 808519.00 362600.30
.6000 .8592 .5398000 .4518601 .1661815 954330.10 860502.70 422340.30
.6500 .8831 .5461000 .4985869 .2050476 947590.90 897992.60 482474.40
.7000 .9047 .5516000 .5345897 .2478731 940626.10 923039.60 542553.30
.7500 .9243 .5564900 .5602209 .2944064 933560.40 937417.10 602318.30
.8000 .9421 .5607300 .5764297 .3443724 926293.30 942637.30 661660.10
.8500 .9584 .5644400 .5844699 .3974837 918897.00 940004.50 720580.90
.9000 .9734 .5676400 .5856907 .4534494 911346.60 930669.00 779165.40
.9500 .9872 .5704900 .5814027 .5119816 903775.30 915665.60 837556.40
1.0000 1.0000 .5728000 .5728000 .5728000 895939.30 895939.30 895939.30
.0266 .1001 .0001914 .0001677 .0002101 1585.29 1388.56 1739.51
.0578 .1998 .0004521 .0004239 .0005046 3435.55 3221.74 3833.39
.0952 .2998 .0010870 .0013029 .0012158 7506.54 8989.14 8391.09
.1406 .3997 .0026577 .0044481 .0029249 16476.74 27388.97 18114.95
.1971 .4997 .0070830 .0155612 .0070491 38655.10 82635.23 38474.54
-------
203
Table B— 11: Aniline Solubility in Methanol/Water Mixtures
Solvent Solvent UNIFAC Excess Log-linear UNIFAC Excess Log-linear
Mole Volume Mole
Frac. Frac. Frac.
Sol.
Free
Energy
Mole
Frac.
Sol.
Mole
Frac.
Sol.
Sol.
Free
Energy
Sol.
Sol.
[-] C-]
[-]
E-J
[-]
[mg/l] [mg/i]
tmg/l]
.0000
.0500
.1000
.1500
.2000
.2500
.3000
.3500
.4000
.4500
.5000
.1482
.1500
.2000
.2052
.0000
.1055
.1993
.2833
.3590
.4275
.4898
.5468
.5990
.6470
.6914
.2805
.2833
.3590
.3665
.0110590
.0172169
.0252667
.0353631
.0475984
.0619990
.0785244
.0970695
.1174715
.1395167
.1629487
.0692000
.0686000
.1375000
.1653000
.0066620
.0094280
.0135468
.0194627
.0277103
.0389022
.0537133
.0728612
.0970842
.1271191
.1636797
.0192127
.0194627
.0277103
.0287259
.0066620
.0113025
.0180887
.0275601
.0402697
.0567653
.0775724
.1031813
.1340363
.1705294
.2129950
.0271662
.0275601
.0402697
.0417996
5545.52
78461.61
106426.10
137740.80
171586.20
207111.50
243505.80
280043.90
316115.80
351230.60
385010.70
245574.40
243486.70
399764.10
452162.30
33430.
44183.
59298.
79512.
105490.
137691.
176279.
221075.
271565.
326959.
386292.
78688.
79512.
105490.
108544.
00 33430.00
44 52608.98
05 77993.89
74 109859.70
50 148062.80
60 192073.40
80 241063.30
60 294025.70
10 349896.70
90 407659.00
10 466413.90
53 108600.50
74 109859.70
50 148062.80
00 152381.50
-------
204
Table B-12: Aniline Solubility in Ethanol/Water Mixtures
Solvent Solvent UNIFAC
Mole Volume Mole
Frac. Frac. Frac.
Sol.
Excess
Free
Energy
Mole
Frac.
Sol.
Log-linear UNIFAC
Mole Sol.
Frac.
Sol.
Excess Log-linear
Free Sol.
Energy
Sol.
[-]
[-3
C-l
[-]
[-]
[mg/l] [mg/1]
Cmg/l]
.0000
.0500
.1000
.1500
.2000
.2500
.3000
.3500
.4000
.4500
.0160
.0402
.0651
.0716
.0843
.0000
.1453
.2641
.3631
.4466
.5185
.5806
.6349
.6829
.7255
.0499
.1192
.1836
.1994
.2292
.0110590
.0294523
.0636084
.1180791
.1956449
.2968152
.4197624
.5605067
.7132159
.8707010
.0202530
.0378900
.0814300
.1275000
.1417000
.0066620
.0124878
.0226907
.0387426
.0618342
.0926518
.1313011
.1773568
.2299874
.2881057
.0081415
.0110487
.0150382
.0162694
.0189236
.0066620
.0137988
.0250274
.0410941
.0625069
.0895357
.1222394
.1605056
.2040930
.2526693
.0085548
.0121049
.0167201
.0180987
.0210112
54545.52
123620.30
223424.90
342889.20
468177.90
588794.80
699264.90
797884.00
884922.90
961395.30
93426.36
157456.40
286619.90
396477.30
420407.30
33430.00
55442.07
89260.42
135007.70
190863.80
253680.20
320000.60
386866.10
452172.50
514667.00
39271.06
50234.19
64366.99
68550.41
77322.62
33430.00
60990.54
97782.72
142357.80
192659.40
246579.40
302312.80
358502.20
414238.50
468989.30
41200.42
54833.25
71176.57
75815.55
85305.48
-------
205
Table B-13: Aniline Solubility in Ethanol/Water Mixtures
Solvent
Solvent
UNIFAC
Excess
Log-linear UNIFAC
Excess
Log-linear
Mole
Volume
Mole
Free
Mole
Sol.
Free
Sol.
Frac.
Frac.
Frac.
Energy
Frac.
Energy
Sol.
Mole
Sol.
Sol.
Frac.
sol.
[-]
[-3
[-]
C-]
[-]
[mg/1]
[mg/1]
[mg/1]
.0000
.0500
.1000
.1500
.2000
.2500
.3000
.3500
.4000
.4500
.5000
.5500
.6000
.6500
.7000
.7500
.8000
.8500
.9000
.9500
1.0000
.0472
.1003
.1604
.2292
.3084
.4008
.5099
.6408
.8005
.4555
.6791
.8153
.9310
.0000
.1055
.1993
.2833
.3590
.4275
.4898
.5468
.5990
.6470
.6914
.7325
.7707
.8062
.8394
.8705
.8996
.9270
.9528
.9770
1.0000
.0999
.1999
.2997
.3998
.4998
.5998
.6998
.7999
.8999
.6521
.8258
.9082
.9680
.0000000
.0000001
.0000003
.0000010
.0000024
.0000056
.0000121
.0000248
.0000482
.0000893
.0001585
.0002704
.0004454
.0007105
.0011003
.0016584
.0024940
.0036100
.0051230
.0071390
.0097860
.0000001
.0000003
.0000010
.0000040
.0000137
.0000487
.0001767
.0006535
.0025034
.0000953
.0009196
.0027990
.0063060
.0000003
.0000005
.0000011
.0000021
.0000042
.0000081
.0000153
.0000279
.0000494
.0000847
.0001407
.0002268
.0003555
.0005426
.0008078
.0011748
.0016719
.0023317
.0031913
.0042922
.0056800
.0000005
.0000011
.0000025
.0000062
.0000170
.0000499
.0001550
.0005030
.0016776
.0000897
.0006860
.0018549
.0038426
.0000003
.0000008
.0000021
.0000048
.0000101
.0000199
.0000369
.0000647
.0001084
.0001742
.0002699
.0004050
.0005904
.0008386
.0011639
.0015815
.0021084
.0027625
.0035626
.0045284
.0056800
.0000008
.0000021
.0000056
.0000152
.0000407
.0001092
.0002932
.0007876
.0021143
.0001831
.0010176
.0022942
.0041406
.30
1.02
2.98
7.90
18.89
41.93
87.12
170.75
317.94
565.21
963.96
1583.47
2513.67
3867.34
5781.20
8415.52
12223.80
17092.26
23425.72
31510.57
41659.97
.93
2.98
7.98
30.34
97.95
320.96
1066.55
3580.60
12265.64
600.58
4903.30
13574.43
28212.43
2.89
5.08
9.41
17.71
33.20
61.16
109.94
192.07
325.67
535.76
855.73
1328.42
2007.09
2955.87
4249.68
5973.57
8221.45
11094.20
14697.21
19137.48
24520.33
4.91
9.44
20.21
47.56
120.99
328.35
935.66
2757.76
8246.91
564.89
3661.66
9029.35
17344.77
2.89
7.71
18.40
39.96
80.16
150.17
265.23
445.07
714.13
1101.56
1640.97
2369.93
3329.26
4562.20
6113.40
8027.90
10350.01
13122.33
16384.74
20173.45
24520.33
7.32
18.49
46.47
116.54
290.31
719.31
1769.00
4312.78
10375.44
1152.81
5423.40
11148.63
18669.60
I
-------
206
Table B-14: Phenanthrene Solubility in Ethanol/Water Mixtures
Solvent Solvent UNIFAC
Mole
Frac.
Volume
Frac.
Mole
Frac.
Sol.
Excess
Free
Energy
Mole
Frac.
Sol.
Log-linear UNIFAC
Mole Sol.
Frac.
Sol.
Excess Log-linear
Free sol.
Energy
Sol.
[-]
[-]
[-]
[-]
[-]
[mg/lj [mg/l] [mg/i]
.0000
.0500
.1000
.1500
.2000
.2500
.3000
.3500
.4000
.4500
.5000
.5500
.6000
.6500
.7000
.7500
.8000
.8500
.9000
.9500
1.0000
.0419
.0716
.1167
.1705
.2357
.3163
.4185
.5523
.7351
.3836
.6101
.7864
.8946
.0000
.1453
.2641
. 3631
.4468
.5185
.5806
.6349
.6829
.7255
.7636
.7979
.8289
.8571
.8829
.9065
.9282
.9482
.9667
.9840
1.0000
.1238
.1994
.2991
.3990
.4990
.5991
.6992
.7994
.8996
.6678
.8348
.9224
.9648
.0000000
.0000002
.0000009
.0000032
.0000089
.0000213
.0000474
.0000852
.0001500
.0002473
.0003861
.0005762
.0008277
.0011510
.0015567
.0020560
.0027253
.0034810
.0043780
.0054310
.0066500
.0000002
.0000004
.0000015
.0000050
.0000168
.0000557
.0001817
.0005864
.0018967
.0001256
.0008869
.0025427
.0042740
.0000003
.0000010
.0000034
.0000102
.0000269
.0000623
.0001293
.0002437
.0004230
.0006844
.0010429
.0015104
.0020943
.0027976
.0036192
.0045542
.0055949
.0067314
.0079524
.0092460
.0106000
.0000008
.0000017
.0000050
.0000155
.0000496
.0001606
.0005093
.0015347
.0042641
.0003560
.0022267
.0053019
.0078169
.0000003
.0000013
.0000047
.0000132
.0000319
.0000677
.0001299
.0002297
.0003800
.0005942
.0008865
.0012706
.0017597
.0023659
.0030998
.0039710
.0049870
.0061541
.0074768
.0089582
.0106000
.0000011
.0000024
.0000068
.0000193
.0000552
.0001577
.0004510
.0012907
.0036966
.0003243
.0018724
.0046959
.0073264
.30
1.86
7.58
23.73
60.98
134.69
280.24
472.03
781.49
1216.15
1798.07
2547.53
3482.34
4618.12
5968.44
7545.13
9587.23
11756.70
14214.59
16972.40
20025.43
1.44
3.57
11.35
35.66
108.80
322.31
926.54
2586.33
7050.87
667.33
3695.09
9046.77
13935.29
2.89
9.09
27.67
75.74
183.37
394.55
763.76
1348.67
2201.26
3359.98
4844.83
6655.87
8774.74
11168.26
13792.89
16599.33
19536.47
22554.56
25607.50
28654.18
31659.28
7.55
14.86
39.25
110.47
320.54
928.02
2592.81
6746.79
15747.03
1889.40
9237.38
18727.51
25277.40
2.89
11.95
37.79
97.85
217.36
428.27
766.97
1271.29
1977.66
2918.55
4120.69
5603.97
7380.97
9457.16
11831.40
14496.72
17441.27
20649.38
24102.39
27779.64
31659.28
9.69
20.21
52.96
137.97
356.55
911.36
2296.89
5679.19
13672.63
1721.60
7776.19
16613.55
23718.29
-------
207
Table B-15: Xylene Solubility in Methanol/Water Mixtures
Solvent Solvent UNIFAC Excess
Mole
Volume
Mole
Free
Mole
Frac.
Frac.
Frac.
Energy
Frac
Sol.
Mole
Sol.
Frac.
Sol.
[-]
[-]
[-]
[-]
[-]
Log-linear UNIFAC
Sol.
Excess Log-linear
Free
Energy
Sol.
[mg/1] tmg/1]
Sol.
[mg/1]
.0000 .0000 .0000177 .0000333 .0000333 103.99 195.62
.0500 .1055 .0000438 .0000669 .0000988 242.48 369.92
.1000 .1993 .0000980 .0001376 .0002600 511.90 718.51
.1500 .2833 .0002015 .0002824 .0006182 997.00 1397.11
.2000 .3590 .0003863 .0005702 .0013489 1815.39 2677.76
.2500 .4275 .0006981 .0011228 .0027336 3121.85 5012.47
.3000 .4898 .0012210 .0021462 .0051971 5203.75 9114.33
.3500 .5468 .0020230 .0039741 .0093466 8227.01 16048.03
.4000 .5990 .0032325 .0071257 .0160108 12553.48 27308.72
.4500 .6470 .0050040 .0123779 .0262761 18563.37 44850.04
.5000 .6914 .0075350 .0208536 .0415180 26696.74 71002.37
.5500 .7325 .0110800 .0341222 .0634254 37466.18 108216.50
.6000 .7707 .0159550 .0543130 .0940160 51423.95 158598.80
.6500 .8062 .0225600 .0842350 .1356443 69175.89 223296.70
.7000 .8394 .0450000 .1275014 .1909992 126831.40 301923.20
.7500 .8705 .0625000 .1886516 .2630937 164901.00 392296.50
.8000 .8996 .0900000 .2732677 .3552468 219069.00 490699.30
.8500 .9270 .1500000 .3880804 .4710585 320771.60 592615.70
.9000 .9528 .2000000 .5410592 .6143802 388055.70 693652.70
.0472 .0999 .0000418 .0000643 .0000933 231.90 356.59
.1003 .1999 .0000984 .0001382 .0002614 514.08 721.40
.1604 .2997 .0002070 .0003274 .0007320 1013.24 1602.06
.2292 .3998 .0005494 .0008499 .0020546 2507.57 3874.43
.3084 .4998 .0013328 .0023856 .0057568 5635.27 10046.30
.4008 .5998 .0032560 .0071907 .0161434 12635.47 27534.15
.5099 .6998 .0081480 .0230414 .0452672 28605.06 77417.20
.6408 .7999 .0211930 .0778464 .1270383 65594.48 210311.30
.8005 .8999 .0950000 .2742542 .3562815 228965.30 491708.80
.3576 .5550 .0021773 .0043519 .0101737 8792.34 17437.61
.6184 .7841 .0181600 .0640197 .1079163 57481.34 180725.50
.8407 .9220 .1250000 .3640919 .4475534 280116.30 573602.70
.9033 .9544 .2000000 .5527156 .6249045 387636.50 700198.10
195.62
546.29
1357.12
3053.80
6313.10
12123.85
21815.93
37026.61
59572.32
91208.16
133292.30
186427.00
250192.40
323089.70
402742.80
486303.90
570923.30
654140.70
734111.00
517.46
1364.12
3575.19
9319.08
23937.45
60002.62
142933.10
309089.80
571766.00
39935.21
276067.10
638862.00
739242.60
-------
208
Table B-16: Xylene Solubility in Acetone/Water Mixtures
Solvent Solvent UNIFAC Excess Log-linear UNIFAC Excess Log-linear
Mole Volume Mole
Frac. Frac. Frac.
Sol.
Free
Energy
Mole
Frac.
Sol.
Mole
Frac.
Sol.
sol.
Free
Energy
Sol.
Sol.
[-] M
[-]
[-3
[-]
[mg/l] [mg/l] [mg/l]
.0000 .0000 .0000177
.0500 .1764 .0000603
.1000 .3114 .0001641
.1500 .4180 .0003797
.2000 .5043 .0007786
.2500 .5756 .0014561
.3000 .6356 .0025369
.3500 .6866 .0041823
.4000 .7307 .0066026
.4500 .7690 .0100744
.5000 .8027 .0149668
.5500 .8326 .0217785
.6000 .8592 .0311917
.6500 .8831 .0441513
.7000 .9047 .0619798
.7500 .9243 .0865494
.8000 .9421 .1205400
.8500 .9584 .1678190
.9000 .9734 .2340221
.0266 .1001 .000035
.0578 .1998 .000071
.0952 .2998 .000150
.1406 .3997 .000327
.1971 .4997 .000748
.2691 .5997 .001864
.3642 .6998 .005087
.4953 .7997 .016964
.6884 .8999 1.000000
.1364 .3912 .000407
.1546 .4266 .002021
.3634 .6991 .014591
.4783 .7886 .021650
.5229 .8168 .050920
.6161 .8672 1.000000
.6547 .8853 1.000000
0000333
.0000333
103
0001495
.0002052
307
0007662
.0008252
737
0032383
.0024766
1525
0106516
.0060310
2827
0277985
.0125835
4821
0597693
.0233439
7711
1098951
.0395218
11738
1783794
.0622295
17188
2622739
.0924151
24415
3564927
.1308257
33867
4551634
.1779950
46114
5527651
.2342502
61892
6448202
.2997295
82159
7281607
.3744067
108157
8008907
.4581180
141500
8621866
.5505885
184272
9120377
.6514571
239131
9509948
.7602997
309413
0000699
.0000934
190
0001939
.0002611
356
0006590
.0007324
682
0025171
.0020508
1343
0100072
.0057543
2735
0380217
.0161303
5968
1275534
.0452621
13960
3473550
.1268488
38474
7097207
.3562688
880202
0022425
.0018804
1685
0036512
.0027088
7998
1265194
.0449243
39292
3147074
.1131061
49708
4014827
.1513177
106390
5831916
.2543259
880202
6530637
.3063591
880202
.97 195.62 195.62
.01 761.09 1044.34
.28 3433.68 3697.16
.70 12879.90 9876.65
.62 37526.13 21549.67
.45 85795.70 40422.53
.89 159270.20 67508.01
.26 250285.50 102929.10
.07 346929.10 145994.40
.62 439364.40 195463.80
.50 522252.80 249871.40
.32 593920.20 307799.50
.82 654713.40 368053.30
.67 705780.40 429737.30
.70 748421.00 492260.60
.20 783814.40 555303.10
.50 812940.30 618766.90
.80 836582.40 682728.20
.20 855360.10 747397.60
.63 379.76 507.29
.19 966.76 1301.55
.71 2988.28 3320.11
.27 10236.71 8354.58
.05 35512.88 20689.80
.57 111127.40 49773.16
.48 277665.30 114428.80
.34 514932.90 244586.40
.30 739214.10 477701.30
.19 9211.28 7734.05
.21 14364.36 10691.72
.21 276115.80 113765.00
.03 487623.20 225746.50
.70 556478.30 276044.10
.30 672155.50 387793.80
.30 710127.90 435585.60
-------
209
Table B-17: Xylerfe Solubility in Ethanol/Water Mixtures
Solvent Solvent UNIFAC Excess Log-linear UNIFAC Excess Log-linear
Mole Volume Mole
Frac. Frac. Frac.
Sol.
Free
Energy
Mole
Frac.
Sol.
Mole
Frac.
Sol.
Sol.
Free
Energy
Sol.
Sol.
[-] [-]
[-]
[-]
[-3
[mg/l] [mg/l]
[mg/l]
.0000
.0500
.1000
.1500
.2000
.2500
.3000
.3500
.4000
.4500
.5000
.5500
.6000
.6500
.7000
.7500
.0419
.0716
.1167
.1705
.2357
.3163
.4185
.5523
.7351
.2612
.4026
.4968
.5779
.6072
.6354
.6955
.7705
.8047
.7977
.8357
.9013
.0000
.1453
.2641
.3631
.4468
.5185
.5806
.6349
.6829
.7255
.7636
.7979
.8289
.8571
.8829
.9065
.1238
.1994
.2991
.3990
.4990
.5991
.6992
.7994
.8996
.6579
.6852
.7613
.8156
.8331
.8492
.8806
.9156
.9301
.9272
.9426
.9672
.0000177
.0000749
.0002339
.0005834
.0012853
.0024716
.0043430
.0071085
.0109980
.0162530
.0231390
.0319330
.0550000
.0775000
.1000000
.1500000
.0000607
.0001264
.0003250
.0008181
.0020710
.0051350
.0127700
.0400000
.1250000
.0028240
.0112350
.0226430
.0475000
.0600000
.0675000
.1000000
1.000000
1.000000
1.000000
1.000000
1.000000
.0000333
.0001071
.0003265
.0008988
.0022125
.0048979
.0098588
.0182608
.0314772
.0510040
.0783622
.1150017
.1622221
.2211136
.2925221
.3770352
.0000887
.0001752
.0004636
;0013179
.0039423
.0121567
.0378852
.1169325
.3504551
.0236907
.0323238
.0763481
.1399707
.1699605
.2026562
.2855656
.4155590
.4848886
.4701825
.5532041
.7147806
.0000333
.0001490
.0005070
.0014063
.0033330
.0069809
.0132463
.0231971
.0380269
.0590005
.0873988
.1244696
.1713854
.2292125
.2988877
.3812054
.0001193
.0002603
.0007273
.0020373
.0057132
.0160295
.0450027
.1264030
.3553112
.0293791
.0389550
.0853345
.1493635
.1790166
.2111413
.2921099
.4187651
.4865014
.4721148
.5534883
.7131453
103.99
395.94
1122.70
2562.51
5198.27
9248.54
15092.02
23007.27
33228.88
45922.18
61224.18
79211.43
125417.40
163968.50
197662.10
269272.90
326.22
640.12
1513.13
3471.65
7920.40
17430.54
37630.55
97541.42
233611.50
12785.63
33825.50
60162.04
111762.20
134893.50
146646.00
198264.60
880202.30
880202.30
880202.30
880202.30
880202.30
195.62
565.57
1566.10
3942.91
8918.35
18183.78
33709.10
57377.38
90542.98
133674.00
186222.50
246768.30
313361.70
383919.90
456552.50
529752.70
476.49
886.75
2156.86
5581.84
14982.98
40449.76
105347.40
249714.90
507951.20
98700.99
92540.64
182601.10
283316.40
323325.40
363024.50
449973.00
559667.60
609242.90
599136.80
653701.10
745976.10
195.62
786.79
2430.25
6157.06
13381.23
25743.77
44848.96
71957.99
107730.80
152097.00
204292.30
263038.10
326792.40
393997.30
463264.70
533482.60
640.68
1316.99
3380.30
8605.32
21586.05
52760.99
123171.70
265873.00
512511.80
119794.40
109830.00
200740.10
298097.30
336292.50
374103.10
456977.30
562350.20
610452.30
600618.40
653894.40
745062.60
-------
210
Table B-18: Xylene Solubility in Propanol/Water Mixtures
Solvent Solvent UNIFAC Excess Log-linear UNIFAC Excess Log-linear
Mole Volume Mole
Frac. Frac. Frac.
Sol.
Free
Energy
Mole
Frac.
Sol.
Mole
Frac.
Sol.
Sol. Free
Energy
Sol.
Sol.
[-] [-]
[-3
[-3
[-]
[mg/l] [mg/1] tmg/l]
.0000
.0500
.1000
.1500
.2000
.2500
.3000
.3500
.4000
.4500
.5000
.5500
.6000
.6500
.0270
.0588
.0967
.1427
.1998
.2725
.1917
.4201
.5960
.6971
.0000
.1735
.3071
.4131
.4993
.5707
.6309
.6823
.7267
.7655
.7996
.8298
.8568
.8811
.0997
.1995
.2992
.3990
.4990
.5991
.4861
.7429
.8547
.9018
.0000177
.0001076
.0004055
.0011387
.0025805
.0050480
.0088650
.0143440
.0217690
.0400000
.0575000
.0800000
.0800000
.1500000
.0000505
.0001399
.0003956
.0009804
.0025730
.0065800
.0022786
.0300000
.1000000
1.000000
.0000333
.0001601
.0006436
.0020804
.0055199
.0124245
.0244727
,0432913
.0702183
.1061557
.1515224
.2062847
.2700343
.3420840
.0000789
.0002077
.0005912
.0017759
.0055003
.0171081
.0047524
.0835477
.2646184
.4167671
.0000333
.0001992
.0007897
.0023560
.0057290
.0119666
.0222561
.0378063
.0597522
.0890854
.1266124
.1729366
.2284593
.2933924
.0000930
.0002604
.0007282
.0020374
.0057106
.0160224
.0050015
.0706065
.2236727
.3632086
103.99
549.93
1831.07
4600.53
9412.17
16737.14
26862.41
39895.35
55779.16
93329.70
123534.40
158457.50
151438.60
251621.10
274.59
698.61
1800.03
4023.57
9388.51
20938.09
8448.87
73807.15
185305.50
880202.30
195.62
817.57
2903.73
8376.79
19948.43
40366.48
71409.52
113225.10
164364.60
222388.00
284623.90
348740.00
413009.70
476335.90
428.73
1036.88
2687.90
7267.23
19886.14
52971.22
17482.30
187015.00
407892.00
534608.90
195.62
1017.39
3560.70
9477.21
20690.81
38927.34
65285.12
100009.90
142528.20
191679.00
246023.70
304126.80
364745.50
426923.20
505.58
1299.71
3309.34
8329.15
20632.95
49748.03
18383.82
161567.60
359827.80
486331.30
-------
211
Appendix C
ERROR ANALYSIS FOR THE PREDICTION OF
SOLUTE SOLUBILITY IN CO-SOLVENT/WATER SYSTEMS
-------
212
Table C-1: Error Analysis for Naphthalene Solubility
in Methanol/Water System
Solvent
Experiment UNIFAC
Error
Free
Error
Log
Error
Energy
Linear
[% Vol.]
[mg/l]
[mg/l]
[%]
[mg/l]
[%]
[mg/l]
[%]
.0999
59.00
33.11
-43.88
47.45
-19.58
68.39
15.92
.1999
135.00
75.83
-43.83
81.81
-39.40
152.51
12.97
.2948
243.00
151.70
-37.57
146.91
-39.54
319.18
31.35
.3998
463.00
403.64
-12.82
319.56
-30.98
749.46
61.87
.4889
986.30
857.05
-13.10
647.10
-34.39
1512.86
53.39
.4998
1230.00
939.94
-23.58
707.83
-42.45
1647.77
33.97
.6225
2956.02
2680.84
-9.31
2042.20
-30.91
4296.77
45.36
.7061
6362.04
5493.30
-13.66
4377.16
-31.20
8185.01
28.65
.7493
9961.19
10923.72
9.66
6563.93
-34.10
11394.02
14.38
.8443
19831.08
18701.93
-5.69
16236.98
-18.12
23315.86
17.57
.9241
36590.70
37818.34
3.36
35038.51
-4.24
41992.95
14.76
.9968
70556.86
71586.50
1.46
70122.80
-.62
70667.29
.16
.9986
71093.43
72746.55
2.33
71351.28
.36
71588.69
.70
UNIFAC Excess Fre« Energy Log-Linear
Average Error -14.4 -25.0 25.5
Standard Deviation 18.0 15.1 19.2
Number of Points * 13
-------
213
Table C-2: Error'Analysis for Naphthalene Solubility
in Acetone/Water System
Solvent
Experiment UNIFAC
Error
Free
Energy
Error
Log
Linear
Error
[% Vol.]
tmg/l]
Emg/I]
[%]
Emg/I]
[%]
[mg/l]
[%]
.1001
111.00
28.86
-74.00
62.25
-43.92
81.88
-26.23
.1998
418.0
59.04
-85.88
169.42
-59.47
216.99
-48.09
.2998
1076.00
124.67
-88.41
566.60
-47,34
572.31
-46.81
.3997
3539.00
271.46
-92.33
2112.19
-40.32
1492.19
-57.84
.4997
10194.00
614.63
-93.97
8021.32
-21.31
3848.23
-62.25
.5514
23006.55
953.56
-95.86
15562.54
-32.36
6236.90
-72.89
.6214
40209.35
1750.25
-95.65
35873.58
-10.78
11883.48
-70.45
.6838
72889.01
3149.76
-95.68
69197.59
-5.06
20887.11
-71.34
.7093
106553.50
4027.69
-96.22
87882.03
-17.52
26218.75
-75.39
.7659
134162.00
7110.94
-94.70
138813.50
3.47
42958.41
-67.98
.8011
164479.00
10690.71
-93.50
174782.90
6.26
57945.71
-64.77
.8349
196467.00
15886.97
-91.91
209417.00
6.59
76769.38
-60.93
.8670
234097.00
23806.16
-89.83
239393.50
2.26
99623.70
-57.44
UNIFAC Excess Free Energy Log-Linear
Average Error -91.4 -20.0 -60.2
Standard Deviation 6.10 22.7 13.5
Number of Points « 13
-------
214
Table C-3: Error'Analysis for Naphthalene Solubility
in Ethanol/Water System
Solvent
Experiment UNIFAC
Error
Free
Energy
Error
Log
Linear
Error
[% Vol.]
[mg/l]
t mg/l 3
[%]
[mg/l]
[%]
[mg/l]
[%]
.3482
370.00
305.84
-17.34
399.87
8.07
586.00
58.38
.3929
.981.00
450.86
-54.04
586.51
-40.21
842.72
-14.10
.4486
1510.00
699.65
-53.67
975.62
-35.39
1350.57
-10.56
.4428
1895.00
796.21
-57.98
841.76
-55.58
1170.48
-38.23
.5375
3951.00
1426.09
-63.91
2192.58
-44.51
2802.79
-29.06
.6439
9853.00
3258.43
-66.93
5774.13
-41.40
6620.10
-32.81
.6998
13821.00
4972.19
-64.02
9503.83
-31.24
10317.38
-25.35
.7914
23653.00
10048.80
-57.52
20821.92
-11.97
21018.14
-11.14
.8620
36400.00
16980.26
-53.35
36583.27
.50
35739.49
-1.81
.9833
76588.00
42446.46
-44.58
85819.80
12.05
84959.86
10.93
1.0000
95116.73
48310.11
-49.21
95166.72
.05
95166.72
.05
UNIFAC Excess Free Energy Log-Linear
Average Error -53.0 -21.8 -8.52
Standard Deviation 13.6 24.0 26.8
Number of Points « 11
-------
215
Table C-4: Error Analysis for Naphthalene Solubility
in Propanol/Water System
Solvent Experiment UNIFAC Error
[% Vol.] [mg/l] [mg/l] [%]
Free Error Log Error
Energy Linear
[mg/l] [%] [mg/l] [%]
.2779 991.00
.3190 2003.00
.3951 4063.00
.5092 9996.00
.6515 19938.00
.7637 30839.00
.8783 74325.00
.9408 113061.00
193.47 -80.48
278.33 -86.10
538.16 -86.75
1397.98 -86.01
4325.33 -78.31
10329.17 -66.51
24207.25 -67.43
38680.04 -65.79
295.49
-70.18
432.49
-78.41
887.24
-78.16
2625.20
-73.74
9628.46
-51.71
24216.22
-21.48
53309.67
-28.27
75305.15
-33.39
339.36
-65.76
481.90
-75.94
918.09
-77.40
2382.16
-76.17
7591.44
-61.92
18294.27
-40.68
42822.42
-42.38
66215.20
-41.43
UNIFAC
Average Error -77.2
Standard Deviation 9.26
Number of Points = 8
Excess Free Energy Log-Linear
-54.4 -60.2
23.8 16.4
-------
216
Table C-5: Error Analysis for Naphthol Solubility
in Methanol/Water System
Solvent
Experiment UNIFAC
Error
Free
Energy
Error
Log
Linear
Error
[% Vol.]
[mg/l]
[mg/l]
[%]
[mg/l]
[%]
[mg/l]
[%]
.0000
845.90
1367.50
61.66
845.27
-.07
845.27
-.07
.0999
1283.00
2620.27
104.23
1202.34
-6.29
1619.56
26.23
.1999
2655.00
4903.62
84.69
1869.71
-29.58
3091.91
16.46
.2997
5104.00
8072.99
58.17
3143.46
-38.41
5871.45
15.04
.3998
9086.00
16448.31
81.03
5661.64
-37.69
11096.72
22.13
.4998
16788.00
29268.96
74.34
10774.56
-35.82
20776.85
23.76
UNIFAC
Excess Free Energy Log-Linear
Average Error
-77.4
-24.6
17.3
Standard Deviation
16.81
17.03
9.51
Number of Points » 6
-------
217
Table C-6: Error Analysis for Naphthol Solubility in Acetone/Water System
Solvent Experiment UNIFAC Error
[% Vol.] [mg/l] [mg/l] [%]
Free Error Log Error
Energy Linear
[mg/l] [%] [mg/l] [%]
.0000 845.90
.1001 2109.60
.1998 3653.30
.2998 6419.10
.3997 14948.00
.4997 71163.00
1367.50 61.66
2855.90 35.38
6142.49 68.14
13563.86 111.30
30769.84 105.85
95013.48 33.52
845.27 -.07
1359.75 -35.54
2872.76 -21.37
7314.78 13.95
20347.10 36.12
56111.40 -21.15
845.27 -.07
1675.63 -20.57
3289.25 -9.96
6413.70 -.08
12350.15 -17.38
23453.76 -67.04
UNIFAC Excess Free Energy Log-Linear
Average Error 69.3 -4.68 -19.2
Standard Deviation 33.4 26.6 24.9
Number of Points = 6
-------
218
Table C-7: Error Analysis for Quinoline Solubility
in Methanol/Water System
Solvent Experiment UNIFAC Error
[% Vol.] [mg/l] [mg/l] [%]
Free Error Log Error
Energy Linear
[mg/l] [%] [mg/l] [%]
.0000 6760.00
.0999 9872.00
.1999 19231.00
.2997 32840.00
.3998 71567.00
.4998 105925.00
3874.71 -42.68
8788.05 -10.98
19175.61 -.29
36549.58 11.30
89503.40 25.06
123049.20 16.17
6832.62 1.07
10047.33 1.78
15915.14 -17.24
26835.63 -18.28
47619.57 -33.46
87273.59 -17.61
6832.62 1.07
12861.90 30.29
24043.24 25.02
44442.00 35.33
80909.25 13.05
143448.40 35.42
UNIFAC Excess Free Energy Log-Linear
Average Error -0.238 -14.0 23.4
Standard Deviation 24.3 13.4 13.7
Number of Points = 6
-------
219
Table C-8: Error Analysis for Quinoline Solubility
in Acetone/Water System
Solvent
Experiment UNIFAC
Error
Free
Error
Log
Error
Energy
Linear
[% Vol.]
[mg/l]
C mg/l ]
[%]
I mg/l]
[%3
Cmg/I]
[%]
.1001
14603.00
7779.03
-46.73
10673.41
-26.91
12605.04
-13.68
.1998
34048.00
15829.47
-53.51
21111.05
-38.00
22969.19
-32.54
.2998
75378.00
33679.62
-55.32
48618.28
-35.50
41372.56
-45.11
.3997
125493.00
76713.59
-38.87
117552.30
-6.33
73060.05
-41.78
.4997
251189.00
210232.90
-16.30
266766.90
6.20
125827.90
-49.91
UNIFAC Excess Free Energy Log-Linear
Average Error
Standard Deviation
Number of Points *
-42.1
15.8
5
-20.1
19.3
-36.6
14.3
-------
220
Table C-9: Error Analysis for 3,5-Dichloroaniline Solubility
in Methanol/Water System
Solvent Experiment UNIFAC Error Free Error Log Error
Energy Linear
[% Vol.] [mg/l] [mg/l] [%] [mg/l] [%] [mg/l] [%]
.0000
692.00
732.27
5.82
781.19
12.89
781.19
12.89
.0999
1108.00
1822.23
64.46
1310.28
18.26
1789.81
61.54
.1999
2301.00
4073.73
77.04
2399.61
4.29
4069.70
76.87
.2948
3423.00
7434.55
117.19
4506.32
31.65
8663.40
153.09
.3998
7689.00
16764.61
118.03
10148.03
31.98
20642.87
168.47
.4998
13964.00
31669.08
126.79
22855.78
63.68
45653.98
226.94
UNIFAC Excess Free Energy Log-Linear
Average Error 84.9 27.1 117
Standard Deviation 46.1 20.9 79.5
Number of Points ¦ 6
-------
221
Table C-10: Error Analysis for 3,5-Dichloroaniline Solubility
in Acetone/Water System
Solvent
Experiment UNIFAC
Error
Free
Energy
Error
Log
Linear
Error
[% Vol.]
[mg/l]
[mg/l]
t%]
[mg/l]
[%]
[mg/l]
[%]
.1001
1551.00
1585.29
2.21
1393.32
-10.17
1745.47
12.54
.1998
2191.00
3435.55
56.80
3231.67
47.50
3845.21
75.50
.2998
3876.00
7506.54
93.67
9013.68
132.55
8414.01
117.08
.3997
8879.00
16476.74
85.57
27453.70
209.20
18158.00
104.51
.4997 21004.00
38655.10
84.04
82797.10
294.20
38552.01
83.55
UNIFAC
Excess Free Energy Log-Linear
Average Error
64.4
135
78.6
Standard
Deviation
37.5
122
40.5
Number of Points = 5
-------
222
Table C-11: Error Analysis for Aniline Solubility in Methanol/Water System
Solvent Experiment UNIFAC Error
[% Vol.] [mg/l] [mg/l] [%]
Free Error Log Error
Energy Linear
[mg/l] [%] [mg/l] [%]
.2805 81331.07 136564.40 67.9 78688.53 -3.25 108600.50 35.5
.3665 168783.40 175217.00 3.81 08544.00 -35.7 152381.50 -9.72
.4462 414731.70 217610.60 -47.5 48226.00 -64.3 205810.10 -50.4
UNIFAC Excess Free Energy Log-Linear
Average Error 8.06 -34.4 -8.85
Standard Deviation 57.8 30.5 42.0
Number of Points « 3
-------
223
Table C-12: Error Analysis'for Aniline Solubility in Ethanol/Water System
Solvent Experiment UNIFAC Error
[% Vol.] tmg/l] tmg/l] [%]
Free Error Log Error
Energy Linear
[mg/l] [%] [mg/l] [%]
.0499 33684.00
.1192 43070.00
.1836 50295.00
.2292 63534.00
93426.36 177.36
157456.40 265.58
286619.90 469.88
420407.30 561.70
39271.06 16.59
50234.19 16.63
64366.99 27.98
77322.62 21.70
41200.42 22.31
54833.25 27.31
71176.57 41.52
85305.48 34.27
UNIFAC Excess Free Energy Log-Linear
Average Error 369 20.7 31.4
Standard Deviation 178 5.40 8.36
Number of Points ¦ 4
-------
224
Table C-13: Error'Analysis for Phenanthrene Solubility
in Methanol/Water System
Solvent
Experiment UNIFAC
Error
Free
Energy
Error
Log
Linear
Error
[% Vol.]
[mg/l]
[mg/l]
[%]
[mg/l]
[%]
[mg/l]
[%]
.0000
2.90
.30
-89.66
2.89
-.34
2.89
-.34
.6521
1036.00
600.58
-42.03
494.65
-52.25
1009.51
-2.56
.8258
5133.00
4903.30
-4.47
3426.72
-33.24
5075.90
-1.11
.9082
10150.03
13574.4
33.7
8720.4
-14.0
10767.8
6.09
.9680
17786.99
28212.43
58.61
17136.88
-3.65
18446.07
3.71
1.0000
24520.33
41659.97
69.90
24520.33
.00
24520.33
.00
UNIFAC Excess Free Energy LogrLinear
Average Error 4.35 -17.3 0.963
Standard Deviation 61.9 21.3 3.26
Number of Points * 6
-------
225
Table C-14: Error Analysis for Phenanthrene Solubility
in Ethanol/Water System
Solvent
Experiment UNIFAC
Error
Free
Energy
Error
Log
Linear
Error
[% Vol.]
[mg/l]
[mg/l]
[%3
[mg/l]
[%J
[mg/l]
[%]
.6678
2404.00
667.33
-72.24
1664.61
-30.76
1516.75
-36.91
.8348
10317.00
3695.0
-64.1
8676.5
-15.9
7303.6
-29.21
.9224
17124.00
9046.77
-47.17
18188.32
6.22
16134.48
-5.78
.9648
22663.00
13935.29
-38.51
24946.03
10.07
23407.00
3.28
1.0000
31659.28
20025.43
-36.75
31659.28
.00
31659.28
.00
UNIFAC Excess Free Energy Log-Linear
Average Error -51.8 -6.07 *-13.7
Standard Deviation 15.8 17.0 18.2
Number of Points = 5
-------
226
Table C-15: Error Analysis for Xylene Solubility in Methanol/Water System
Solvent
Experiment UNIFAC
Error
Free
Error
Log
Error
Energy
Linear
[% Vol.]
Cmg/I]
[mg/l]
[%]
[mg/l]
[%]
[mg/l]
[%]
.0000
196.00
103.99
-46.94
195.62
-.19
195.62
-.19
.5550
8839.00
8792.34
-.53
17437.61
97.28
39935.21
351.81
.9220
217688.00
58471.34
-73.14
573602.70
163.50
638862.00
193.48
.9544
428636.00
387636.50
-9.57
700198.10
63.35
739242.60
72.46
.9709
697318.00
880202.30
26.23
765734.20
9.81
790482.70
13.36
UIMIFAC Excess Free Energy Log-Linear
Average Error -20.8 66.8 126
Standard Deviation 39.3 67.1 148
Number of Points * 5
-------
227
Table C-16: Error Analysis'for Xylene Solubility in Acetone/Water System
Solvent
Experiment UNIFAC
Error
Free
Error
Log
Error
Energy
Linear
[% Vol.]
[mg/l]
[mg/l]
[%]
[mg/l]
[%]
[mg/l]
[%]
.3912
3938.00
1685.19
-57.21
9211.28
133.91
7734.05
96.40
.4266
4813.00
7998.21
66.18
14364.36
198.45
10691.72
122.14
.8672
179336.00
880202.30
390.81
672155.50
274.80
387793.80
116.24
.8853
186956.00
880202.30
370.81
710127.90
279.84
435585.60
132.99
UNIFAC Excess Free Energy Log-Linear
Average Error 193 222 117
Standard Deviation 223 69.4 15.4
Number of Points = 4
-------
228
Table C-17: Error Analysis for Xylene Solubility in Ethanol/Water System
Solvent Experiment UNIFAC Error Free Error Log Error
Energy Linear
[% Vol.] [mg/l] Cmg/I] [%] [mg/l] t%3 tmg/l] [%]
.6579
10912.10
12785.63
17.17
98700.99
804.51
119794.40
997.81
.6852
56531.00
33825.50
-40.16
92540.64
63.70
109830.00
94.28
.7613
112270.00
60162.04
-46.41
182601.10
62.64
200740.10
78.80
.8156
197255.00
111762.20
-43.34
283316.40
43.63
298097.30
51.12
.8331
236654.00
134893.50
-43.00
323325.40
36.62
336292.50
42.10
.8492
285539.00
146646.00
-48.64
363024.50
27.14
374103.10
31.02
.8806
490114.00
298264.60
-39.14
449973.00
-8.19
456977.30
-6.76
.9156
663875.00
880202.30
32.59
559667.60
-15.70
562350.20
-15.29
.9301
716126.00
880202.30
22.91
609242.90
-14.93
610452.30
-14.76
.9272
753712.00
880202.30
16.78
599136.80
-20.51
600618.40
-20.31
.9426
786326.00
880202.30
11.94
653701.10
-16.87
653894.40
-16.84
.9672
809721.00
880202.30
8.70
745976.10
-7.87
745062.60
-7.99
UNIFAC Excess Free Energy Log-Linear
Average Error
Standard Deviation
Number of Points * 12
-12.6
32.9
79.5
231
101.
285
-------
229
Table C-18: Error Analysis for Xylene Solubility in Propanol/Water System
Solvent Experiment UNIFAC Error
[% Vol.] [mg/l] [mg/l] [%]
Free Error Log Error
Energy Linear
Cmg/I] [%] [mg/l] [%]
.4861 37964.00
.7429 148648.00
.8547 312010.00
.9018 548198.00
8448.87 -77.75
73807.15 -50.35
185305.50 -40.61
880202.30 60.56
17482.30 -53.95
187015.00 25.81
407892.00 30.73
534608.90 -2.48
18383.82 -51.58
161567.60 8.69
359827.80 15.33
486331.30 -11.29
UNIFAC Excess Free Energy Log-Linear
Average Error -27.0 0.028 -9.71
Standard Deviation 7.48 38.9 31.1
Number of Points « 4
------- |