v)
PB84-157148
MINTEQ--A COMPUTER PROGRAM FOR CALCULATING AQUEOUS
GEOCHEMICAL EQUILIBRIA
Battelle Pacific Northwest Laboratories
Richland, WA
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PROTECTION AGENCY
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MINTEQ—A COMPUTER
PROGRAM FOR CALCULATING AQUEOUS
GEOCHEMICAL EQUILIBRIA
-84-032
PB84-157148
ri
so
by
A. R. Felmy
D. C. Glrvln
E. A. Jenne
Battelle, Pacific Northwest Laboratories
Richland, Washington 99352
Contract No.
68-03-3089
Project Officer
R. B. Ambrose
Technology Development and Applications Branch
Environmental Research Laboratory
Athens, Georgia 30613
ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
ATHENS, GEORGIA 30613
REPRODUCED 8Y
NATIONAL TECHNICAL
INFORMATION SERVICE , ir, ,__,
U.S. DEPARIMENr OF COMMERCE UO'E'-A
SPRINGflElO. »A. 221J1, , , - . ,., .....
Heaaauarters ana Gnemical Libraries
EPA Was? Bida Room 3340
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
EPA-600/3-84-032
3. RECIPIENT'S ACCESSION-NO.
?%% u L > / 1« 8
4. TITLE AND SUBTITLE
MINTEQ—A Computer Program for Calculating Aqueous
Geochemical Equilibria
5. REPORT DATE
February 1984
6. PERFORMING ORGANIZATION CODE
7. AUTMOR(S)
A.R. Felmy, D.C. Girvin, and E.A. Jenne
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Battelle
Pacific Northwest Laboratories
Richland WA 99352
10. PROGRAM ELEMENT NO.
CCUL1A
11. CONTRACT/GRANT NO.
68-03-3089
12. SPONSORING AGENCY NAME AND ADDRESS
U.S. Environmental Protection Agency—Athens GA
Office of Research and Development
Environmental Research Laboratory
Athens GA 30613
13. TYPE OF REPORT AND PERIOD COVERED
Final, 9/81-8/83
14. SPONSORING AGENCY CODE
EPA/600/01
15. SUPPLEMENTARY NOTES
16. ABSTRACT •
MINTEQ is a computer program for computation of geochemical equilibria. MINTEQ
was developed for incorporation into the Metals Exposure Analysis 'Modeling System
(MEXAMS), a modeling system for the assessment of the fate and migration of selected
priority pollutant metals in aquatic systems. MINTEQ combines the best features of
two existing geochemical models MINEQL and WATEQ3. The mathematical structure was j
taken from MINEQL. The WATEQ3 features were added to this basic structure. The main •
features obtained from WATEQ3 are the well referenced thermodynamic data base, temper-!
ature correction of equilibrium constants using either the Van't Hoff relationship or
analytical expressions for the equilibrium constants as a function of temperature and
ionic strength correction using either the extended Debye-Huckel equation or the
Davies equation. Six different adsorption algorithms: an "activity" Kd, an "activity"
Langmuir equation, an "activity" Freundlich equation, an ion exchange algorithm, a
constant capacitance surface complexation model, and the triple layer surface complex-
ation model. In addition, a large number of user oriented features such as the abili-
ty to handle alkalinity inputs, an initial mass of solid, and different analytical in-
puts were incorporated.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.IDENTIFIERS/OPEN ENDED TERMS C. COSATI Field/Group
13. DISTRIBUTION STATEMENT
RELEASE TO PUBLIC
19. SECURITY CLASS (ThisReport)
UNCLASSIFIED
21. NO. OF PAGES
20. SECURITY CLASS (Thispage)
UNCLASSIFIED
22. PRICE
EPA Form 2220-1 (9-73)
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DISCLAIMER
The information in this document has been funded wholly or in part
by the United States Environmental Protection Agency under Contract No.
68-03-3089 to Battelle, Pacific Northwest Laboratories. It has been
subject to the Agency's peer and administrative, review, and it has been
approved for publication as an EPA document. Mention of trade names or
commercial products does not constitute endorsement or recommendation
for use.
The MINTEQ computer code has been tested against other computer
programs to verify its computational accuracy. Nevertheless, errors in
the code are possible. The U.S. Environmental Protection Agency assumes
no liability for either misuse of the model or for errors in the code.
The user should perform verification checks of the code before using
it.
ii
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FOREWORD
As environmental controls become more costly to implement and the
penalties of judgment errors become more severe, environmental quality
management requires more efficient analytical tools based on greater
knowledge of the environmental phenomena to b« managed. As part of
this Laboratory's research on the occurrence, movement, transformation,
impact, and control of environmental contaminants, the Technology
Development and Applications Branch develops management or engineering
tools to help pollution control officials achieve water quality goals.
Concern about environmental exposure to heavy metals has increased
the need for techniques to predict the behavior of metals entering
natural waters as a result of the manufacture, use, and disposal of
commercial products. Previously, mathematical models have been developed
to provide data on aquatic geochemistry, including metals speciation at
equilibrium. The modeling technique described in this manual combines
the best elements of two of these models and permits the user to examine
what species of a metal are likely to be present under different chemical
conditions in a water body. Because different species of a metal cause
different biological effects, this model should help users better relate
metals concentration and aquatic chemistry to observed effects. .
William T. Donaldson
Acting Director
Environmental Research Laboratory
Athens, Georgia
iii
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ABSTRACT
MINTEQ is a computer program for computation of gebchemical equilibria.
MINTEQ was developed for incorporation into.the Metals Exposure Analysis
Modeling System (MEXAMS) a modeling system for the assessment of the fate
and migration of selected priority pollutant metals in aquatic systems.
MINTEQ combines the best features of two existing geochemical models,
MINEQL and WATEQ3. The mathematical structure was taken from MINEQL. The
WATEQ3 features were added to this basic structure. The main features
obtained from WATEQ3 are the well referenced thermodynamic data base,
temperature correction of equilibrium constants using either the Van't Hoff
relationship or analytical expressions for the equilibrium constants as a
function of temperature, and ionic strength correction using either the
extended Debye-Huckel equation or the Davies equation. Six different
adsorption algorithms were added: 1) an "activity" Kg, 2) an "activity"
Langmuir equation, 3) an "activity" Freundlich equation, 4) an ion exchange
algorithm, 5) a constant capacitance surface complexation model, and 6) the
triple layer surface complexation model. In addition, a large number of
user oriented features such as the ability to handle alkalinity inputs, an
initial mass of solid, and different analytical input units were incorporated.
This report was submitted in fulfillment of Contract No. 68-03-3089 by
Battelle, Pacific Northwest Laboratories under the sponsorship of the U.S.
Environmental Protection Agency. This report covers a period from September
14, 1981 to August 31, 1983, and work was completed as of August 31, 1983.
iv
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CONTENTS
Foreword ii:L
Abstract ' * v
Figures • • • ' ' * * vi
Tables . . • • ' • • • • .• ' * " . V±1
List of Abbreviations and Symbols . . . • • • • viii
1. Introduction ...••••••
2. Conclusions . . • • • • • • *
A
3. Recommendations . • . - . .
4. Model Theory 5
Basic Formulations ...•••• 5
Adsorption ....«••• 15
Solid Phases • .37
5. Numerical Method . • « • • • • • 42
6." Thermodynamic Data Base 50
Introduction ...••••• ^0
Data in MINTEQ ....'•••• 51
s?
Accessory Data . . • • • • • Jf-
53
References - '
Appendix A
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FIGURES
Number Page
1 Schematic Representation of Surface Species and Surface
Charge-Potential Relationship for the Triple Layer
Model • *••....•• 24
2 Schematic Representation of Surface Species and Surface
Charge-Potential Relationship for the Constant
Capacitance Layer Model . .' . . ... . 25
3 Logic Diagram for Modified Line Search . . . 47
4 Example Convergence Pattern for Fe^*" Using the Modified
Line Search ......... 48
vi
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TABLES
Number . Page
1 * Derivatives for the Constant Capacitance and Triple
Layer Adsorption Models ....... 44
2 - Supplementary Data in the MINTEQ Data Base for Each
Species .......... 52
A.I Thennochemical Data for Aqueous Complexes
(Default Type II) 65
A.2 Thermochemical Data for Recox Reactions and
Gases (Default Type VI) ....... 75
A.3 Thermochemical Data for Minerals and Solids
(Default Type V or VI) . . . . . . . 76
vii
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List of Abbreviations and Symbols
A - Davies equation A parameter
A
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I - ionic strength
J. - - Jacobian matrix
*K - equilibrium constant for adsorption reactions written in terms of the
neutral sites (XOH) rather than the charged site (SO").
Kd - distribution coefficient
Kjct - "activity" Kd
Kex - equilibrium constant for ion exchange reactions
Kp - Freundlich constant
Kp-ct - "activity" Freundlich constant
K.J - equilibrium constant for reaction i
K|_ - Langmuir adsorption constant
K^ct - "activity" Langmuir constant
K° - equilibrium constant for reaction at 298.15°K
X - F/RT
m - total number of aqueous species
M.J - mass of solid phase i
n - total number of components
1/n - Freundlich constant
Na - Avagadro's number
Ns - surface site density
* - electrostatic potential at a designated adsorption plane
q.j - noncarbonate alkalinity factor for species i
R - ideal gas constant
s - number of aqueous species plus number of solid phases
S - total mass adsorbed in molal units
S - free or unoccupied surface sites
IX
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SA - specific surface area
a - total charge at a designated adsorption plane
SI - saturation index
Sj - maximum quantity adsorbed in Langmuir isotherm
TJ - total analytical concentration of component j
Xj - activity of component j
Yj - difference function (relaxed mass balance constraint) for component j
Z-j - charge on species i
Z(j,k) - Jacobian matrix of partial derivatives 3Yj/aXK.
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SECTION 1
INTRODUCTION
This report describes MINTEQ, a computer program for computation of
geochemical equilibria. MINTEQ combines the best features of its precursors
MINEQL (Westall et al.,1976) and WATEQ3 (Ball et al. 1981). Financial support
for the development of MINTEQ has come from several sources. Development of
the original WATEQ3 data base (Ball et al. 1981) was done by the United States
Geological Survey (USGS). Development of the mathematical structure in MINEQL
was supported under an earlier project funded by the Environmental Protection
Agency (EPA). Incorporation of the WATEQ3, features and adsorption algorithms
into the MINEQL mathematical structure was performed as part of EPA Contract
No. 68-03-3089. The objective of this contract was to develop a predictive
methodology for the assessment of the migration and fate of priority pollutant
metals in aquatic systems. To meet this objective, MINTEQ was coupled vTith
EXAMS, the Exposure Analysis l-fodeling System, through a user interactive
program. The complete geochemical-transport modeling system is called MEXAMS,
the Metals Exposure Analysis Modeling System. A separate report entitled
MEXAMS - The Metals Exposure Analysis Modeling System provides guidelines for
the use of MINTEQ. This report presents the chemical and mathematical concepts
embodied in MINTEQ. Since the mathematical structure in MINTEQ is the same as
in MINEQL, Westall's (1976) original notation will be used in this report.
MINTEQ provides a great deal of*flexibility in the way the user defines
the chemistry of the system being modeled. Although one does rvot need to
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master the concepts presented in this report to effectively use MINTEQ, a basic
understanding of the program will allow experienced users to solve a very broad
range of chemical equilibrium problems. It is recommended that the user begin
by reading the report entitled, MEXAMS - The Metals Exposure Analysis Modeling
.System.
This report is divided into three major sections. The first section
describes the equations for computing equilibria with regard to aqueous
speciation, adsorption and solid phases. The second section describes the
numerical methods employed to solve the chemical equilbrium problem and the
third section describes the thermochemical values which constitute the data
base.
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SECTION 2
CONCLUSIONS
The geochemical model MINTEQ is capable of calculating equilibrium aqueous
speciation, adsorption, gas phase partitioning, solid phase saturation states
and precipitation/dissolution. MINTEQ combines the best features of two
geochemical precursors; MZNEQL and WKSEF&. MINTED can solve a much broader
range of chemical equilibrium problems than WATEQ3, is more user-oriented than
MINEQL, contains a well referenced thermodynamic data base, and contains six
different algorithms for calculating adsorption.
MINTEQ, like MINEQL, has a general mathematical approach to solving the
chemical equilibrium problem. The general mathematical approach allows MINTEQ
to solve a broad range 'of chemical equilibrium problems.
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SECTION 3
RECOMMENDATIONS
The capabilities of MI-NTEQ would be extended if the thermodynamic data for
aqueous species and solid phases of additional elements were added to the data
base. Available data in the literature should be critically reviewed and the
most accurate values incorporated into the.MINTEQ data base. Furthermore, as
more reliable thermodynamic data for important aqueous species and solid phases
already in the model become available, they should be used to update the data
base thereby increasing the overall competency of the model.
MINTEQ does not have a kinetic capability, it is only a thermodynamic
equilibrium model. In many environmental systems the equilibrium assumption
may not be valid. Kinetics of solid precipitation or dissolution may dominate
the geochemistry of the system. Therefore, including kinetics of precipita-
tion/dissolution and of oxidation-reduction would be an important extension.
The elementary ion association models used in MINTEQ for computing
activity coefficients and aqueous speciation are not valid for high ionic
strength solutions (i.e., ionic strengths equal to or greater than sea
water). Higher order-ion interaction models described by (Pitzer 1973; Pitzer
and Mayorga 1973, Pitzer and Kim 1974) appear to be more reliable at high ionic
strengths (Harvie and Weare 1980). Such models should be incorporated into
MINTEQ for treating high ionic strength solutions where the ionic strength
exceeds approximately 0.7 molal.
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SECTION 4
MODEL THEORY
This section describes the formulation of the chemical equilibrium problem
in MINTEQ.. The equilibrium equations for aqueous speciation, adsorption and
solid phases are described.
BASIC FORMULATIONS
The chemical equilibrium problem can be described by a set of mass balance
equations, one for each component, and a set of mass action expressions, one
for each species. The problem then reduces" to solving the non-linear mass
action expressions with the linear mass balance equations. This is commonly
termed the equilibrium constant approach to the chemical equilibrium problem.
There are other formulations of the chemical equilibrium problem that are also
possible. As an example, at fixed temperature and pressure the chemical
equilibrium problem can also be solved by a direct minimization of the Gibbs
free energy or the Helmholtz free energy if the volume and temperature are
specified [see Van Zeggeren and Storey (1970)].
The equilibrium constant approach is used in MINTEQ. A basic set of
components is chosen and all mass action equations are written in terms of the
components [Equation (1)],
T1C1 = Kj l_ X/^'J) (1)
-------
where
Y-J - activity coefficient for species i
Cj = concentration of species i
Ki = equilibrium constant for reaction i
Xj = activity of component j
a(i,j) = stoichiometric coefficient of component j in species i
n = number, of components j.
The mass balance equations can then be written as a summation of the Ci
terms (Westall et al. 1976),
m
T, = I a(1.j) C (2)
J . i Jl '
Where
Tj = total analytical concentration of component j
m = number of aqueous species.
Equation (2) can be reformulated to make the solution to the chemical
equilibrium problem easier to solve by relaxing the mass balance constraint at
intermediate iterations (Westall et al. 1976),
m
Y = I a(i,j) C - T (3)
J i=1 i .J
-------
where
Yj = difference function for component j.
The solution is the set of all Xj terms such that all Yj terms equal
zero. The convergence criterion is described in Section 5.
The previous mathematical formulations are defined for systems without
solid phases. Solid phases are handled in basically two ways. The first
method treats the mass of each solid phase as an independent variable and
thereby expands the basic set of unknowns (i.e., the Xj terms) to include a
variable M.J for each solid phase. The mass balance equations can then be
written,
m s
Y, - -T. + I a(i,j) C - I a(i,j) M (4)
J J i=l n i=m+l n
where s = number of solid phases plus number of aqueous species. The summation
over the Mi terms then represents the mass of component j in solid phases.
This method is used in other geochemical models such as EQ3/EQ6 (Wolery
1979) and PHREEQE (Parkhurst et al. 1980).
The second method for handling solid phases is by what is termed a
"transformation of basis." This is -the method used in MINEQL and retained in
MINTEQ. The transformation of basis reduces the number of independent
variables which must be determined and also allows the treatment of different
chemical reactions in a mathematically general way. This latter attribute
allows MINEQL and MINTEQ to solve a wide range of chemical equilibrium
problems. The mathematical description, given in Appendix One in Westall
-------
et al. (1976), wi-11 not be reproduced here. Instead, the following example is
presented to clarify the approach. Suppose there exists a four component
system Ca , H+, COg and HgO, and the following reactions occur in aqueous
solution.
Ca2+ + H20 + CaOH+ + H+
Ca2+ + H+ + CO2' t
CO2" t CaCO° ,
H20 * OH" + H
log K°- = 12.6
log K° = 11.33
log K" = 3.15
log Kjl = -13.98
(5)
(6)
(7)
(8)
where log K° is the equilibrium constant for the stated reaction at 298.15°K.
If the solid calcite is now imposed as an equilibrium solid then one of
the Xj terms in the calcite dissolution reaction, Equation (9), is eliminated
computationally and all the reactions containing that component are rewritten
with calcite [CaC03(s)] as a component (Westall et al. 1976),
Ca2"*" + CO2" t CaC03(s) , log K° = 8.475
(9)
As an example, suppose XQ02- is eliminated then the reactions would be written
J
as:
Ca2+ + H20 * CaOH+ + H+ , log K° = 12.6
(10)
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CaC03(s) + H* + CaHCOj , log K° = 2.855 (II)
CaC03(s) t CaCOj , log K° = -5.325 . (12)
H20 * H+ + OH" , log K° = -13.98 (13)
Since the activity of pure calcite is equal to one, the set of independent
variables (Xj terms) is reduced by one. The transformation of basis is
completely general and, for example, can be applied to species present at a
fixed activity, gases at a fixed partial pressure, solids not present at unit
activity, or redox reactions which establish a fixed relationship between
components. . .
Activity Coefficients
The activity is related to the concentration by the activity coefficient
(y). MINTEQ corrects the equilibrium constants for ionic strength by a simple
rearrangement of the mass action expressions, thus
(14)
The resulting equilibrium constant Is termed a "mixed constant" because the
species formed in the reaction' is in terms of concentration and the components
are in terms of activities.
MINTEQ uses two alternate formulations for computing activity
coefficients: 1) an extended Debye-Huckel equation which contains two
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adjustable parameters (Truesdell and Jones 1974), and 2) the Davles equation
(Davies 1962). The extended Debye-Huckel equation,
where •
A(j and BQ- are the Debye-Huckel constants which depend upon the
dielectric constant and temperature,
Zi = charge on species i
a^ = ion size parameter
bj = ion specific parameter which allows for the decrease in solvent
concentration in concentrated solutions (Truesdell and Jones 1974)
I = ionic strength.
The Ad and Bd constants are computed as described in Truesdell and Jones
(1974). The a-j and b^" parameters were taken directly from the WATEQ3 data base
(Ball et al. 1981). The ionic strength is,
1 m 9
I =i )' -£ C. . (16)
c i=l 1 1
The a^ and b-j parameters are only available for the major ions and certain
trace metals such as Cu and Mn. In cases where a-j and'b^ are not available for
the species formed in the reaction, MINTEQ defaults to the Davies equation for
calculation of single ion activity coefficients,
10
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log YI »'-A-zf(—£—•--0.3 II (17)
1 1 1 + /T
Activity coefficients for neutral aqueous species are represented by
(Helgeson 1969),
log
MINTEQ sets aj to 0.1 for all neutral aqueous species.
The ion association models used in MINTEQ are not valid in high ionic
strength solutions (brines). The ion-interaction models published by Pitzer
(1973), Pitzer and Mayorga (1973) and Pitzer and Kim (1974) expand the basic
Debye-Huckel equation by adding a series of ion interaction terms* These
interaction terms are analogous to virial coefficients for non-ideal gases.
Such ion interaction models should be added to MINTEQ before it can be
accurately applied to high ionic strength solutions.
Activity of Water
The activity of water is calculated in MINTEQ by the relationship
m
n n = 1 - 0.017 £ C, (18)
2U i=l 1
where m is the total number of aqueous species. The expression is derived from
Raoult's law and is valid only for dilute solutions. The constant 0.017 is
11
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obtained from a plot of the activity of water versus number of solute ions
(Garrells and Christ 1965).
Temperature Correction
The equilibrium constants in the MINTEQ data base are valid at 298°K or
25°C. MINTEQ corrects these equilibrium constants to temperatures other than
298°K by. using either the Van't Hoff relationship or, whenever available,
analytical expressions for log K°. as a function of temperature.
The analytical expressions for log K° as a function of temperature are
expressed as:
log KT = A + BT + C/T + D Log1Q(T) + ET2 + F/T2 + 6//T (19)
where T is temperature in degrees Kelvin and A through 6 are empirically
derived coefficients. When analytical expressions for log K with temperature
are not available, the Van't Hoff relationship is used. The Van't Hoff
relation (Lewis and Randall 1961) takes the form:
AH° , .
log KT = log KJr - ^T (f - f-) (20)
r
where Tp is the reference temperature (298.15°K), AH0, is the enthalpy of
reaction, T is the specified temperature and R is the ideal gas constant. Data
for the enthalpy of reaction were taken from the WATEQ3 data base (Ball et al.
1981) and will be tabulated in Appendix A.
12
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The Van't Hoff relation assumes that AH0, is independent of temperature.
This assumption is not strictly valid so the Van't Hoff relationship may
produce substantial errors at temperatures significantly different from 25°C.
Unfortunately, data for AH°j298 or Io9 K expressions as a function of
temperatures are not available for all species in the MINTEQ data base. In"
such cases, the log Kr>298 is used at a^ temperatures. Because of these
»
limitations, applications of MINTEQ should definitely be limited to
temperatures less than 100°C.
Alkalinity Correction
Frequently, analytical data are available for total alkalinity but not
total inorganic carbon. In such cases, MINTEQ can convert total alkalinity to
total inorganic carbon. There are three important steps in the conversion.
The first step is to convert the input alkalinity expressed as carbonate
to equivalents; This is simply done by multiplying the input alkalinity value
by two since carbonate ion will consume two equivalents of acid per mole,
Equation (21).
T* = 2.0 T (21)
JJ
where jj represents C0|~, T 2 is the titration alkalinity in molality,
CUo
and Pjj is the titration. alkalinity in equivalents. -
The next step is to subtract the difference between the equivalents of
acid consumed by a carbonate containing--species and the stoichiometry of
carbonate in the species. As an example, the following species all would
13
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consume two equivalents of acid per mole, C0^~, PbCO°j, MgCO°j, and contain.only
one carbonate ion. This means each species consumes one excess equivalent of
acid per mole. This difference must be subtracted from the total alkalinity in
equivalents to obtain the correct total inorganic carbon. The number of equi-
valents of acid consumed per-mole of a carbonate containing species is termed
the carbonate alkalinity factor. The excess equivalents of acid consumed per
mole of carbonate containing species is then.
m
Ec = E Ci [fi •*(1»JJ)3 (22)
c n n
where
Ec = excess equivalents of acid
fi = carbonate alkalinity factor for species i •
a(i»jj) = molality of carbonate in species i.
The next step is to subtract the noncarbonate alkalinity. Noncarbonate
alklinity results from such species as OH", A1(OH)4, or HPof" which consume
acid during the alkalinity titration but do not contain carbonate. The
equivalents of acid consumed by nonarbonate containing species is,
(23)
where
EN = equivalents of noncarbonate alkalinity
q^ = noncarbonate alkalinity factor for species i.
14
-------
The noncarbonate alkalinity factor is the number of equivalents .of H+
consumed by a noncarbonate containing species if the solution were titrated to
approximately pH 4.6.
The final step in computing total inorganic carbon is to add the mass of
). The overall conversion can be 'summarized,
m m • •
0 (f-«>-l*c <24>
where -
TJJ = molality of inorganic carbon
f^ = carbonate alkalinity factor,
q-j = noncarbonate alkalinity factor
G.J.J = mass of H2C03(aq).
ADSORPTION
MINTEQ contains six algorithms for treating adsorption: an "activity Kd,"
an "activity Langmuir" isotherm, an "activity Freundlich" isotherm, an ion
exchange model and two surface complexation models, the constant capacitance
surface complexation model (Huang and Stumm 1973; Schindler et al. 1976; Stumm
et al. 1976), and the triple layer surface complexation model (Yates et al.
1974; Davis et al. 1978). This section presents a brief reviewof each model
and an outline of the mathematical formalism used by each model. For further
detail on the mathematical formalism of the constant capacitance model and the
triple layer model see (Westall 1979a, L979b; Westall 1980; Westall and Hohl
1980).
15
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The KH and the Langminr and Freundlich Isotherms
In this section, the traditional concentration K^ and the Langminr and,
Freundlich isotherms will be defined in terms of the total dissolved
concentration of the adsorbate. These isotherms and the K^ will then be
redefined in terms of the activity of the bare adsorbate ion and the
limitations of this treatment of adsorption will be discussed.
The distribution coefficient Kd is defined as the ratio of the amount
adsorbed to the amount remaining in solution. This can be conceptualized and
written as any other reaction. An example for cadmium is,
Cdtotal * SCd (25)
where S represents free or unoccupied surface sites, Cdtota^ = total dissolved
cadmium remaining in solution, and SCd = adsorbed cadmium in molal units.
The mass action expression for Equation (25) is the common definition of
the Kd,
(26)
where the implicit assumption is made that S is in great excess with respect to
Cdtotal and tne activity of S is set to one since with an assumed excess the
variability of S is negligible.
16-
-------
Activity Langmuir Isotherm
The'LangmuIr equation can be formulated as,
K.STC
rHrr. <27>
.
where
S = the amount adsorbed in molality
K|_ = the Langmuir adsorption constant
C = the total dissolved concentration in solution at equilibrium
ST = the maximum quantity that can "be adsorbed in molality.
Assuming that each adsorbing ion occupies only one adsorption site, then
Sj is also equal to the total number of adsorption sites. The Langmuir iso-
therm has the advantage over the activity Kj in considering a mass balance on
surface adsorption sites. The Langmuir equation as formulated in Equation (27)
is simply a combination of a mass action expression for adsorption and a mass
balance equation for surface sites,(a)
C + St S , (28)
ST = "S + S , (29)
(a) Note: In this formulation, competition between ions for surface sites can
be readily included by formulating additional mass action expressions
[Equation (28)] and then including the adsorbed species in the mass balance
[Equation (29)].
17
-------
where
S represents surface sites unoccupied by adsorbate.
If the adsorption data do not conform to a Langmuir plot, the Freundlich
equation frequently provides a fit to the data. The Freundlich equation is
formulated as,
S = KFC1/n . (30)
where Kp and 1/n are constants and C is the equilibrium total dissolved
concentration. For cadmium adsorption then,
SCd - Kp(Cdt()t)1/n . (31)
In this example, if the data conform to a Freundlich isotherm a plot of the
logarithm of SCd versus the logarithm of the concentration of total Cd in
solution at equilibrium (Cdtot) would yield a straight line with slope 1/n and
an intercept of log Kp. The Freundlich isotherm can then be thought of as an
adsorption reaction where the stoichiometry of the adsorbing species equals
1/n,
I + 1/n (Cd ) * SCd . (32)
tot
The mass action expression is then,
18
-------
(33)
tot-
There is no mass balance on surface sites and assuming an excess of sites with
respect to the absorbate the activity of the free sites (S) is set equal to
one. There is one complication in use of the Freundlich isotherm in MINTEQ and
that is in the stoichiometry of the adsorbing species. The stoichiometry of
the adsorbing species in the mass action expression equals 1/n; however, the
stoichiometry of the adsorbing species in the Cd mass balance equation equals
one. Thus, to use the Freundlich isotherm in a geochemical model requires
using separate stoichiometries for mass balance and mass action expressions.'3)
Equations (25) through (31) are written in terms of the total
concentration of the adsorbate Ctot (or Cdtot). Since Ctot involves all
aqueous species, this formulation implicitly assumes that all species absorb
with equal strength. There is abundant experimental evidence to support the
hypothesis that only certain aqueous species react with the surface (Huang and
Stumm 1973; Hohl and Stumm 1976; Davis and Leckie 1978). If Ctot is replaced
with .the activity of the aqueous species which dominates the adsorption
2+
reaction with the surface sites, say Cd in the above examples, then the
activity 1^ is
(a) Only the UNIVAC and VAX versions of MINTEQ have this capability. Thus,
the "activity" Freundlich isotherm cannot be used in the POP 11/70 version
unless 1/n = 1.0.
19
-------
The activity Langmuir equation is
..act ,. ,rH2+.
K, ST {Cd }
S = "SCa = L J - (35)
K {Cd}
and the activity Freundlich equation is,
S = K*ct {Cd2+}1/n (36)
where { } denote the activity of the adsorbing species, in this example Cd+^
ion, in bulk solution.
The dependency of the 'concentration' Kd and isotherms on adsorbate
aqueous complexation and ionic strength effects has been removed by usirrg the
'activity1 representation in Equations '(34) to (36). KJjct and the activity
isotherms are thus applicable over a wider range of natural water compositions
than the standard concentration representations.
A number of limitations remain, however. These descriptions of adsorption
do not consider: 1) a charge balance on surface sites and adsorbed species;
*
2) electrostatic interactions between the adsorbing ion and the charged
surface; and 3) reaction of the solid with aqueous constituents other than the
adsorbate'ion, e.g., H+ and major supporting electrolyte anions and cations.
The effect of these factors varies with changes in solution composition. Thus
failure to include these factors in describing adsorption limits the range of
applicability of that description. The surface complexation models described
below incorporate these effects and are thus more generally applicable.
20
-------
To use "activity" Langmufr/Freundlich isotherms in MINTEQ. the following
procedure (see MEXAMS - The Metals Exposure Analysis Modeling "Systems) should
be followed. For the activity Langmuir isotherm, include a surface site (i.e.,
SOH1 or SOH2) as a component and specify a mass total (equal to Sj) for that
component. Then enter the adsorption reaction as a type II inserted species
with an equilibrium constant of Kj[ct, and set the adsorption model (IADS) to
one. For the activity Freundlich isotherm, include a surface site (i.e., SOH1
or SOH2) as a.component and give it .a type III designation. Include the
adsorption reaction as a type II inserted species with an equilibrium constant
of Kpct» and set the adsorption model (IADS) to one. Finally, set the
stoichiometry of the adsorbing component to 1/n and set the stoichiometry in
the "8" matrix to 1.0.(a)
Ion Exchange
Ion exchange reactions are modeled in the same way as in the geochemical
model PHREEQE (Parkhurst et al. 1980). The reader is referred to this document
for details; only a brief summary will be presented here.
Ion exchange reactions involve the exchange of ions of like charge on the
solid surface. As an example, K+ ion could exchange for Na+ ion on the surface
of the exchanger S,
+ KS * .1C + NaS (37)
(a) Only the UNIVAC and VAX versions of MINTEQ have this capability. Thus,
the "activity" Freundlich isotherm cannot be used in the POP 11/70 version
unless 1/n = 1.0.
21
-------
where KS represents exchanger bound potassium'and NaS represents^exchanger
bound sodium.
MINTEQ, like PHREEQE, can model ion exchange reactions by maintaining a
fixed activity ratio of the exchangeable species. Equations (38) and (39)
present an example,
{Na+} (KS| ex
'-v 1_ /3g\
" ' ' ( '
The use of K£x assumes an infinite reservoir of exchanger at a constant solid
phase composition [i.e., KS/NaS remains fixed in Equation (39)]. This is
equivalent to assuming that the concentration of exchangeable species on the
surface is much greater than the concentration in solution. Therefore, even if
the concentration of the exchangeable species in solution is changed, the
activity ratio of the species in solution will re-adjust to the original fixed
value due to the large reservoir of exchangeable species on the solid.
Surface Complexation Models
The "activity" Kd, "activity" Langmuir, ""activity" Freundlich and ion
exchange treatments described above all ignore electrostatic effects due to
surface charge and the effect of solution chemistry on the solid. An
electrical charge frequently exists on the surface of solid particles and
creates an electrostatic potential which extends into solution. This
22
-------
electrostatic potential can significantly influence the adsorption of charged
species. In addition, pH and the concentration and composition of the
electrolyte alter the distribution and availability of the surface hydroxyl
groups which act as adsorption sites for the trace constituents, e.g., Cd. The
surface complexation models described below include treatment of these effects.
Both of the surface complexation models of adsorption in MINTEQ, the
constant capacitance model and the triple layer model, were developed for and
have been primarily applied to crystalline oxides (Davis et al. 1978). These
models have also been applied with considerable success to amorphous iron
oxyhydroxides (Davis and Leckie 1978, Benjamin and Leckie 1981) and to clays
(James and Parks 1982). Each model treats the oxide surface in contact with
water as an array of hydroxyl groups designated as XOH, where X represent
structural Si, Fe, Ti, Al, Mn or other atoms at the solid liquid interface.
(Figures 1 and 2). These hydroxyl groups or adsorption "sites" can be treated
as ligands which: 1) have specific acid/base characteristics, and 2) form
complexes with supporting electrolyte ions, metal ions or other ion-pairs in
solution. Adsorption reactions, i.e., the coordination of these solute ions
with surface hydroxyl groups, are treated by analogy with complexaton in bulk
solution. Thus, for an assumed stoichiometry of reaction, an association
(adsorption) constant can be used to describe the adsorption reaction. The
description which follows for surface sites,-XOH, can be generalized to include
additional surface sites, SOH or TOH, whose acid/base or cation/anion
coordination behavior differ from those of XOH.
Examples of surface equilibria for oxides are typically written for
protonation and deprotonation reactions as
23
-------
SCHEMATIC OF
SURFACE SPECIES
I
I
X--O-H°
X--0-O"
X--0-H2*
X--0-()"-Cda*
X--0-()~-CdOH*
X--0-H0 I
X - -0 - ( f- Na*
X--Q-H2*-CI
X--0-
SCHEMATIC
OF CHARGE-
POTENTIAL
RELATIONSHIP
"KCdOH
CONSTANTS IN TEXT
CORRESPONDING
TO SURFACE
SPECIES
DIFFUSE LAYER
'OF COUNTER IONS*
DISTANCE FROM SURFACE (x)—*•
FIGURE 1. Schematic Representation of Surface Species and Surface
Charge-Potential Relationship for the Triple Layer
Model. Brackets in the 'zero' plane indicate
deprotonated surface sites.
24
-------
SCHEMATIC OF
SURFACE SPECIES
SCHEMATIC
OF CHARGE-
POTENTIAL
RELATIONSHIPS
5
_r_t_
•3-
I
z
114
»-
o
Q.
X-
X-
X-
X-
X-
X-
X-
j
0
1
1
-0-H°
-o - { r
-0 - H8*
-0-H"
-0-Cd*
-o, 1
Cd°
-O'v
1
,
'
•
1 1
—• k2-
IX
V*i
V
1 \
V
-^-«aa |
~* Kai I CON*
} CORRES
** 'KCd, I TO SI
j SP!
f
•O' PLANE AT POTE
CHARGE O-Q
^ . 'd' PLANE OR OUT£
PLANE (OH)
mmtMjf\
* '
I
AND
ffo
|-«—DIFFUSE LAYER OF COUNTER IONS
DISTANCE FROM SURFACE (x) —*-
FIGURE 2. Schematic Representation of Surface Species and Surface Charge-
Potential Relationship for the Constant Capacitance Layer
Model Brackets in the 'zero1 plane indicate deprotonated
surface sites.
25
-------
+ + . lAurw /4QN
XOH + H* + XOH,, K . = :—S-T— v '
5 * 31 {XOH9} {H+}c
1 2J s
ynu - VfT 4. H 1^ . . => f41)
AUn - MJ -r H_ , N- - I vnul - • \^Ay
s a2
2+
respectively, and for adsorption of a divalent cation, M , as
Ixo~ Ml IH+I
XOH + M2+ I [XO- - M2Y + \f. *KM • -!— U—•*• (42)
5 S M 2t
where K, , Ka » are the first and second surface acidity constants, *KM is an
a -I "2 II.
adsorption constant, { } represents the activity of surface species XOH, XO",
XOHt, and (XO" - M2+) in moles per liter and { }s represents the activity of an
• y i
ion in the electrical double layer. The subscript "s" (Hs, M| ) indicates that
the H+ and M^+ ions are in the electric double layer rather than in the bulk
solution. The asterisk on the adsorption constant is a convention which
indicates that the adsorption reaction is written in terms of-the neutral site
XOH rather than a deprotonated site X0~.
A fundamental difference between adsorption reactions at the solid-
solution interface and aqueous coordination reactions in bulk solution is that
a variable electrostatic interaction energy exists between the charged
adsorbing ion and the surface charge on the solid (Figures 1 and 2). A
difference in chemical potential of the charged ion develops near the surface
due to the electrostatic potential, if>, produced by the surface charge, o.
Because of these nonideal interactions, the activities of ions approaching the
26
-------
surface are modified by the electrical work necessary to bring them from the
bulk solution to a specific adsorption plane within the -electric double
layer. The activities near the surface are related to the activities in bulk
solution by an exponential Boltzman factor which is a function of potential.
For any ion A , this relation is,
(AZ}S = {AZ}aq exp {-ZF
where 's' and 'aq1 refer to activities in the electrostatic double layer and in
bulk solution, respectively, Z is the charge on ion A, F is Faraday's constant,
R is the ideal gas constant in joules, T is the absolute temperature, and t is
the electrostatic potential on the surface or at the designated adsorption
plane within the double layer..
In MINTEQ, the activity coefficients for ions are calculated using the
Debye-Huckel or Davies equations. Since no adequate theory exists for
calculation of the activity coefficients for surface species, the activity
coefficients in MINTEQ for all surface species are set equal to one and the
activities, { }, of all surface species are replaced by concentrations, [ ]. .
The major differences betwen the constant capacitance and the triple layer
models, as normally formulated, are: 1) the set of surface species considered
{e.g., whether surface-electrolyte species are considered), and 2) the
description of the electric double layer, i.e., the definition and assignment
of ions to "mean" planes of adsorption within the double layer and the
mathematical form of the surface charge-potential relation, a = f(i|>).
27
-------
The mass action and mass balance equations in both the constant
capacitance and the. triple layer models are similar. For mathematical
simplicity in MINTEQ, the Boltzman factor in the mass action equations for
surface species, e.g.,
[XOH+ 1 = [XOH] {H}a exp (-F+/RT)
aq
is treated as though it is just another chemical component. This new component
is the coulombic or electrostatic component, X(o). From Equation (3) above,
the mass balance equation used in MINTEQ to check convergence of each
electrostatic component is,
m
Y(o) = I a(1»o) C. - T(o)
The electrostatic components are unique in that there is no measurable
analytical value for total surface charge, T(a). A value for T(a) is
calculated using the mathematical expression relating surface charge to
potential, a = f(ip)i where f(ip) depends on the model of the electrical double
layer used. Thus, T(o) = f(i|») B, where the factor B converts coulombs of
charge per square meter into moles of charge per liter.
With this b'rief introduction, the constant capacitance and triple layer
models will be described below for the case where adsorption occurs from a
28
-------
solution containing Na+, Cl" and so|~ as the major electrolyte ions and Cd2+
ion as the dilute adsorbate. Surface ligands consist of a single amphoteric
surface site, XOH.
Constant Capacitance Model
With this model, all specifically adsorbed ions (H+, OH~, and Cd2+) are
considered to be located in the surface lo' plane, contribute to the charge 00'
and are .subject to a potential, ip0, as shown in Figure 1. Ions which are not
specifically adsorbed are excluded from the double layer and are assumed to be
located in the diffuse layer. The dominant contribution to o0 is from the
potential determining ions H+ and OH~. It is assumed that the ions of the
background electrolyte, Na+, Cl~, and S0^~ do not coordinate with the surface
sites.
In the double layer, the surface charge-potential relationship used is the
simple linear expression, a0 = C1^, where the capacitance of the double layer,
C1 , is assumed to be constant. The surface hydrolysis and adsorption reactions
together with the acidity and adsorption constants for the surface species as
shown in Figure 1 are,
[XOht]
XOH + Hit XOH~ K. = - ^-r- exp (Xt!>) (43)
5 c 1 [XOH] (H >
XOH = XO- + H+ Ka = rrc^olfl * exp (-**„} (44)
4* — ?4* 41
XOH + Cd2+ = (XO- -Cd2+) + H^ *KrH = rXO -Cd 1 f H 1 ^ j (45)
S S . Cdl [XOH] J
?x 9+ n C(XO")9 -Cd2+] {H+}2
(XOH)2 + Cd2+ = f(XO-)2 -Cd2+)° + 2H!, *KC = - ? - - '— (46)
L S * S W2 [(XOH)]
-------
where X = F/RT, { }aq = { } represents the activity in the bulk solution;
(XOHJg and (xo~)2 represents two adjacent XOH and XO" sites, respectively,
acting as a single surface ligand,(a) and [ ] represents the concentration of
surface species.
In MINTEQ, the surface sites, XOH, are treated as a chemical component,
X(XOH). The mass balance equation for surface sites is,
Y(XOH) = I (all surface sites) - T(XOH) (47)
where
= [XOH] + CXO"] + [XOH2] + [XO" -Cd2+] + 2HXO')2 -Cd2+]
is the sum of the concentrations of all of the surface sites as calculated from
the mass action equations and T(XOH) is the analytical total concentration of
surface sites in moles of sites per liter,
T(XOH) = Ns SA CS/NA
Here, NA is Avagadro's number, SA is tne specific surface area of the solid
0" /g)» Cs is the concentration of the solid in suspension (g/fc), and Ns is the
analytically determined surface site density (number of sites/m2).
In the case of the coulombic or electrostatic component, X(aQ), the
equation describing the surface charge balance is,
(a) The UNIVAC and VAX versions, but not the PDP/11-70 version, of MINTEQ have
the capability to model reactions with different stoichiometries in the
mass action and mass balance equations.
30
-------
Y(OO) = I (charged species in V) - T(a- ) (48)
where the total surface charge (i.e., the net concentration of charged sites in
the 'o' plane in moles/fc) calculated from the mass action equations is,
Hspecles'tn v) = CXOHj] - [XCT] + [X(T -Cd2+].
Since no analytical value of J(o0) is available, the model dependent charge-
potential relation is used to define T(ao) 1n mo1es of charge per liter as,
T(°o) = a0 B = C !|;0 B ,
where B = ($A CS)/F. By analogy with all other components in the formulation
of the equ.ilibriiiim problem, the sum of charged surface species in Equa-
tion (48), calculated from the mass action equations, must equal the electro-
statically calculated charge T(o0), Equation (49), when the problem is solved.
When using the constant capacitance model, the coulombic component X.(ao)
(PSIO in the MINTEQ code), must be designated as Type VI (see users manual
MEXAMS - The Metals Exposure Analysis Modeling Systems) Since it has no mass in
aqueous solution. The input to MINTEQ requires: 1) an initial guess for the
value of the electrostatic component, e.g., for \p > 0, let log CX(aQ)] = -1.0;
2) the same value for the capacitance (C1) for a given ionic strength and
electrolyte as that used to derive the adsorption constants; 3) analytical
values for the surface site density (N$), the specific surface area (S^) and
the concentration of the solid in suspension (Cs); and 4) acidity and adsorp-
tion constants for surface hydrolysis and complexation reactions, determined
experimentally for a given ionic strength and electrolyte composition.
31
-------
For this model, in which coordination of the background electrolyte ions
with surface sites is ignored, both the capacitance, C1, and the adsorption
constants depend on the type and concentration of the background electrolyte,
and are applicable only at the ionic strength and for the specific electrolyte
for which the adsorption data were obtained. However, for applications where
the background electrolyte.is fixed and the concentration of strongly
coordinated electrolyte ions remain unchanged, use of the constant capacitance
model requires less experimental characterization than is required by the
triple layer model (described below). If, however conditions include variable
concentrations of strongly coordinating electrolyte ions, use of the constant
capacitance model would require new adsorption constants, derived from
experimental adsorption data, for each set of conditions, reminicent-of the
early Kd approach previously described. For.these conditions, the experimental
characterization required by the triple layer is less extensive than that
required by the constant capacitance model. This is a direct consequence of
the tr.iple layer model's inclusion of known electrolyte/surface reactions.
Triple Layer Model
This model treats the solid solution interface as being composed of two
constant capacitance layers bounded by a diffuse layer (Figure 2).
Specifically, adsorbed H+ and OH" ions are located in the surface 'o' plane,
contribute to the surface charge $Q, and experience an electrostatic potential,
a0. All other specifically adsorbed ions, including major electrolyte ions,
are located in the 'b1 or inner Helmholtz plane and are bound pairwise to
oppositely charged surface sites by either a specific chemical or an
electrostatic energy or both. These ions contribute to the charge, a^, and are
subject to an electrostatic potential", ^. The outer Helmholtz plane or the
32
-------
'd1 plane is-the inner boundary of the diffuse region of nonspecifically bound
counter ions. From theoretical considerations of monovalent electrolytes, the
potential, i^, in the 'd' plane is related to the total charge in the diffuse
region, o
-------
and in the 'd' plane
°d • C2(*d - *b)
The expressions for the surface hydrolysis reactions are identical to
those given.in Equations (43) and (44) for the constant capacitance model. The
adsorption reactions and constants for the other surface species shown in
Figure 2 are,
XOH + Na* = (X0~ -Na+)° + H*
[X0~ -Na+] {H+}
*KM, = —'- exp f-X(
-------
~ ~
XOH + (SOJ-)S + H+ = (XOH+ -
[XOH* -SOJj~]
*Kcn = » — exp (A(;p
iU4 [XOH] {-SOj"} {H*> °
Here, three electrostatic components, X(a0j, X(ob')> and X(od)> in addition to
the surface site component, X(XOH), are added to the normal set of chemical
components describing the aqueous equilibrium problem. Within the content of
the triple layer model, no bidentate surface species [(X0~)2 - Cd2+] have been
considered. The set of surface species shown in Figure 2, although not
necessarily unique, usually provides an adequate fit of experimental adsorption
data for mono- and divalent cations and anions.
As a consequence of the inclusion of surface-electrolyte coordination
reactions and the multiple layer structure of the interface, the acidity and
adsorption constants defined for the triple layer model are 'intrinsic'
constants, i.e., they are applicable over a wide range of pH, electrolyte" and
dilute adsorbate (Cd^+) concentrations. However, experimental data over a wide
range of chemical conditions is needed to determine these intrinsic constants
(Davis et al'. 1978; James et al. 1978; Balistrieri and Murray, 1979, 1981,
1982).
The mass balance equation for the surface site component, X(XOH), is
identical to Equation (47) except that,
? (surface sites) = [XOH] + [XOH2] + [XO"] + [XOH2 -C1"] + [XO" ~Na+]
+ [X0~ -Cd2+] + [X0~ -CdOH+] -t
35
-------
For the electrostatic components X(a0) and X(ab), the surface charge
balance equations are, respectively,
Y(°0) = I (charged species in V) - T(aQ)
Y(ab) = y (charged species in V) - T(ob)
where
+ [XOH2 -C1"] ' WH - W -Na+]
- [XO" -Cd2+] - [X0~ -CdOH+] + [XOH+ -SO2"]
and
* fspeci^in 'b<) = CX°" •Na+] ' CX°H2 -C1"3 + 2[X°" ^^.
+ [XO" -CdOH+] - aCXOH^ -SO2"]
The expressions for the T terms in these charge balance equations are T(o0) =
o0 B, and T(at,) = <*b B» wnepe B is. a constant defined on Page 31 and a0 and ob
are defined by the Equations (50) and (51). The summations of the charged
surface species in the V and V planes, calculated from mass action
equations, must equal the electrostatically calculated charge, T(o0), and
T(ob), respectively, when the equilibrium problem is solved. Since in this -
model there are no surface species assigned to the 'd1 plane, the net charge in
the diffuse layer, given by the Gouy-Chapman equation, must balance the
electrostatic charge on the 'd' plane given by Equation (52). Thus, the charge
balance equation for the electrostatic component, X(od), is,
36
-------
Y(ad) = ((-8e£oRTI)1/2 slnh(F*d/2RT)) - (C^ - y).
As equilibrium is approached during the numerical solution of the problem,
Y(0d) and the values of Y for all components approach zero.
When using the MINTEQ code to solve problems with the triple layer model,
an initial quess is supplied as input to the code for the electrostatic
components X(o0), X(ob), and x(ad) (PSIO, PSIB, and PSID, respectively in
MINTEQ). These components are given a Type VI designation (see the users
manual MEXAMS - The Metals Exposure Analysis Modeling System) because they have
no mass in aqueous solution. Other input data is similar to that required for
the constant capacitance model except that a second capacitance, C2, is
needed. It should be noted that the K values defined for the triple layer
model are not conditional constants, as is the case for the constant
capacitance model, but are invariant with respect to adsorbate concentration
below a surface loading threshold vfoich depends upon the adsorbate/surf ace
combination (Benjamin and Leckie 1981) and within the experimental range of pH
and ionic strength for which they were determined.
SOLID PHASES
Saturated Indices
The saturation indices are used to describe the apparent closeness to
equilibrium of a solid phase and the aqueous solution with which it is in
contact. For solid dissolution reactions, saturation indices can be formulated
in the following straight-forward manner:
37
-------
Si! -log (Kp)1 -log (I X^i'J)
i ii -j=l J
(53)
where SI, is the saturation index for species (solid) i.
The thermodynamic data base in MINTEQ was taken from WATEQ3 (Ball et al.
1981). All reactions involving solid phases were written as dissolution
reactions in WATEQ3. The mathematical formalism in MINTEQ requires all
reactions to be written as formation reactions. Therefore, all equilibrium
constants for solid phases in WATEQ3 were multiplied by minus one to convert
the log Kr values to association reactions. This also resulted in
Equation (53) being rewritten as
SI .log (K ) +.log [ J X^1'^]
1 r 1 j=l J
(54)
The Stable Phase Assemblage
This section describes how MINTEQ selects the thermodynamically stable
solids from the array of all considered solids (i.e., Type V solids) described
in MEXAMS - The Metals Exposure Analysis Modeling System. The procedure
described here has been modified only slightly from the original MINEQL
model. 'Equatiorv (55) is the mathematical relation which details whether a
solid will be present (i.e., in equilibrium),
r). + log £ X' < 0.
J ~X
log (K). + log £ X' < 0.0 . (55)
38
-------
This inequality simply means that at equilibrium all solids being considered
must either be in equilibrium o.r undersaturated. "To solve this inequality,
MINTEQ first ranks all considered solids by their tendency to precipitate. The
tendency to precipitate is estimated by dividing the saturation index by the
number of ions in the solid formation reaction. Dividing by the number of ions
is necessary because the saturation indices are a function of the manner in
which the chemical reaction is written. In the example below, doubling the
reaction stoichiometry doubles the saturation index. If the activities of Ca2+
and SOj-
are j x
Ca2+ + SO2" ± CaS04(s) , log Kp =4.0 , SI = -2.0 (56)
'2 Ca2+ + 2S02" ± 2CaS04(s) , log Kp = 8.0 , SI = -4.0 (57)
Dividing the saturation indices by the number of ions in the solid helps to
eliminate this effect.
After the solids have been ranked, MINTEQ, like MINEQL, precipitates the
solid with the highest ranking (i.e., equilibrates the solution with that
solid). The solids are ranked again and the process repeated until
Equation (55) is satisfied. If the selection process makes a wrong choice and
the mass of a previously precipitated solid becomes negative, then MINTEQ will
redissolve the amount of that solid phase which was precipitated and continue.
-------
Effect of Solids on pH and pE
The dissolution or precipitation of"solid phases can alter the pH or pE of
the solution, MINTEQ can model the changes in pH or pE as solids dissolve or
precipitate as long as the appropriate mass totals are known.
The mass total for H+ ion is-.determined by use of a form of the
electroneutrality condition called the "proton condition" which is defined as
the excess or deficiency of protons over the "zero level" species (Stumm and
Morgan 1970). The "zero level" species in MINTEQ are the components. If
anionic components are in their unprotonated forms and all cationic components
are the uncomplexed ions, then the proton condition corresponds directly to a-
mass total for hydrogen ion or the total ionizable hydrogen (Morel and Morgan
1972). If components are chosen which contain H+, for example HS~ or HCOo,
then'the proton condition does not have the physical interpretation of a total
mass of hydrogen ion but is still computationally valid.
To correctly predict changes in pH during precipitation or dissolution,
the initial proton excess or deficiency first must be determined and then
entered as the total mass of H+. To obtain the initial proton excess or
deficiency, one enters the measured pH and models the solution in MINTEQ
without permitting precipitation or dissolution of solids. The computed
aqueous mass of H+ is then the initial proton excess or deficiency. When this
value is entered as the total mass of H+, MINTEQ will compute the correct pH as
precipitation or dissolution occurs.
Electrons do not exist in aqueous solution. Therefore, to allow the pE to
vary during the precipitation or dissolution of solids, the mass totals for all
components of redox reactions must be known in the absence of solids. This may
require an initial modeling run at fixed pH and pE to obtain the mass totals
for all components of redox couples. Then one merely reenters the electron as
40
-------
Type VI (see the Users Manual" for MEXAMS - The Metals Exposure Analysis
Modeling System) and remodels the solution in the presence of solids. MINTEQ
will recompute the correct pE during precipitation or dissolution.
One of the advantages to this method of computing pH and pE is that H+ and
the electron are treated identically to all other components and the new pH and
pE are recomputed along with all other component activities.
Initial Mass of Solid
MINTEQ can accept input of a starting mass of solid. The initially
specified mass is added to the mass computed by MINTEQ from equilibrium
constraints. If the mass of solid (i.e., computed mass plus initial mass)
should become negative, then MINTEQ will dissolve the initially specified mass
of sol-id by adjusting the mass totals in the solid formation reaction and
removing the equilibrium constraint.
41
-------
SECTION 5
NUMERICAL METHOD
MINTEQ utilizes a Newt.on-Raphson iterative technique to solve the series
of simultaneous nonlinear equations relating component activity to total
mass. The technique is identical to that described by Westall et al. (1976)
except for modifications required for the constant capacitance and triple layer
adsorption models.
Given an initial estimate of all Xj values, MINTEQ computes all C^ terms
by Equation (1). The difference function (i.e., relaxed mass balance
constraint) defined by Equation (3) is then computed. The problem now reduces
to one of finding new estimates for the Xj values. In the Newton-Raphson
iteration technique, a new estimate for the set of components Xj is computed by
first differentiating the set of relaxed mass balance equations, Equation (3),
with respect to the components, Xk, to obtain the elements Zj^ of the n x n
Jacobian matrix,
Zjk = 8X = a(1»J) aC**) Ci/Xk
l\
where j and k vary from 1 to n and
42
-------
*V
^k =
except for electrostatic components. For a derivation of Equation (58) see
Westall et al . 1976. The correction vector &x_ is computed from the matrix
equation,
= y_
where A_X_ is equal to (^ - _Xj\|+i)» N is the iteration number and Z is the
Jacobian matrix of partial derivatives just computed. The system of linear
equations represented by this matrix equation is then solved by gaussian
elimination, and a new set of Xj terms are computed.
The convergence criteria used in MINTEQ is identical to the criteria in
MINEQL which is,
max Y.
J
(59)
where max Yj is the maximum of the terms comprising Yj and e equals 1 x 10~3 in
MINTEQ. In the absence of solids, maximum Y,- equals Tj.
In the case of the constant capacitance and triple layer adsorption models
gT-i/gXi f ° for the electrostatic components since the total charge depends
J J
upon the potential. The derivatives for the electrostatic terms have been
computed by Westall (1979b) and are summarized in Table 1.
43
-------
TABLE 1. DERIVATIVES FOR. THE CONSTANT CAPACITANCE AND
TRIPLE LAYER ADSORPTION MODELS (UESTALL 1979b)
Constant Capacitance Model
. B
Triple Layer Model
-- B
-' B
~* B
Z*b*d = * C2 TT- * B
ZV»b " " C2TT"''B
C^~' B
44
-------
Modified Line Search
The Newton-Raphson numerical method usually converges rapidly.
Unfortunately, there are cases when the method does not converge. One of the
most common instances of nonconvergence results from extremely poor starting
estimates for the component activities. This frequently occurs for such
components as Fe or U where the actual component activity is a small
fraction of the mass total. In such cases the default starting estimate of one
hundredth the mass total may be 20 or 30 orders of magnitude too high. Another
common case of nonconvergence is when an aqueous solution contains two major
components with essentially all of the mass of each component tied up in a
common complex. In such cases, the ionic strength also varies with the major
components activities and the numerical problem may become unstable.
For both' of these cases of nonconvergence, the problem can usually be
solved by making more accurate guesses for the component activities.
Unfortunately, this may be a time consuming process. To help solve these
problems, a modified line search has been included.
The modified line search is based on the fact that at convergence the
component activities at the current iteration are approximately equal to the
.activities at the previous iteration (i.e., XN « XN+1).(a) The line search
uses this fact to modify the component activities (Xj terms) computed by the
Newton-Raphson method. To understand the method, let X represent the component
activity before Newton-Raphson correction and Y the value after Newton-Raphson
correction. This means that at convergence, X = Y. The modified line search
then simply monitors the progress of the iteration scheme and uses previous X-Y
points to project new values for the component activities. The new values for
(a) The principal idea behind the modified line search was originally sug-
gested by Dr. John R. Morrey, Battelle, Pacific Northwest Laboratories.
45
-------
the component activities are obtained by either, extrapolation or interpolation
to the X = Y convergence line. The overall principal of the method is to
refine the component activities to be close enough to the.final solution values
that the Newton-Raphson method will converge. The new values for the component
activities are then used as the new starting estimates for the Newton-Raphson
iteration. Figure 3 presents a logic diagram of the method.
.An example convergence pattern for Fe is shown in Figure 4. Figure 4 is
a schematic of the following discussion. An initial estimate of the logarithm
of the activity of Fe3+ (X0) was made of -4.00. The Newton-Raphson iteration
then produced a new estimate (Y0) of -4.35. Since this is the first point, a
new X} was computed,
= -4.18
Newton-Raphson iteration then yields Yj = -4.52. Since both points are on the
same side of X = Y, and the computed slope is 0.96 and;since there are only two
points on this side of the line, the model chooses the closest point on the
X = Y line [i.e., X2 = (Xj + Yj)/2.0 = -4.35]. Newton-Raphson iteration
produces Y2 = -4.70. The point (X2,Y2) is on the same side of the X = Y line
as the previous points, and the computed slope between the last two points
equals 1.01. Now, however, there are three points on the same side of X = Y
and the algorithm extrapolates^ X'3 = 2 * X£a) = -8.70. Newton-Raphson then
returns a value of Y3 = -9.00. Since this is also on the same side of the
X = Y line and the slope is still approximately equal to one, the model
(a) In comparing Figure 3 XN_3 equals zero for the first extrapolation.
46
-------
c
START
MASS
BALANCE
WITHIN
50%
ARE
THERE AT
LEAST 3 POINTS
ON THIS SIDE
OFx
ALL
POINTS ON
SAME SIDE
OF x = y
SLOPE
> 0.95 and
< 1.05
FIND CLOSEST
POINT ON
OPPOSITE SIDE
OFx-y
EXTRAPOLATE
LAST 2 POINTS
TOx = y
LINE
INTERPOLATE
TOx = y
=(2.0-x«
•*
-------
-14
y -8-
-4 -
-2
-6
-8
-10
-12
-14
FIGURE 4. Example Convergence Pattern for Fe3+ Using the Modified Line
Search. All values as logarithm.
48
-------
extrapolates again X4 = 2X3 - XQ = -13.40. Newton-Raphson then returns Y4 =
-13.1. The point (X^.Y^) is now on the other side of X = Y and the model
interpolates a new point [X5 = (-slope-X4 + Y4)/(1.0 - slope)] = -10.9.
Newton-Raphson then .returns -11.1 which satisfies the mass balance criteria
within 50% and the line search is complete.
It should be remembered that the line search utilized in MINTEQ was tested
on only a few sample problems. The method is not intended to be used unless
the user has been unable to get the Newton-Raphson method to converge. In such
cases the method may prove useful but the users are advised that this option
should be used at their own peril.
49
-------
SECTION 6
THERMODYNAMIC DATA BASE
INTRODUCTION
The use of mass action expressions in MINTEQ requires the use of
equilibrium constants (log Kp.) at a reference temperature of 298. 15°K and zero
ionic strength for entry into the data base. Equilibrium constants are
extrapolated by MINTEQ to temperatures other than 298°K by use of the Van't
Hoff relation which requires the enthalpy of reaction (AH0, oga)' wnen
analytical expressions for log K°. are not available.
The equilibrium constants can be determined directly from solubility,
potentiometric, ion exchange or other analytical methodologies (Rossotti 1981),
or computed from calculated Gibbs free energies of reaction by the
relationship,
!09 K
r.298 2.303 RT
where AG° 298 = 5:AGf 298 (Products) - ^Gf 298* (reactants). The free energy of
formation (AG^gg) 1S related to the heat of formation and entropy by,
AGf,298 = AHf,298 ' 298'15 AS298 -'
50
-------
Calori metric measurements of the heat of solution and heat capacity can be
used to compute, AH0: and AS°>gg, respectively. The enthalpy of reaction is
readily computed,
r 298 = ^AHf 298 (Products) - 5-AH° 298 (reactan
-------
references do not give the primary source of the data but are intended as
indexes to the tabulations which give the specific reactions and data sources.
ACCESSORY DATA
In addition to thermodynamic data, the MINTEQ data base also contains
necessary supplementary data for each species. The data are summarized in
Table 2. Most of these parameters have been previously described in this
document or. the accompanying User's Guide MEXAMS - The Metals Exposure Analysis
Modeling System.
All Debye-Huckel parameters were taken directly from the WATEQ3 data base
(Ball et al. 1981), the majority of which were in turn obtained from the
tabulation in Truesdell and Jones (1974). Many of the Debye-Huckel parameters
in the WATEQ3 data base for aqueous species of Cu, Mn and Zn were estimated.
TABLE 2. SUPPLEMENTARY DATA IN THE MINTEQ DATA BASE FOR EACH SPECIES
- Charge
- Gram formula weight
- Carbonate alkalinity factor
- Extended Debye Huckel parameters
- Name
- ID Number
52
-------
REFERENCES
Baes, C. F., and R. E. Mesmer. 1976. The Hydrolysis of Cations. John Wiley
and Sons, New York, New York.
Balistrieri, L. S., and J. W. Murray. 1979. "The Surface of Goethite (aFeOOH)
in Seawater." In Jenne, E. A., ed., Chemical Modeling in Aqueous Systems
Speciation, Sorption, Solubility, and Kinetics. Am. Chem. Soc. Symposium,
Sen. -93, p. 275-298.
Balistrieri, L. S., and J. W. Murray. 1981. "The Surface Chemistry of
Geothite (aFeOOH) in Major Ion Sea Water. Amer. J..Sci. 281:788-806.
Baltstrieri, L. S., and J. W. Murray. 1982. "The Adsorption of Cu, Pb, Zn,
and Cd on Goethite from Major Ion Sea Water." Geochim. et Cosmochim. Acta.
46:1253-1265.
Ball, J. W., E. A. Jenne and D. K. Nordstrom. 1979. "WATEQ2: A Computerized
Chemical Model for Trace and Major Element Speciation and Mineral Equilibria
of Natural Waters." In Chemical Modeling in Aqueous Systems, ed.
E. A. Jenne, pp. 815-835. Amer. Chem. Soc. Symp. Series 93.
Ball, J. W., E, A. Jenne and M. W. Cantrell. 1981. WATEQ3: A Geochemical
Model with Uranium Added. U.S. Geol. Survey, Open File Report 81-1183.
53
-------
Ball, J. W., D. K. Nordstrom and E. A. Jenne. 1980. Additional and Revised
Thermochetnical Data and Computer Code for WATEQ2—A Computerized Chemical
Model for Trace and Major Element Sped at ion and Mineral Equilibria of
Natural Waters. U.S. Geol.. Survey Water Res. Invest. 78-116.
Benjamin, M. M., and J. 0. Leckie. 1981. "Multiple-Site Adsorption of Cd,
Cu,Zn and Pb on Amorphous Iron Oxyhydroxide." J. Colloid Interface Sci.
79:209-221.
Davies, C. W. 1962. Ion Association. Butterworths Pub., Washington D.C.
190 pp.
Davis, J. A., R. 0. James, and J. 0. Leckie. 1978. "Surface lonization and
Complexation at the Oxide/Water Interface: I. Computation of Electrical
Double Layer Properties in Simple Electrolytes. J. Colloid Interface Sci.
63:480-499. .
Davis, J. A., and J. 0. Leckie. 1978. "Surface lonization and Complexation at
the Oxide/Water Interface: II. Surface Properties of Amorphous Iron Oxyhy-
droxide and Adsorption of Metal Ions." J. Colloid Interface Sci. 67:90-107.
Garrels, R. M. and C. L. Christ. 1965. Solutions, Minerals, and Equilibria.
•Freeman, Cooper and Company, San Francisco, California.
54
-------
Harvie, C. E., and J. H. Weare. 1980. "The Prediction of Mineral Solubilities
in Natural Waters: the Na-K-Mg-Ca-Cl-S04-H20 System from Zero to High
Concentration at 25°C." Geochemica et Cosmochimica. Acta. 44:981-987.
Helgeson, H. C. 1969. "Thermodynamics of Hydrothermal Systems at Elevated
Temperatures and Pressures." Amer. J. of Sci. 267:729-804.
Helgeson, H. 'C., J. M. Delany, H. .W. Nesbitt and D. K. Bird. 1978. "Summary
and Critique of the Thermodynamic Properties of Rock-Forming Minerals."
Amer. J. Sci., 278-A.
Hohl, H., and W. Stumm. 1976. "Interaction pf Pb2+ with Hydrous y-Al203."
Colloid Interface Sci. 55:281-288.
Huang, C. and W. Stumm. 1973. "Specific Adsorption of Cations on Hydrous
Y-A1203." J. Colloid Interface Sci. 43:409-420.
James, R. 0., J. A. Davis and J. 0. Leckie. -1978. "Computer Simulation of the
Conductometric and Potentiometric Titrations of the Surface Groups on
lonizable Latexes." J. Colloid Interface Sci. 65:331-344.
James, R. 0.,' and G. A. Parks. 1982. "Characterization of Aqueous Colloids by
Their Electrical Double-Layer and Intrinsic Surface Chemical Properties."
Surface Colloid Sci. 12:119-216.
55
-------
Krupka, K. M., and E. A. Jenne. 1982. WATEQ3 Geochemical Model:
Thermodynamic Data for Several Additional Solids. PNL-4276. Pacific
Northwest Laboratory, Rich!and, Washington.
Lewis, G. N., and M. Randall. Revised by K. S. Pitzer and L. Brewer. 1961.
Thermodynamics. Second Edition, McGraw-Hill Book Company, New York,
New York.
Morel, F., and J. 0. Morgan. 1972. "A Numerical Method for Computing
Equilibria in Aqueous Chemical Systems." Environ. Sci. Tech. 6:58-67.
Nordstrom, D. K., L. N. Plummer, T. M. L. Wigley, T. J. Wolery, J. W. Ball,
E. A. Jenne, et al. 1979. "A Comparison of Computerized Chemical Models
for Equilibrium Calculations in Aqueous Systems." In Chemical Modeling in
Aqueous Systems, ed. E. A. Jenne, pp. 857-892. Amer. Chem. Soc. Symp.
Series 93.
Parker, V. B., D. D. Wagman and W. H. Evans. 1971. "Selected Values of
Chemical Thermodynamic Properties. Tables for the alkaline earth elements
(elements 92 through 97 in the standard order of arrangement)." U.S. Natl.
Bur. Standards Tech. Note 270-6.
Parkhurst, D. L., D. C. Thorstenson and L. N. Plummer. 1980. PHREEQE - A
Computer Program for Geochemical Calculations^ U.S. Geol. Survey Water Res,
Invest. 80-96, 210 p.
56
-------
Pitzer, K. S. 1973* "Thermodynamics of Electrolytes. I. Theoretical Basis and
General Equations.". Jour, of Phys. Chem. 77:268-277.
Pitzer, K. S., and J. J. Kim. 1974. "Thermodynamics of Electrolytes. IV.
Activity and Osmotic Coefficients for Mixed Electrolytes." J. Am. Chem.
Soc. 96:5701-5707.
Pitzer, K. S., and G. Mayorga. 1973. "Thermodynamics of Electroytes. II.
Activity and Osmotic Coefficients for Strong Electrolytes with One or Both
Ions Univalent." Jour, of Phys. Chem. 77:2300-2308.
Plummer, L. N., B. F.- Jones and A. H. Truesdell. 1976. WATEQF - A FORTRAN IV
Version of WATEQ, A Computer Program for Calculating Chemical Equilibrium of
Natural Waters. U.S. Geol. Survey Water Res. Invest. 76-13*
Robie, R. A., B. S. Hemingway, and J.. R. Fisher. 1978. "Thermodynamic
Properties of Minerals and Related Substances at 298.15 K and 1 Bar
(10^ Pascals) Pressure and at Higher Temperatures. U.S. Geol. Survey,
Bulletin 1452.
Rossotti, F. 1981. The Determination of Stability Constants. McGraw-Hill
Co., Inc., New York, New York.
Schindler, P. W., B. Furst, R. Dick and P. U. Wolf. 1976. "Ligand Properties
of Surface Silanol Groups: I. Surface Complex Formation with Fe , Cu ,
Cd2+, and Pb2+. J. Colloid Interface Sci.-55:469-475.
57
-------
Stumm, W., and J. J. Morgan. 1970. Aquatic Chemistry - An Introduction .
Emphasizing Chemical Equilibria in Natural Waters* John Wiley and Sons
Inc., New York, New York.
Stumm, W., H. Hohl and F. Dalang. 1976. Interaction of Metal Ions with
Hydrous Oxide Surfaces. Croat. Chem. Acta. 48:491-504.
Truesdell, A. H., and B. F. Jones. 1974. "WATEQ, A Computer Program for
Calculating Chemical Equilibria of Natural Waters." U.S. Geol. Survey J.
Res. 2:233-248.
Van Zeggeren; F., and S. H. Storey. 1970. The Computation of Chemical
Equilibria. Cambridge Univ. Press, London, England.
Wagman, D. D., W. H. Evans, V. B. Parker, I. Halow, S. M. Bailey and
R. H. Schumm. 1968. "Selected Values of Chemical Thermodynamic
Properties. Tables for the first thirty-four elements in the standard order
arrangement." U.S. Natl. Bur* Standards Tech. Note 270-3.
Wagman, D. D., W." H. Evans, V. B. Parker, I. Halow, S. M. Bailey and
R. H. Schumm. 1969. "Selected Values of Chemical Thermodynamic
Properties. Tables for elements 35 through 53 in the standard order of
arrangement." U.S. Natl. Bur. Standards Tech. Note 270-4.
58
-------
Wagman, D. D.,-W. H. Evans, V. B. Parker, R. H. Schumm and R. L. Hutall.
1981. "Selected Values of Chemical Thermodynamic Properties. Compounds of
Uraniuim, Protactinium, Thorium, Actinium, and the Alkali Metals. U.S.
Natl. Bur. Standards Tech. Note 270-8, U.S. Government Printing Office,
Washington, D.C.
Wolery, T. J. 1979. Calculation of Chemical Equilibrium Between Aqueous
Solution and Minerals. The EQ3/6 Software Package. UCRL-52658, Lawrence
Livennore Laboratory, Livermore, California.
Westall, J., 1979a. MICROQL I. A Chemical Equilibrium Program in BASIC. Swiss
Federal Institute of Technology EAWAG, CH-8600, Duebendorf, Switzerland.
Westall, J. 1979b. MICROQL II. Computation of Adsorption Equilibria in
BASIC. Swiss Federal Institute of Technology EAWAG, CH-8600, Duebendorf,
Switzerland.
Westall, J. 1980. "Chemical Equilibrium Including Adsorption on Charged
Surfaces." In Particulates in Water, ed. M. C. Kavanaugh and J. 0. Leckie,
pp. 33-44, Advances in Chem. Series 189.
Westall, J. C., J. L. Zachary and F. M. M. Morel. 1976. MINEQL, A Computer
Program for the Calculation of Chemical Equilibrium Composition of Aqueous
Systems. Tech. Note 18, Dept. Civil Eng., Massachusetts Institute of
Technology, Cambridge, Massachusetts.
59
-------
Westall, .0., and H. Hohl. 1980. "A Comparison of Electrostatic Models for the
Oxide/Solution Interface." Adv. Coll. Inter. Sci. 12:265-294.
Yates, D.. E., S. Levine and T. W. Healy. 1974. "Site-binding Model of the
Electrical Double Layer at the Oxide/Water Interface." Chem. Soc.
Faraday I. 70:1807-1818.
60
-------
APPENDIX A
REACTIONS AND THERMODYNAMIC DATA
This appendix contains a listing of the thermochemical data in MINTEQ.
The references are for the equilibrium constants and enthalpy of reaction data.
61
-------
Footnotes for Tables A-l, A-2, A-3.
(a) reaction written in terms of H+(aq) and
(b) reaction written in terms of CO^'(aq) rather than HCO^aq). For the
reaction:
H+ + GO?" ^ HCOo
*J O
log K = 10.33, AH° = -3.617 taken from Ball et al. (1981) to maintain
consist*
series.1
consistency with that data base. Log K is the same as in NBS 270
•ies.va;
(c) reaction written in terms of P0|-(aq) rather than HPof'(aq). For the
reaction:
log K = 12.346, AH° = -3.53 taken from NBS 270-3 and identical to the
values in Ball et al. (1981).
o
(d) reaction written in terms .of PO^aq) rather than HgPO^aq). For the
reaction:
2H+ + ~
log K =19.553, AH° = -4.52 taken from NBS 270-3(b) and identical to
the values in Ball et.al. (1981).
(e) reaction written in terms of Cu+l rather than Cu+2 and e~. For the
reaction:.
log K = -2.72 and AH° = -1.65 from NBS 270-4, which is also the same
values used in Ball et al. (1981).
(f) addition of WATEQ3 reactions 544 and 542 in Ball et al. (1981).
(g) reaction written in terms of COo'(aq) rather than H2C03(aq).
Thermodynamic data taken from NBS 270-3.
(h) reaction written in terms of HS~(aq) rather than S2~(aq). AG$ and
AH0: for HS'(aq) from NBS 270-3.
(a) The NBS 270 series referred to here consists of NBS technical notes 270-3
(Wagman et al. 1968), 270-4 (Wagman et al. 1969), 270-6 (Parker et al.
1971), and 270-8 (Wagman et al. 1981).
(b) AG? for H2P05(acl) in NBS 270-3 is in error and should be
-270.17 kcal.
62
-------
(i ) reaction written in terms of ^AsO^aq) rather than AsO^-(aq). For
the reaction: • -
+ 3H+ ^
log K = 20.6, AH° = -3.43 from NBS 270-3.
63
-------
Data Sources for Tables A-l, A-2, A-3.
1. Ball et-al. (1980)
2. Ball et al. (1981)
3.. Plummer et al. (1976)
4. Truesdell and Jones (1974)
5. Recomputed by Krupka et al. (a) who reference Dongarra and Langmuir (1980)
for the equilibrium constants.
6. Computed by Krupka et al. (a) who reference NBS 270-8 (Wagman et al.
1981).
7. Recomputed as part of this study using the data of Robie et al. (1978).
The calculations are consistent with the accepted ancillary data of Krupka
and Jenne (1981).
8. Recomputed as part of this study. AG* and AH* taken from Helgeson et al.
(1978). . •
9. Recomputed as part of this study. AG° = 65.9 taken from Truesdell and
Jones (1974) for:
Al2Si4010(OH)2 + 12 H20 ^2A1(OH)4 + 4H4Si04l + 2H+.
Reaction rewritten in terms of Al3+(aq) consistent with the ancillary data
of Krupka et al. (1982).
10. Recomputed as pact of this study. A 6° computed from log K in Baes and
Mesmer (1976) written with C02(g). AH2 taken from Robie et al. (1978).
All ancillary data taken from NBS 270-5 except Or+(aq) and Cu(0) from
Robie et al. (1978).
11. Krupka and Jenne (1982).
(a) Krupka, K. M., E. A. Jenne, and W. J. Deutsch (DRAFT). "Validation of the
WATEQ4 Geochemical Model for Uranium." PNL-4333. Pacific Northwest
Laboratory, Richland, Washington.
64
-------
TABLE A.I. Thermochemical Data for Aqueous Complexes (Default Type II)
cn
2
8937320
a
8937321
2
693S600
3
893sa01
3
•939802
3
6939603
3
893sa04
3
8937700
3
7)17)0*
3
7)17301
3
7317302
)
7)1730)
)
7317104
3
1,000 89)
KU02S04 AO S.IU0
1.0H0 091
NU02S04)2.2 b.ttfB
1,000 89)
KU02HPU4 AU -.tf.100
1.000 89)
1
1
it
1
KU02HP04I2 -11.39*
1.000 893
KU02H2PU4*! .1.700
l. ewe 693
MU02H2PU4)2 «!*,&
1.000 Of)
HU02H2P04)) »££.*
1,1(00 89)
KU02H3S104
1.000 89)
KS2 *2 II. 4
1,000 7J0
K63 .2 |U,4
1.000 U0
K84 «2 9.7
1.000 734
KS5 -2 9.3
I.UU0 730
KSt "i
1.000 7J|)
2
1
2
3
1
1
2
3
«
9
,000 180
2.709
,000 732
4.18)
,000 7)2
20.614
,000 986
42.986
,000 980
22,643
,000 960
44.70
,000 980
66,245
,000 980
•2.4
,000 770
•14,926
.000 Ml
•13,282
,000 731
•9.829
.000 731
•9.999
.000 731
•9.681
.000 731
I.OVO
2,0«0
2.0M0
4,000
6.000
•1,000
•1,000
•1,000
•1,000
•1,000
•1.0U0
330
310
3)0
330
330
330
330
330
330
330
330
•2.
0.
•2.
1.
0,
• | .
| ,
-2.
•2,
•2.
•2.
•2.
0.0'
0,0
0.0
0.0
0.0
0
0
0
0.0
»,*'
0.0
o.o
0.0
0,0
0,0
0.0
0.0
0,0
0
0
0
0,0
0,0
>>•
0,0
0,0
462.1910
966.0072
461.96*9
167.0191
464.002
960,969
169,139
64,186
96.192
120, 236
160,120
192,364
REFEHtNCC
2
2
2
9'
2
2
2
2
1
1
1
1
1
MAttO
REACTION NUN0ER
990
991
992
**»«
994
999
996
609
902
903
904
909
906
Reproduced from
best available
-------
TABLE A.I, (contd)
KEFCNtNCe
HATCQ
2 1.008 142 1.808 116 NBACUON N
^^^^^^
CTXJ
ni a
U.-D
-^
< £•
=^8
jj*n,-
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6912703
6912784
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6915600
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6919602
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KUDU tl ll.MJ .0,656
1.008 69| |,B06 2
«U(OH)2 »2 17.740 .•2,276
•2.808 110 1.008 691
KU(OH|1 t| 22.645 •4.919
1,008 691 4,688 2
NU(OH)4 AU 24.760 .6,494
1,000 B9| 4.608 2
KU(UH)5 -I 27.975 •11,120
1.000 091 9,808 2
HUF «1 5.050 6.699
1,000 691 1.6*6 270
KUF2 *2 7,200 14,497
1 1 0(00 V9| 4*0110 470
KUFJ-tl 7,150 19. 119
1.800 09| 1.688 278
KUM AD 4,600 21,640
1.000 891 4.808 276
»UFS .| 4,a5tf 29.218
1.000 69| 5.886 27B
KUF6 .2 3.SU0 27,716
1,800 091 6.686 278
KUCL »1 9.911 1,336
1.808 691 1,808 168
KU6U4 «2 3,700 9.461
1.000 09| 1.008 712
KU(604)2 «0 7.600 9.749
1.000 09| 2.608 712
KUHP04 »2 7.500 24.441
1.000 691 1.088 960
KU(HPO«)2AU |,7tf0 46,614
1,008 69| 2.688 968
KU(HP04)l-2 -7,600 67,964
1.000 69t 4.800 960
KU(nP04)4.4 -ib.sen 66.461
1.000 691 4,006 968
R|jU«J 11,161
l.tfuo 6Vt 1,000 270
KUU4F« -2 -l.lrf.1 12.607
l.tftfH OVt <4,000 270
Ki)U4Cl. tl 1 ,<*i3 U.220
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2,0MB
•1,0MB
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•9,800
1,606
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1,808
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338
336
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8.8
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•72.6417
•69.6911
186.8966
121,6699
•97,6274
•76,6296
199. 6249
114,0226
111,6216
192,6196
•71,4626
114,6986
418.1922
114,0864
429.9677
929. 96M
621(9469
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974.8781
699.1201
138,0172
190,0465
490,0559
269,0262
IBB. 8246
127,0210
346.6214
105.4608
2
2
a
2
2
2
2
•
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2
2
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8
2
2
1
9
2
2
2
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i
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949
946
947
946
94*
996
9S7
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996
999
961
961
564
* V
565
966
967
566
969
S7B
• •**
979
976
561
962
963
565
566
997
566
569
-------
TABLE A.I, (contd)
HATCO
a\
2 1,000 20 1.000 732
0204920 KA6N03 AO 0.riUUU .0,2900
2 I.0lfi0 2tt 1,000 492
02049|0 KAG(N02)2 • *.ri000 2,2200
2 1,00* 20 2.000 491
0201302 KA6UM3 .2 0.00B0 6.7100
2 1,000 2H 1.000 1)0 .
020)602 KACI) .2 .27.0)00 11.1700
2 1,000 M 1.000 )60
0201*01 HA614 .) 0.X000 14.0600
2 1,000 t» 4,006 380
0207302 KA6184)2 .3 0.0000 0,9910
4 1,000 20 2.000 7)0 •2,000 )30
0207)0) KA6»4»5 *) 0,0000 0,6600
4 1,000 2H 2,600 7)0 •2,000 110
0207104 KAB(H6)34.2 0.0U00 10.4)10
4 1,000 20 2,000 7)0 ^1,000 130
0201410 KAC FUCVATS 0,00*0 2,3990
2 1,000 20 1,000 141
0201420 HAG HUNATE 0.0000 2,1990
2 1,000 20 1,000 142
3300600 KH2A803 • 6.5b00 .V.2200
2 1,000 60 *1,000 130
1)00601 KHASOl «2 14,1990 •21.31
2 1,000 60 .2.000 330
1)00602 KA*U3 .) 20,2500 .14.7440
2 1,000 66 .3.000 330
1100610 HN4ASU1 « 0.0U00 .0.3090
2 1,000 60 1.000 330
1100611 KH2A804 . .I.H900 .2.2430
2 I.0U0 61 .1,000 330
1)00612 NHA»04 .2 -0.S200 .9.0010
2 I.0V0 61 i2,000 330
1100611 NAS04 *! 1.4100 .20.5970
2 1,000 61 .3.000 330
3101400 KMCOl . .1.6170 10,1300
1.00 2 1.000 140 1,000 330
1)01401 KH2C01 AO .2.2470 -16.601
2 1,000 140 2.000 3)0
1107)20 KHS04 . 4.9100 1.9870
2 1.0*0 712 1.000 110
1102700 KHF AW 1.4b00 1.1690
2 1.000 270 1.000 330
1302701 KHF2 - 4,5bU0 3.7490
2 2,0*0 270 1.000 330
1102702 KH2F2 *U u.Hrtiou 6.7660
2 2. HUB 2TM 2.000 130
13050U* KMPU4 -2 -J.ilUU 12.1460
2 l.dUtj ban 1.000 330
3105tt01 HM2P04 . -t.bcidD 19.5510
2 1.04* 500 2.000 330
31B7100 «M2» AQ -b.lorf 6,9940
2 I.Ome 710 1.000 130
3307)ul MS >2 Iri.lrtdd .|2,9|»0
2 I,JKB 7i4 «l,000 1)0
11U14|«I KH fULVATl 'J.^.lHd 4.2700
2 l.MMH 14) l.dOB JJB
1101420 KH rtUMilt rt.H.ioO 4.2700
0, 0.0 0,0 16,9,6720
•i. 0.0 0,0 199,6790
•2, 0,0 0,0 147,3600
•2, 0,0 0,0 460,5610
•3, 0.0 0.0 613,4650
•3, 22, • 0,0 364.1600
6,000 731
•). 24.0 0,0 196.4440
7,000 73}
•2. 19,0 0,8 269,1960
3.000 711
•1. U.0 0.0 797.0600
•1, 0.0 0,1 1107.6670
•1. 0.0 0,0 124.9350
•2. 0.0 0,0 123.9270
•3, 0.0 0.1 122.9190
1. 0.0 0,0 126,9910
• 1. 0.0 .0,1 140,9330
•2, 0.0 0,0 119.9270
•3, 0,0 0,1 130,9190
•1, 5.4 0,0 61.0170
0. 0.0 0,0 62,0290
•1, 4.9 0,0 97,0690
0. 0,0 0,0 20.0060
*l, 1,> 0,0 19,0040
0. 0.0 0.0 40,0120
>2. 5.0 0,0 99,9790
•i. b,4 0.0 96,9670
0. 0.0 0,0 34,0790
•i. b.0 0.0 12,0640
•1, u.tf 0,0 691,0060
>1, 0,0 0,0 2001.007k)
1
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473
414
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908
909
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462
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404
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39
202
203
937
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523
924
Reproduced from
best available copy.
-------
TABLE A.l. (contd)
00
2.00 2 .I.00H 64it 1,000 140
6001105 KC0(OH)4 -2. M.*tf00 .39,6990
i I.0BH 6»a 4.000 2 *4.0»0 3J0
6007121 KP0(I04)2.2 0.0000 1,4700
2 1.0U0 6«M 4,000 712
6001402 Kf>BhC03 * 0.0000 11,200
1.0' 1 I.0U0 6U0 1.000 140 1.000 3J0
9401100 NNiBft * 0.0000 ,,»»«„
2 . 1.000 •> . B0a 110
5401401 NNKul AU 0.0M00 ' 6.0700 '
2.00 2 1.0011 S4M t 000 Ua
5401402 KN11C01J2-2 0.0000 10,1100
9407121 HNI(SU4)2«2 0.0000 * I.020M
2 1,000 540 2. til a 732
020H00 KAIittft AU . 0.0000 4,2400
2 1,00(1 art i a00 IIB
020|10i KAUUN2 * . «i,0Mtf0 7,2000
2 1.00H 2» 2,000 1)0
0201400 KAbCL AU .rf,t>»00 3.2700
2 1.0 tit) «» t,000 100
0201801 KAUCL2 . .1.9300 5.2700
.1. . i i-1:"*8 "^ *••"• •••
0201802 KAGCul .2 0.0000 9.8900
on a <«0«a 2« i.«00 it«
U-D 020t«03 nAutui .3 a.0ui«0 9.5|00
0,0 2 1.0U0 ft 4.000*100
£g. aeajr,,,, KABf AQ .d.tt,MB' S,iJS0
£ij> 2 l.tlllH d4 1.H00 270
n 2_ 0207300 MAI>M$ AU il.MrtUU 14.0500
21 2 |,0t)U in l.tUt 730
"^ 02«<710I KAb(rlS)2 . M.UUtft) Id. 4900
53 2 J.UIDH in 2,000 730
t< 2 |,0t)M c!H 1,000 la*
^^ aatljanj KAU12 . r-.OOl.d 10,6800
E'jfi P203ii<0 AAUIIH AU H,«1HBB ' »}2 0*HW
^B^ 1 l.t«.»n ^» l,0t)0 *2 »i,0uo jia
1 ' l.i«nn !>.< tf,Mt)0 2 «2 Utfa li»i
ean/120 KAbsoa . i.^wu i.*v0«>
•" •»»! ||*
MKACTION N
•2. 0,0 0.0 17S.2I90
"»t 0,0 0,0 199.1110
1. 0.0 0.0 168,2070
1. 0.0 0.0 110,6140
It 0.0 0.0 ,94,1610
1, 0.0 0.0 77.7000
>. 0t0 0.0 79,7170
0. 0.0 0.0 92,7240
-It 0t0 0*0 109.7120
• (54.7710
0, 0,0 0,0 189.6160
It 0.0 0^0 119.7270
0. 0,0 0,0 110.7190
•2, 0.0 0,0 IT0.7280
-«, 0.0 0,0 290.0110
«. 0.0 0,0 107,7720
•t, 0,0 0,0 267.6760
•. 0.0 0.0 141,1210
•1, 0,0 0,0 (70,7740
.2. 0.0 0.0 214,2270'
.1, 0.0 0,0 249,6790
0. 0.0 0.0 126.8660
«, 0.0 0.0 140,9190
•1. 0.0 0.0 I74.UIIU
«. *.U 0,0 214,7720
-1, 0,0 0,0 361,6760
0, «.tt 0,0 124,67*0
•>!. 0,0 0,0 141,d820
•1. 0,0 0,0 201,9290 .
t
1
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1
t
,
1
t
1
1
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1
1(0)
1
1
1
1
1
t
1
1
1
1
1
t
1
I
1
1
1
469
470
401
404
409
406
407
408
409
518
919
920
921
***
522
421
422
421
424
425
426
427
428
429
430
431
412
433
414
-------
TABLE A.I, (contd)
HATED
NtACT ION NUMBER
2
16014M1
2
1.00 3
Ib0|40l
2.04 2
I6B712I
2
Ib0|4|0
2
1691420
2
600180)9
2
600|0ttt
2
b0UtV02
2
6B0|ttul
2
b00|400
4. 04 2
6H02700
2
bu027lo|
2
6002702
CD a
IfV
6002701
2
6003100
3
6003101
1
6001102
3
6001101
3
6004920
2
600T320
2
600T100
2
btlBTlttl
2
600JI04
3
bit)! IBM
2
b0B|30t
2
60I1J8B0
2
bB0J6ul
2
t>43\*al
I.OM0 IOH 1.000 letl
KCOI2 AU tt.mw* 3«*900
l.lftkM IB* 2.000 380
HCUhCUl « M, «« 12.400
1.000 Ib* 1.000 140 1.0t>0 310
KCUbOl AQ i*.HU«l0 5.1990
|.*0H Ibri 1.000 140
KCO(SJ4)2-2 «l,<«>i«i0 3,5000
t.itldtl Ibfl 2.000 732
KCU FULVATfc B.dilUll 3.5000
1, ft'* Ibg 1.000 141
KCU HOMATt H,H)«1«1 1.5H00
1,0MB Ib* 1.000 142
KPBCL t fl.JB^O 1.6000
1.00U avtit 1.000 180
HPBCL2 AQ l.rtBrlv) 1,8000
I.MOU 6>10 2.000 180
KPBCLl - i.tlM I.b990
I.Uikifl btie 1.000 180
APBCL4 -2 J.'JIOH 1.3800
1.HOI0 bu« 4.000 180
KPB(C03J2-2 *..IH«J« 10.6400
l.fciMM bMM 2.B00 140
NpttF * ti.viviotl 1.2S00
l.iDvlH b»n 1.000 270
HPB»-2 AU d.rtmJO 2.5600 •
1.000 b«iM 2.000 270
KPBI-3 - H.t^JKI.) 3.4200
I.0U0 bn^ 1.000 270
K,fi*M -2 0.«i«t)M 3,1000
1,0019 bu'il 4,000 270
Npoun t e.^udu -7.7100
l.titin bum 1.000 2 -1,0»0 310
UPBtOMJJ AU GI.I94b>0 .17,1200
I.0ti0 bt)«l 2.000 2 -2,000 310
KPt»(OH)l -
------- An error occurred while trying to OCR this image.
-------
TABLE A.I, (contd)
NCFCNtNtE
HATCO
KfcACTION NUM0ER
2.04 2
2311401
4.04 2
2311000
2
2311*01
2
2311602
2
2)l|801
2
2312700
2
2313)00
3
2313301
3
2313)02
3
2313303
3
2313)04
3
2317320
2
2317300
2
2)11402
1.00 3,
23t|410
2
2311420
2
9501800
2
9501001
2
9501802
2
9501003
2
9502700
2
950])00
)
95B))Hl
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950))k<2
)
95U))U)
J
9S01dt>4
1
•>4Hf)»i(*
i
95B71HI
«H7J*V>
1.000 2)| I
KCU(C03)2-2 0.tiil*0
1.000 231 2
KCUCl * fl. 65*0
1.000
KCUCi.2 AO
1.000
KCUCL) -
1,000
KCUCL4 .2
1,0*0
KCUK »
1,000
KCUUH *
1.0*0
KCUIOHI2 A
I.00HI
KCU IOM)) .
1.0*0
KCU ion) « .
1.000
2)| 1
10.5600
2)1 2
|). 6900
2)1 )
17.7H00
2)1 4
1.6200
2)1 1
0.0000
2)1 1
a 0.0000
2)1 2
0.0U00
2)1 3
2 0.0*00
241 4
KCU2(OH)2t2 ir.b)90
2.000
KCUS04 Afl
1,0*0
KCU(HS)) .
1,000
KCUhCOl t
1,0*0
2)1 2
1.22*0
2)1 I
0.0*00
2)1 )
a.0**B
2)1 1
KCU FUUVATE m,*0*0
1,000
KCU MUMATt
t,tJ*«
KZNCU »
1 «**0
KZNCt2 AQ
1.000
KZNUL3 •
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KZNCL4 .2
1.0*0
KZNf »
1.0*0
KZNUH t
1 .lADu
KZNCOH)2 A
1 . t)*M
KZNlOiOi -
1 •t**tl
KJN (OHM -
1 ,Bdi>
K/NUHCL AIJ
I.Mt'rt
KZN(Hi),! 4
I , <>l't<
H/NlrtiJi .
Mrtsn^Au
2)1 1
2)1* 1
7.7900
950 t
a(t>**0
950 i
9«^btt0
9bl» )
!*.96B0
9!>a 4
2,22u*
9it» 1
t 5.1990
9SM 1
i1 1
H.>IM»)«1
''bm 1
i) H.^IMH^I
4b<* 2
l'.»<«M
1 . lu.l.1
,
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,
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,
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,
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,
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000 140
9,8)00
000 140
0,4)00
000 160
0.1600
000 160
.2.2900
000 180
.4,5940
000 160
1.2600
000 270
.6,0000
000 2 "1.0B8 110
•11,6600
000 2 -2.000 330
.26,0990
000 2 .3,000 3)0
•)9,*000
000 2 .4,000,330
•10,1590
000 2 .2,0*0 1)0
2,3100
000 7)2
23,6990
000 730
13.000
000 140 1.0U0 3)0
*,I990
000 141
*,I990
000 142
0,4300
000 160
0.4500
000 160
0,5000
000 180
0.1990
000 160
1.1500
B00 270
.8,960*
000 2 *l,0*0 310
•16,6990
BBO 2 >2,0*0 1)0
-28,)99I>
000 2 •1,0*0 1)0
•41,199*
000 2 '4,*utf 1)0
-r.aaB*
HUB 2 •1,0*0 110
14,94*0
BB0 7 IB
16. 1MB*
"""z.l"*!
•2,
1.
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•1.
•2,
1,
1.
0,
•1,
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1.
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1.
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•2.
1,
1.
0.
•1.
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0.
1.U00
0.
-1.
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0,0
4.0
0.0
4,0
i.0
*>.0
4.0
0,0
0,0
0,0
0.0
0.0
0.0
0,0
0,0
0,0
4.0
0,0
. 4.0
b.0
0.0
U,0
0.0
0.U
tt.0
M.0
180
B.0
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0.0
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0
0
0
0
0
0
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10
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101,5*40
90,9990
134,4920
1*9,9050
205,1560
02,9440
00,99)0
97,9*00
114.9*00
131.9730
1*1,106*
199,*070
1*2,7*10
124,5*10
713.54*0
20*3,9450
100,0210
13*. 27*0
171.7290
207,1020
04,3*00
82.3770
99.3040
1
ll*,3920
133,3990
117,0)00
131.9130
1*4.5850
lbl,431U
1
1
1
1
1
1
1
1
t
1
1
1
1
lib)
1
1
t
1
1
1
1
1
1
1
1
t
t
1
1
2|0
211
212
219
*>•
219
216
217
210
219
220
221
222
910
927
920
291
292
293
294
295
29*
257
290
259
2*0
261
2*2
263
-------
TABLE A..1. (contd)
(0 fl> I
i*T) 1
i°
I rf»i 3.008 taa
HFtUMi t 0.0000 .5.6700
1.000 261 2, 000 8 .2,000 310
KFEUM)> AU 0,0000 •11,6000
1,000 26| 3,088 a -3, 8MB 330
KFIOH4 . 0.0000 •21,6008
1.00(1 2«l 4.000 3 -4,008 138
KFH12C04 »2 0.0088 24,980
1,000 2»| 1.008 980 2,000 130
1,000 2B|' 1.888*878
»FtF2 t 4,6000 t0.aaaa
|,B00 841 2.800 870
KFEF1 AU 5,1998 14,800
1.000 261 3.808 878
*Ft(a04)8 • 4,6888 5,428*
1,000 2»| 2,000 738
KFE FULVATt 0.0080 9,1448
I.0BB 88i i.aaa lit
HFC HUHATC 0.8000 9,1990
1.000 261 1.808 148
KFE2(OH)8t4 13.5000 .8,4300
. 2.800 86i a.aaa a .2,808 na
!b -
1 tfwti
ntULQi HI
470
".
470
a,
47ri
14
470
•t 0.
470
0.
47U
2.
Aij -H
47H
4.
4/M
.«
•fiit
^ ikl
-S a.
•i 4l1
1 >1.
^3(1
n.
I
000B
a
0008
1
,3998
|
0080
3
0000
1
1700
t
.3960
2
0000
1
.42
2
26
j
0
j
n
Jt
0MII0
.808 188
8.0418
.Baa taa
.,18900
,808 168
•10,5900
.800 8 -1.0W8 330
•34, 8000
.000 2 •1,000 330
0,8500
.800 878
8.8688
.800 732
0.6880
.808 492
11.680
,000 140 1.008 3J0
5.5
.800 160
5.78
,000 160
3,39
.000 730 6,000 fJi
2.66
.000 730 7.0U0 711
6.7300
1.
8,
a,
a.
i.
0.
i,
i.
9,
•1.
1.
1.
1,
a,
•it
i.
•it
i.
B.
0.
1.
•1.
.2,
•3.
•2,000
-3.
•2,000
B.
0.0
9,0
0.0
0,0
a. a
8.0
8.0
8,8
5.0
0,0
5,0
S.0
9.8
5.0
. 8.0
0.0
5.0
4.0
5.0
i!),0
310
25.0
310
0.0
8.8
••a
8.8
8.8
8.8
•.8
8.8
8,8
•*•
8.8
8.8
8,8
•.8
",8
8.8
8.8
8.8
0.8
8.8
0.8
0.0
8,8
0.0
69.6610
106.6690
181,8760
138,6)48
74,8490
93,0410
112.8420
847.9700
789.8478
8899.8460
145.7888
839,9788
101,8000
184,6870
134.347V
98,3910
125,6448
161.8970
161.8978
105,9608
1
73.9360
158.9990
178.9470
115,95*0
134. 4S2
169, 90S
320,056
352.122
123.b!>b0
HtFtHtNCt MATED
RUCTION NUMBER
1 102
1 183
1 104
MO! 196
1 169
1 166
t 167
1 331
1 989
1 986
1 334
t 139
4 126
41AI 189
4l*JI 130
t 178
1
1
1
1
1
1
1
UB)
I(F)
MF)
un
HF|
1
171
178
171
174
179
176
177
176
206
207
465
486
209
-------
TABLE A.I, (contd)
HtrtHtNLt
HATEO .
KEACT10N NUMBER
1.00 3
5007120
2
5005600
5002700
2
4107)20
2
4(05600
1
010)100
3
0)03)01
3
0303)02
3
0)02700
0302701
2
0302F02
2
0302701
2
0307120
2
1307)21
""** 2
00 0303)03
2&U3300
1
2»03)0l
3
2807)20
2
2805800
3
2603)02
2605801
3
2807300
2
2807301
2
2813)00
)
2815800
3
2817)20
2
2611600
2
2811601
2
2611802
I.0J0
KNAHPU4 -
1.00(1
KNAC AH
1,000
HH5U4 -
1.000
KKHPOt >
l.HIOil
KALOH *t
kALlGn)2 '
5,1*1 1.000 140 I.0U0 130
t.UeU 0,7000
5.1U 1.000 718
rt.MUdd 12,616
bwv) 1.400 560 1.000 310
«,ri»00 .0.9560
StM 1.000 870
2.2*00 0.6504
<4|M 1.000 732
M.MV>i!0 12*640
4|«i 1.000 560 1.0«0 I"
|l.dV90 .4.9900
1* 1.000 8 .1.000 330
» «.«000 .10.1000
1.00U 30
AA(.(On)4 . 4<4
1.000
H*U2* +
NAIM'AU
I.00H
KALF4 .
1,000
1.000
i0.
21,1
?.
^t
30*
2.
- 2.
1.00e IB
KALlOrO) AU 0.
I.WM0
KftOM «
1,000
KFtUhJ -I
1,000
KftSOl AU
KFt«2P04
KftUHi AC)
Ju
|i
2l)0
10
26H
2a«'
» 0.
20,1
So
1.000 2««
KftMPUd AH V,
1,00(1
1,000
HFtlHSJJ
1,0X0
KFtMPOd t
1,000
KftSCU *
I.0UH
KftCL «2
1 0M0
KFtcii *
1 ,000
KftlLi Al)
2bt)
AQ U.
2o«i
- «.
28ft
2 000 2 .2.0U0 H0
.W600 -23.0000
4.000 2 •«. 000 330
M»ik>0 7,0100
1 000 270
.U000 12.7500
2 000 270
•i«00 17.0200
3.000 270
*t>00 19,7200
4.000 270
i:>00 3,0200
1.000 732
8400 4.9200
2.000 732
0000 .16.0000
3.000 2 '1.000 310
,1990 -9.5000
1.000 2 -I.0U0 310
.1000 .11,0000
1.000 2 -3,000 310
2100 2.8500
1,000 738 .
MUU0 88.853
1.000 580 2.000 310
.5650 .20.5700
2.000 2 .2.0W0 110
t<000 15.950
1,000 580 1.000 330
M0U0 8,9500
2.000 730
MU00 10.9670
1.000 730
1D.J490 .2.1900
*"i,
).
2at
So/
£D|*
«.
1.000 2 -1.010 330
.Jut) 17*780
I.0U0 560 1.0D0 330
'MUM 3,9200
1.000 738
totttttf 1,4600
1.000. 180
tlUklB 2,1300
2,000 160
1U)«)H 1.110U
-I.
0.
2.
ti
-It
8,
I.
0,
•I.
t.
• 1.
0.
it
•i.
0.
t.
0.
0.
0.
-1.
2.
1.
1.
i.
\.
0.
0.0
5,«
4.4
»,4
4,
s.
*.
0.
4.
4,
4.
0.
b.
*.
0.
i.
0.
0*
0.
0.
5,
5.
5.
5.
i.
4
4
0
5
5
ft
0
0
0
0
4
0
0
0
k)
,
0
4
0
0
0.0
0,0
0,0
0,0
0,0
0,0
0,
0,
».
0,
0,
0t
o.
,0.
0.
0.
0.
0.
0.
0.
0.
0t
0,
0.
0.
0.
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
i.0 0.0
U.0
0.0
119.0510
116.9690
41,9660
135.1630
115,0810
41,9660
60,9960
95,0110
45,9790
64,9760
63,9760
108.9750
181,0410
819,1040
76.0010
78,6540
106,6690
151.9060
158.6140
69.6610
151.8260
121,9900
155,0680
72.6540
151.6260
151,9060
91,3000
186,7530
168,2060
1
UCJ
2
1
Kb)
1
1
1
4
4
4
4
1
1
1
1
t
1
410)
4
41CJ
1
1
. 1
11C)
1
1
I
1
71
30
540
78
32
80
81
82
83
64
65
86
67
68
336
2
3
8
120
105
136
476
477
t
119
. 4
5
6
7
Reproduced (rom
best available copy.
------- An error occurred while trying to OCR this image.
-------
TABLE A.2. Thermochemlcal Data for Redox Reactions and Gases (Default Type VI)
MATED
HtAdioN NUMBER
2«I2«0« rt+3/Ft*2 -10,
s • i.aad 2Bi
4700020 KHNU4 - U6.
4 1,94(1 4M
4700021 KHNU4 -2 1S*».
4 I.0U0 470
4914920 NU2/NU1 -«1.
4904920 NN4/N01 -18/
5 -1,000 49*
0600610 »SOi/AS04 -1*.
S 1.MU0 bl
8908910 U+l/UUf+2 -lit,
S 1.0H0 891
B4ln91iA U*4/U02t2 -14
S |,0UI» 8)5
1 I'. 0*K 891
4714700 HN»imi*2 iS.I
i 1,000 ir*
2102H0 CO»l/Cl)»a 1.61
1 1. HUM 1,
4 l.MUH I'll
3301403 CU2(GA8) -»,i
I l.viuu \<**
1100021 02CAQ) s»10
1 i.fOrt 2
1I«|0022 U2(A<1) CALL H>.
3 2 kH6U ?
89155105 KUblOn)l5t9 4
1 6,d«iti »'M
1100021 02(t>AS) l>i>,
* 41, Bd
8.000 1
tl 18.16
2.000 110
.45.54
•4.000 110
»1 .85,98
-4,000 110
-17,229
15,1100 2 •
t>l .81.120
-4,000 110
I.0W0 1
•e, 000 310
-0.000 110
2.0U0 130
•1.UU0 2
2.0U0 110
4,0U0 310
4,000 310
•1.0B0 892
•1.000 471.
•1.0W0 210
8,000 1
10.0U0 110
•i,0U0 2
•4,««0 1
• 4,0110 1
15,UUt) lit)
• 4.0HI0 0U1
-1. 3.0
•5.UU0 1
•2, 4.0
•4,0d0 1
2,000 |
10,000 110
•1.000 60
.1.0U0 890
•1.000 891
-1,000 710
•1,000 2
9. 0,0
0.0 116.9150
0.0 116. 9150
•|(000 2
0.000 1
•1.000 2
•2.000 2
•2,000 2
•4.000 2
16.0412
41,0100
31.9988
11.9908
0,0 1681.2846
1
1
1
1
1
1
t
2
1
1
4i»r
4 Ct»
Mil.)
4
4
*
4
1
179
180
400
127
'"
542
573
169
20ft
90
94
137
136
151
550
93
Reproduced from
besf available copy.
------- An error occurred while trying to OCR this image.
-------
TABLE A.3. (cantd)
NtftKtNU
HATEO
KUCTION NUMBER
5189102 U02N01.1M2U
1 1,080 491
5|69l0» U02N01.6H20
I i,0ea 0«
2001000 ALOnl(A)
J |,00H 1M
6001000 ALOMS04
4
6001001
4
604I00B
4
10.000
K
4ia
) 1,00(1 4JH
6015000 ANMtORHE
2 1.000 Ibw
5015000 AHAUON1TE
2 l.0ae tsa
5046000 ANUMMt
4 -2,000 110
421000* BAF2
2 i.auid l*«i
6010000 BANITt
2 l.BMIi IM
2001001 BQtMMlTt
BMUCITE
1 1.0*0 46«t
5015001 CALCITE
6040000 CCLlSTm
2 l,B0t» BH*
2 <2.U00 2
CHNYSOTILC
4 -t,«)«e no
0246000 CUtNOtNSTlTfc
4 -i.etie 2
2801002 01ASPOHE
1 -l.tinji 11*
6215000 OlOPSIllt
5 -2,HUB t
5015002 OOUUrtJIt
1 l.HMH Ilk"
68*6000 EPitUMlTt
1 t.HlJH <4btt
StPIOLIU(C)
-J..HIH 11,1
2.0U0
2.485
2,000
-4.770
2,000
27.«4S
1.B00
.080
1.000
.000
4.B00
-7.22B
1.B00
•1.918
1,000
1.769
1.000
1,000
26,742
2.000
-1.000
2.000
•6.2B0
1.000
2B.110
1,000
25.840
2.000
2. 585
l.BBB
.470
1.000
-4.615
1.000
52.485
1.000
20.015
1.000
1.000
24.610'
1.000
12.280
1.0*0
0.290
t.aae
£7.268
2,aaa
,840
492 2,8100 2
-1,642 ,000
492 1.0U0 2
•2.1*0 .00*
492 * 6.0U0 2
•10,180 -9.690
2 .1.0U0 310
10 ' 1.0U0 712
.22,700 .000
10 1.00B 712
, 5,170 ,00«
IB ' 2,8144 712
1,146 .000
IB ' 2,000 712
4,617 .008
712
•,160 ,aaa
140
-9,608 ,aaa
460 1.080 140
9,760 6.740
270
9.9T6 .0*0
712
•8,970 •B.abS
10 2.000 2
•16,792 .000
2 .2.0*0 110
9,475 0,560
140
6,469 ,00*
712
1,521 .00*
770
*12,188 .00*
460 2.0*0 7M
•11,110 -10,972
460 1,0*0 770
1.SB7 .00*
770
10 2.0*0 2
.19,066 .0**
150 l.BBB 4b*
17,0*0 .0**
460 2,*tt0 14*
2,14* ,U0(t
712 7.*l)0 2
2
2
2
2
,*VI*
1.070
1.0*0
,***
10,000
,*00
12,000
,000
6,000
,0*0
.000
,088
5.000
4,658
9.771
,0*0
,080
,0*0
6,149
,0**
1.000 2
11.632
-2.000 110
2,000 770
.«I30
460 1,0100 7ftt
• 4.H91 -J.Vif
eat i.tmi* i
|0£ttUt<«) Kti Pi*'
.Brit) 1,840 ,l<
1.0H0 dt\ a,7«)
-------
TABLE A.3. (contd)
09
3 •I,00W Jin
6026100 FE2($U4)3 ,
2 2,000 2H|
701901*2 FCOIAFATITC
6 9,49* ISi
421500) FLUUN1U
2 l,00« IS*
604»000 FOWtiWt
3 -4,080 13*
2003003 BI0B61U (C)
3 *3,0*W JJ9
2020102 euetHiTt
1 •3,0ow JJa
0*20400 BHUNAUITE
4 >6,0*0 li«
1026001 Btteicm
4 -4,000 JJ«|
60IS00I STPKUN
3 1,000 ISO
4150000 HALITt
• 1 1 0ltflH &(9«|
2026105 MtMATlIt
3 -6,00m 31*
5019003 HUNTItE
3 3,0*0 4**
504*001 HTOMMAUNtSlt
4 S,0»0 4bi)
6030000 JAHU61TE NA
5 -6.0MM 310
6041402 JAHUSITt K
5 -*,4M* JIM
6026101 JAH08irg ti
4 -3.0*1(1 JJM
1026002 M»CMNAH|Tt
3 . -t.ooo Jiii
6450*00 MAGAOIITC
4 -I.OtIM 3JM
2026104 MAbnCniTC
3 -6,VU>& IJii
504b*02 MAl>N£S)ft
2 l.0t)M 4bl)
f- 30260*10 MAl»N£f|lE
jo-jo] * -0,»U» JJ.i
IS"/ bfl24*l)4 MKLANf LNI ft.
l-n 1 . 3 l.ouo 2di
I"1 0.1 fa0%0*Vl lINASlLlTt
1 5 c 1 3 £,O^M 5vM
Ijpo I Ju5u*0M NAtHOM
/cr0-/ J a.rtwH ^vu
111 ^J 3(i4b*03 NtiUUtnllMl It
ln O J 3 1 . »inn •'in
lo 3 I 6b"bid(i| PhLUGL'l* I It
[£ . 1 JM(|WS •»•.-« »^«
>'M 'tii'
inigl 2o7ftl«i2 UUAKl^
^jf^' i -£.Ll''t' c1
ttbObMnKI St K [i)l.| U (<.)
1,000 200 1.000 7i*
49,120 -J,SB0 ,*50
3.000 732
-3<),390 114,400 ,u«0
.160 500 ,|44 4b0
•4.710 10,9*0 .000
2.000 271
46.910 •20.290 .000
2,000 4*0 1,000 770
22.600 -6,770 «0,467
1,000 10 1,000 2
14.460 •,504 ,000
1.000 2*1 2.000 i
.000 -20,*|0 .000
3.000 200 2,000 770
.000 49,035 ,000
2.000 201 |,000 IHtt
•.261 4,646 .000
1.000 7]2 2.000 i
•.916 >l,»62 ,000
1,000 160
34,645 4,006 ,M00
2,000 26| J.000 i
23,760 29,9*0 ,000
1.000 150 4,000 140
42.2IM 0,7k* .000
4,000 140 >2,000 J1U
lb.l*0 11,200 ,«00
' 1,000 500 3,000 201
11,260 14,000 ,000'
1,000 410 3,000 2ttl
33.150 12.100 .000
3.000 261 2.000 732
,000 4,640 ,**0
1,000' 280 1,000 MM
.00* 14.3*0 ,0*0
-9.000 2 1.000 Soo
.000 >*,366 ,000
2,0*0 261 3,000 2
0,169 0,029 D.27V
1,400 140
*«t.4*0 »3,737 •l.lbf
2,0*0 20| 1,000 2b0
-2.66* 2,47* .ODD
1.0*4 732 7.0ua e
-IN, 967 1,114 ,00u
I.OIH0 712 lu.euu i
-13,745 t.lll .*)Mi«
1..1JH 14U 1H. HUM i
3.769 3,*2I i.UJ
1,040 140 1.0*1) i
Ob. JOH -bb.i** .HMO
l.^ud 41W i,*UO H
-11. Jo* l«,4fv .mil)
-li.MHa I I,W«/H <*NM
*h.22U t.MUO . I1OI)
l.MMM 770
.a.i.i -ta./od ,.MII
HtftMtNtt
MATEQ
HEAC7ION NUHbER
.000
.000
4,000 960
.000'
,0*0
•9,440
.000
,000
1,400 2
,000
4.000 730
.000
,00*
.000
,000
,000
6,000- 2
,*0*
2,000 732
,000
*,*40 732
,00*
7,000 2
,400
,000
r,**0 770
,00*
7,77V
•*,34!>
4,1040 2
tu>o*
, JHd
t
-------
TABLE A.3. (contd)
4 -.500 a
5028400 JJDttmt
2 1,000 40U
2077801 8IlHCA,bU
2 -2.000 2
2077084 6104(A,PT)
2 .2.000 2
4260008 IRP2
2 1.0U0 000
7826100 8TRtN6ITE
1 1.0t>u 201
5868000 8THONT1ANIU
2 1.000 000
6646002 TALC
4 -4.000 2
6050002 THfcNAHOlU
2 2,000 5n0
5050401 TNEHMUNATK
1 2, MUD 5k)M
6215001 TKtMOUTE
5 -8.0M0 2
7026001 VIVIANITE
1 3.000 4B0
2 1,000 lie
2047400 PtKOLUSnt
4 -4.000 33rt
-vl 2047001 8IRNESS1TE
«XJ 4 -4.000 130
2047002 NJUTITE
4 .4.00H 3i0
1047108 ttlXbUTE
1 -6, OHM 330
3047000 HAU5CUNNITE
4 >0,000 33'0
2047001 MM4CH01TE
1 >2.000 330
2047104 MANOANITE
1 • -1,000 33o
5047000 ftHOUOCtittOSIT
2 1 . H00 47w
. , 4147408 MNCi,2i <*n2U
O-jo] 1 1.0HH 47«|
jj t
o3 304I0H0 AoCNVflUHtrL H
5 5 -34.01HI 15/1
• 30101000 HUtL A'101 It
^J^l b -3i,HHH J5V
MIW 6 -24.*H'H '31J1
^^ 3K)i|<|iJK0 LlTillUf'iii.lKI 1
2.000 460 1,000 77V<
5,320 10,550 U,I04
1.800 140
-4.448 1.018 .00k>
1,000 770
•3.910 2.710 .000
1.800 778
-1.850 6,»4B V.U0
2.000 270
2.030 26.400 2V. |23 26
1.000 580 2.000 2
.698 9,250 11.769
1.000 140
35,885 .21,055 .10.980 .21
3.008 468 4,000 770
.572 .179 .000
1.880 7)2
2.802 -.125 ,000
1.800 140 I.0U0 2
96,615 .56,546 ,000
2.000 150 5.0100 4b0
,000 16*008 .004
2.000 588 8.000 2
.,160 6.385 13.115
1,000 140
-4,000 330
.000
.000
,00.0
.000
.215
,000
.066
•6,000 310
.000
.000
.000
0,000 770
,000
.000
29,160 .15,061 ,000 .16,016
•1.800 1 1,000 471
.800 .18,091 .000
-1.000 t 1.000 471
,008 .17,504 .000
•1.880 1 1.0U0 471
15.245 ,611 *,226
2,080 471 1,000 2
00,140 .61,540 .000
-2.000 1 1.000 470
22.590 •15,066 .000 -15
1.000 470 2,000 2
,800 ,218 ,00U
1,000 471 2,000 2
2,879 10,410 U.MIM 9
1.000 140
-17.380 .2.710 .800
2,000 180 4.000 2
5,790 .1,000 ,000
1,000 470 1.000 730
15,400 .2.6D9 .000
1.000 732
39,860 5,711 ,000
3.000 732
-£,120 23,027 .wan
2.000 560
.000 .000 ,kl«)0
, 16.U00 471 .0100 410
.AW ,000 ,000
(4,000 471 .0*0 HHk*
.ritttf ,0U0 , UUtf
.393 150 .4*3 46H
.fl0u ,aa* .ami"
2.000 2
.008
2,000 2
.000
2.000 2
.430
.000
4,000 Z
.301
.000
.991
.080
,000
.000
,000
,ri00
.VI00
1 7,i««>U 2
,0k)0
,*70 200
, t>«10
1M.0UU 471
,4«I0
115.6564
60,0040
68,8048
125,6168
186,6490
147,6294
379,2686
142,0412
124,0041
612,4096
•14,800 310
501,6062
,
197,1494
•6,9168
86,9366
•6,9366
157,6742
226,61lb
66,9526
67,9446
114,9474
197.9052
67.002U
I50,999b
398,0bUa
154,7560
775.730<:
•7,400 470
817,4214
16.000 2 -b,«|0 470
S92.4b4I
14,008 2 -J.ttbb 470
1953,3934
MATCO
HtACT ION NUIlbER
'4
4
1
1
4
1
4(AJ
4
4
4(A)
4
1
1
1
I
1
1
1
1
1
1
1
1
1
1
1
1
1
1
9
tee
395
399
146
142
37
65
61
31
106
145
163
164
165
186
187
186
169
198
191
192
162
134
193
195
196
196
199
-------
TABLE A.3. (contd)
6
1015001
5
BB23B0B
2
4123401
2
4223000
2
2021000
1
1023000
3
1023001
4
1023002
4
1023001
4
1021100
4
1021101
1
6021000
2
1023000
4
412)100
00 2
0 5023100
2
4223100
2
4221101
1
2023100
3
4121101
4
9123100
4
6021100
4
6021101
4
6H23I02
4
2025101
1
6023101
4
702310*
2
7023101
1
6023104
2
6H23IMS
•70,000 lia
MANCUIU*
•10,000 5iV
eu nit AL
1,000 «1M
NANTOKIU
I.00W 21tl
CUF
1.000 210
CUPHIIC
•2.000 110
CHAUOCITE
•1.000 110
OJUNLtm
•1.000 310
AN1LI7E
-I.0M0 110
0LAU6UI II
•1.000 110
BLAUftkEI 1
• 1.000 1311
covtune
•I.B0B 114
CU2»04
2,000 210
CuPttOUSFtkIT
•4.00fl l)«l
HClANOTHALLl
1.000 21|
CUC01
l,00u 211
CUF2
It0u0 211
CUF2, 2H2U
1.000 211
CU(UN)2
-2.0*0 lltt
A7ACAH11fc'
•1.000 110
Cu2(On)lNill
•1.0W0 150
ANlLEMTt
•«,au0 ii*
0HUbNANTITC
•6.0tffl ltd
LANbMt
-b.0iip tin
TtNUttITt
-2.«tUH Jirf
CUUCUS04
-2.0W0 11*1
CUl IPU4) 2
l.riOtl 211
Cul(Pu4)2, Jti
i.DHU 211
CU4W
l.tv* <>lt
2.000
.000
.440
-17,110
1.000
•9,900
1.000
12.170
1.000
•6.243
2,000
•49.190
2,000
-47.661
.066
-45.919
.250
.000
.600
.000
.900
•24.010
t.000
4.96B
1,000
1.400
1.000
12.120
2.000
.000
1.B00
11.120
2.000
1.69B
2,000
15.250
1.000
16.690
2.000
17.150
2,000
.000
1.000
.000
4.000
19.610
4.000
15.240
1.000
15.575
2.000
.0*0
2.000
.000
2.H00
ltt.140
l.n<)0
-1.440
440 0.0K0 Ju
.000 ,H00
150 6.000 471
6,760 .000
1
6,760 ,000
1*0
•7,060 ,000
270
1,550 1.670
210 |,B0B 2
14,619 14,920
21B ' 1,000 710
15,920 .000
231 l,*6* 230
11, «7* ,000
211 1,500 230
27,279 ,000
231 ,*0B 210
14,162 .000
211 ,200 210
21,016 ,000
211 1,000 710
1,950 ,000
712
6,920 ,000
210 1.000 201
•1,710 ,000
160
9,610 V.690
140
,620 .000
270
4,550 .000
270 2,0*0 2
••,640 .000
211 2.0B0 2
.7,140 »».240
211 " 1.000 2
•9.240 ,000
211 1,000 2
•6,290 ,U00
231 4.000 2
• 15.140 >1!>.150
231 6.0U0 2
•16,790 ,U00
231 7.0U0 2
-7.620 -'.ISU
231 1.0U0 2
•11,510 .000
211 |,tfu0 2
16.650 .WHO
560
15.120 .0UB
5B0 1.0U0 2
• l,t>10 -£,614
7J2
2.640 C.lbU
20.000
.000
12,000
6.000
6.610
,000
.700
10.900
,000
1.000
.0*0
1,000
,000
1.000
,000
1,000
22,170
,000
6.660
2,000
•4.450
9.610
.000
,000
•9.200
•7,490
1,000
•9.110
1,000
•6,900
1.000
•15.500
1,000
•17,400
1,000
-r.aso
.0140
I.U00
Ib.***
.DUO
-i.««t»)
2. US
471
2
T10
710
710
710
2
J*0
492
712
712
712
712
49,000 2
466.1910
•1,440 470
61.9460
9*, 9990
62,9444
143.0914
199,1560
194.9620
143,2695
121.0264
101,9646
99,6100
221,1916
191,1916
114.4520
121.5592
101.5426
117.57J2
97,5606
211.5669
240,1109
354,7246
452,2654
470,30*6
79,5454
219.1490
360,Sa«tf
414.6264
159.6016
249.6790
Reproduced from
bes» available copy. HJR^
-6,000 470
NtNLI-
1
1
I
1
1
1
1
1
I
1
1
t
1
1
1
1
1
t
1
t
>
\
1
1
1
1
1
1
1
MATED
NtACTION NUHbCR
200
221
224
229
22*
22T
247
939
934
933
246
226
229
23B
231
2 32
233
234
237
231
239
240
241
242
243
244
245
247
24«
-------
TABLE A.3. (contd)
Ktt-tKtNLE
HATED
NEACUON NUMBER
00
1
2023102
1
3023100
4
1023102
4021000
2
4121000
2
U095400
2
2
5095000
2
5095001
3
4295400
2
2095000
1
2095001
1
2095002
1
2095001
1
2095904
3
4195001
4
4195002
4
6095000
4
6095001
4
S1950M0
1
2095005
1
2095006
1
6095002
4
7095404
1
10950*0
3
1095401
1
1095402
I
8295400
4
809S4W4
1,011)0 21)
OlOPTASfc
.2.000 110
CUPKICFEHIT
.6,000 114
CNAUOfMRlTt
•2,000 110
CU0N
1,000 214
Cut
1,000 21m
ZN HE Hi.
1,000 950
ZNCL2
1,000 950
8NITHSONITE
1,000 950
ZNCOlf 1H20
1,000 950
ZNP2
1.000 95«
-2.000 Hit
ZN(OH)2 (C)
•2,000 110
ZN(OH)2 («)
•2.000 110
ZNIUH)2 (G)
•2,000 114
ZN(ON)2 (t)
-2.000 110
ZN2(0(l)3CL
•1,000 110
ZN5lOH)6CL2
ZN2(OH)£ttu4
•2.000 110
ZN4tOr1)6Sn«
•6,000 110
ZNNUl)2«6H2u
1.000 950
ZNUtACriVt)
•2,000 110
ziNcire
• 2,000 lit)
ZNiimotiz
-2,000 110
ZNHP04) i 4*16
WKKTZUfc
-i.aww 11*
ZNM01
-2,itup ll.162 6,^4
1.000 950 t.dlue 71*
ID. 270 .2,910 .BMW .*?*
-1.000 2 1,UU0 950 l,k)k)k)
1S.17B .15,114 •11.15B ,ri«0
3
710
100
180
732
713
2
77*
157,6449
239,2176
103.5110
143,4500
I90.45V5
65,3800
136,2660
123,3092
143.4044
103,3768
99,3946
99,3946
99.3946
99.3946
99,3946
217,2149
933.6644
260.0122
459,6214
297.4810
01.3794
81,im
404.2546
456.1436
97.4400
97.440D
97,4400
141,4617
220.0431
1
1
'I
1
1
1
I
1
1
1
1
I
1
1
1
1
1
1
1
t
1
1
t
1
1
1
1
1
1
420
349
250
459
460
365
267
360
269
270
271
272
273
374
875
376
377
370
379
360
361
262
363
384
285
286
267
288
289
-------
TABLE A.3. (contd)
1 -4,000 1)0
6099001 IINCOSITE
2 i,0u0 V*B
6099004 2*004, iH20
3 1.000. 9!>0
6099009 aiANChlTC
1 1.000 950
6099006 G03LANITE
l 1,000 940
4095000 IN0M2, 2H20
1 1,00* 9511
4199000 ZNii
2 1,000 9bn
6016000 co HEIAL
a 1,000 i6i«
0016001 SANK* cu
2 1.000 16*
901*000 OTAVltt
2 i,00a |60
4H6000 coci2
2 1.H00 UK
4| Item CDCL2, 1H20
1 1,000 tb0
4116002 CUCL2,2,5n2 1 4 «1.000 i
l< O.I 601600) CUSU4
fuCI i l.HMH. IbM
J^nl 6016^04 CUif04, 1H2II
/O-0-/ I I.U0H Uri
/n^f 601600S COSO«|2,7ili;ii
(n ° / > i.dl'W It..)
I ° 3 / 10l6»0i« &KttNUCi>l It
/x / 1 -l,M«m }i«)
1* 1 4016000 CnBMi, Ol^U
MfeJ i 1.0in(l Ibt)
M»®[ 41l6m
0060400 Ptt ntlAt
2.000 «S0 I.HU0 ffll
IV. 200 -3.010 .000
1.000 7)2
10.640 ,»70 ,000
1,000 732 1,000 e
.160 l,?65 .000
1.000 712 6.000 2
•1.100 |,«60 ,000
1.100 712 7,000 i
7.S10 -3,210 .000
2,000 130 2,001 2
11.440 •7,210 ,000
2.000 100
10,100 •|3,4«0 ,000 .
2.000 1
10,140 .|1,»«0 .000
2.000 1
,910 11,740 14,010
1.000 (40
4,470 ,600 .000
2,000 100
1.420 1,710 ,000
2,101 160 1,000 2
•1,710 I«V40 ,000
2,000 100 ' 1,900 2
«,720 2,m .000
2,000 270
20.7T0 •13,710 •11,610 •
1,001 160 2, alia 2
,000 •13.690 ,000
1.000 160 ' 2,000 a
7.407 -3,920 -1,100
1.000 160 1,001 2
,000 -22,960 ,000
1.000 160 4,0U0 2
.000 -6,710 ,000
1.006 160 2.000 2
,000 «20,400 ,000
4.000 160 6,000 2
24,760 -19,120 ,000 -
1.000 160 1.0U0 2
,0a0 12,600 ,000
2.000 960 *
16.630 -V,060 -f,V60
1.000 160 1,000 770
14,740 ,100 .1)0
1.000 712
7.920 I,6b7 1.600
1.000 712 1.000 2
4.100 I,b7i 1,040
1.000 732 «,6'0 i
-16.360 1&.VJ0 .000
i.aeii 160 t.0u0 710
•7.210 2.420 .000
2.000 110 4.000 2
•4,ttd0 1,610 ,000
2.00B 100
-.400 -*,£!* -1.070
•1.V10
,!>00
1,020
!i«'0
,000
,000
11.M0
.000
11.210
,470 .
,000
,000
.000
14,100
,000
,000
1,000 160
,000
1,000 712
,00a
2,000 712
,000 •
1.000 712
15,740
,000
,t)H0
-2,000 110
,050
1.6*0
1,060
11,112
.000
,000
-4,il0
161,4116
!7t,492»
26*. 9260
267,9440
261,2104
II9.U90
112,4100
112.4100
172.4192
103,1160
201,1112
126,1916
190,4060
146,4246
146,4246
164,0701
901,1160
961,1940
647,7414
120,4094
927,1720
|00,4«17
200,4676
226,4020
296,3079
144,4700
144,2700
166,2190
207,2000
HtctNtNtt 'NATEU
REACTION NUMBER
1 290
1 291
1 292
1 293
1 461
1 462
1 912
1 313
t
1 319
1 316
1 317
1 318
1 319
1 328
1 321
1 322
1 323
1 324
1 329
1 326
1 327
1 328
1 329
1 110
1 311
1 3)2
1 463
I 464
1 360
-------
TABLE A.3. (contd)
NtFtRtMt
HATED
hfcACTION NUtlBER
i
4160000
2
4160001
3
4160002
3
S060B0B
2
4260004
2
206000B
1
2060001
3
2060102
3
3B60001
4
6060004
4
6060001
4
6060002
4
7060001
3
7060002
W 4
00 5060002
4
7060003
5
7060404
6
706000S
5
0260000
4
8060000
3
frtfffHlPlf*
O~7Q 2
245 1460001
"1 J
a; g_ 2060403
oi c '4
=rm 30604*0
~~ n a
a~-~ lk)bt)00l
o 4
0 ^ 20644114
5 *
11 60*} Hi
-Kim-h. 4
4 1 b 0 d H 4
^^P' 4
bUbiOUJ
1.000 btlid
CUIUNNITE
1,000 fcum
HATLOCKITE
1,000 6W«*
pnosstNjTE
2.000 6HW
CtKHUSIlf
1,000 BUI*
PHF2
l,0U0 bins'
rtASSjCuT
•2,000 31u
LITNARGt
•2, HBO 310
PBO, t3N2l)
•2,000 llw
PB2UC03
•2,0I«0 11M
LARNAK I It
•2,000 Jl»
PU302S04
•4,40(1 110
P04U3&04
•6.400 311}
CLPVItOMURPH
3,000 6MM
HXYPYMUHORPH
•1,000 Ilk*
•4,000 11*
PUUMUGUMMlIt
•3,000 31*
•6,0HI» lilt
TSUflEOlTE
• 3,000 lit)
Pbsioi
•1,01)0 i
P82SIU4
• 4,000 Hit
ANGLC& I 1 t
1,0(40 6k>!»
GALtNA
-l.aan HM
PUAfTNEKlTt
•4.0U0 ilil
PB2J1
-6.KWH 111*
NJN1UM
-tt.HUd JJn
PB(UH)i (Cl
-2,Ull)k> lit'
LAUHIUMU.
-l.klOM 11.1
fdd (On) iCl
-J.^OM 1JM
M»Dtt«(,440
1,000 140
,780 7,440 ',570
2,000 270
16,700 •12,9|0 .12,7914
1,800 600 1,0140 2
16,300 .12,728 >U,640
1,088 688 1,0140 2
.008 .12,900 .000
1.000 600 1,310 2
It. 468 ,300 ,7«U
2.808 600 1.0U0 2
6,440 ,280 «,300
2,840 600 ' 1,000 732
2M. 758 .10,400 .14110
3,888 680 1,0140 732
15.078 .22,100 ,000
4,000 600 1,0140 712
.000 84,438 ,000
3,080 300 1,0)40 |«t)
.8B8 62,790 .000
3,080 600 3,0140.5011
26,430 .11,020 ,000
3,808 600 1,000 140
,800 32,798 ,000
1,000 600 3,0140 30
,808 2,500 ,000
1.000 600 3.0U0 30
,080 9,790 ,000
2,080 600 1,0140 211
9,260 .7,320 >6,t20
-2.808 330 " !,0t>0 600
26,000 .19,760 .19,220
2.8H0 6BB I.0U0 77(1
•2,150 7,790 J.OTtf
1,000 732
•19,400 15,132 10.452
1,008 600 1,0140 71M
70.730 .49,100 -4V,ttU0
• 2.800 1 ' 1.0U0 6Utl
,800 •61,040 .MM*
-2,008 1 2,0U0 bMkt
1H2.760 .73.694 -TH.flkJe
-2,H0<4 t 3,010 bkJM
11,994 -8,1-jB .MHM
I, Ota bBB 2.0U0 i
,eet) .,b21 ~«!7b
1.400 bUtl l.MUH I&H
, BMU •B,791 , MMkl
2.U40 bU0 1.UV0 2
,04V l/,4«k1 . ilMk)
4,b70
a,bu0
,000
12,03)4
.000
,000
•13,070
,040
,000
1.U00 140
,000
1,000 2
,000
2,000 2
,004
3,000 2
34.514
,000
1.000 2
.000
2.000 2
,000
2,000 500
,000
1,000 500
,000
1.000 500
•7,640
1.000 770
•20,054
M0k)
13«btt2
.HUM
2.000 2
, Otfk)
1,000 2
,0140
4,440 2
-11,61k)
. I1«H)
I.UU0 2
, tfdO
l.tion tat)
.em) id
270,14bU
261.6514
545,3152
267,2092
245,1960
223,1994
223,1994
229,1444
490,4006
526,4570
749.6564
972,8558
1356,3672
1337.9215
T|3,6000
581,1391
6,000 2
581,2174
1,000 732 6,000 002
677,9049
6,000 2
203,2037
506.4831
303,2576
239,26144
239.19BD
462.39B2
685.5976
24l,2|4b
259,bbKil
500,0749
775,bll«»
1
1
1
1
1
1
1
1
1
1
1
I
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
362
363
364
365
366
367
368
369
370
371
372
373
376
377
378
379
380
381
382
383
384
385
386
307
368
38.9
390
391
392
-------
TABLE A,3. (contd)
4
2060009
3
4060400
i
4060001
3
4360001
i
6060404
4
9094000
2
2094000
1
609400)1
4
2094001
3
7094404
2
1094001
3
6B9400I
3
60940U2
3
• 0940011
I
0002000
2
4002000
2
4|02000
2
9002000
2
4202000
3
4302000
2
2002000
3
7002001
2
1002400
}
6002400
2
84*440!
9
86V30P0
4
S64340I
'4
8415404
9
Bu5nn»)2
•2. 0411 Jlrf
P020(OH)2
•4.000 330
PDHM2
1,000 6H»i
PB0H*
1,040 »UH
P0I2
1,000 6MB
P0410H)6»D4
-6.0V0 330
N1CU3
1.000 *44
N1(UW)2
•2,000 33*
N14(Ort)6S(l4
•6,000 350
1UN8EN1TE
•2.000 33H
NI4(PU4)2
3,000 94*
HIU.CMIU
•I.00H 330
fteTueium
1.00(1 5««l
MORtN08ITt
1.000 Sou
NI2JHU4
•4.0M0 ill*
A6 MtUL
1.0V0 *<»
0K01YRIU
1.040 2H
CCfUftCVKIU
I.08H M
AC2C03
2.0DH 2«l
»6f,4MJO
1.000 cJ.I
,ioor«iTt
I,0H0 «!H
A620
•2,000 lit*
AGJP04
l.«IUH /^
»C»NT«l(t
• I,«MH l^M
•liiSOl
a.owc ci'.i
ANALClMt
I.WWM b»M
MAtLOrSITt
2,<)nh }.i
RAULINIU
i.lJllH l.i
LtUMMAHUITt
-1.HWI1 ^
LU« »UH1U
3.040
.••'
2.040
•a. 100
2.000
.000
1.0*0
•19.160
2,000
.•00
4,000
«,«40
1.000
•30.431
t.040
.000
4.000
43.421
1.010
.000
2.000
•2.401
t.000
•t.tei
t.0»0
•2.44I
1,000
3J.360
2,000
•29.214
1,000
-24.178
1.000
•19.692
1.000
-«.930
1.000
•4. 270
1.000
•26,8*0
1.000
10.430
2,000
.000
1.000
-S3. 300
2,040
•4.290
1.000
22.840
1.000
jy.734
2,000
J*.2tt4
2.0U0
oi.Jbm
-16.0140
17.4KI0
600 2.0M0 I4W
2.MM0 2
.26,200 .UV0 '27.100
600 3.000 2
9,104 »,340
130
•«4«0 .000
130 1.000 2Y0
1.070 .000
380
.21,100 ' .000
600 1,000 732
6,040 .000
1481
.10,400 .10,990 •
940 2,0U0 2
.12,000 ,000
940 1,000 7J2
.12,410 .000 .
949 1,001 2
11,304 ,000
980 '
8,042 «.|32
949 1,001 731
2,040 ,000
732 6,100 2
2,168 ,000
712 ' 7,000 2
•I4,b40 ,000
948) ' 1.100 770
13,910 ,000
1
12.270 ,000
130
9,794 .000
180
11,070 ,000
140
.,»!»4 ,000
170 4,000 2
16,070 ,00«
181
•12,980 .000
20 I.0K0 2
17,»94 ,000
980
16,490 ,00U
20 I,4U0 710
. 4,924 .MUD
732
•6.F19 ,400
30 2.0««l 7)0
•a,v94 .untie
770 I.0K0 *
-1.1 io .HUB
770 I.WU0 2
•16»4W0 .WflU
330 2.0U0 I*P
-itttt ,a*a
4,410
.000
,000
,000
6,000 2
.000
13.30U
.000
6.000 2
12.390
,000
,000
,000
,000
,000
.000
,004'
,000
.000
,00U
,000
.1400
.000
,t)4«
.440
,04k)
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,040
-6,000 330
,i0k>0
-6.0IA4 330
.HI)*)
B. 4140 770
.«4tt
464.4144
367,0000
306,1024
461,0090
1026,9014
118.1492
92,7146
432.9014
74,6994
366,0428
90,7600
262,0400
200,0640
209.4811
107,0600
187,7720
141,3210
279.7492
198.9272
230,772*
231.7394
418.97*4
247,70614
3JJ.T936
220.1*90
•4,000 334
258, 16*14
25S.I62U
922.8674
4,004 }£
262.24*14
NtNtE
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
i
1
1
1
1
7
7
7
1
MATCU
KfcACTION NUMBER
393
469
466
467
394
41B
411
412
413
414
415
416
417
418
417
4)8
439
440
441
442
443
444
449
446
—
—
~,
...
Rporoduced from
best available_cop£.
-------
TABLE A.3. (contd)
9 1.000 !>">»•
6490001 ANALBITE
9 1.000 *t)H
4 1.000 *1W
66*1001 ANNlTt
9 1.0BW MlH
6419001 ANOKTHITE
660)002 PTRUPMYLLHt
4 2,0UH IM
6419002 LAUMONTItt
4 1,000 150
6419001 NAINAKITE
5 1,000 IbC
902)101 MALACHITE
4 2»00H 211
9023102 AZUHlTE
4 3,400 211
3006000 AHSfcNOLITE
2 4,000 e>U
3006001 CLAUUfcUTt
2 4,000 6H
4106000 ASH
4 1,000 oil
1006000 OHIPHENT
4 2,000 60
1006001 HEALGAH
3 , 9 |,0U0 bvl
1 3006100 *S4U9
2 2.00H 61
5299000 ZN(D02)2
4 -2.000 2
5216000 CO(B02)2
4 >2.000 '«.
9260000 P0(UQ2)2
4 -2.000 2
7047001 MNHPOI(C)
T% 7060006 PBHP04
"* "O 11 000 QvH9
~o 7060007 Pdl(PU4)2
<0- 2 1.000 6tM
5!.o 007)100 6UIFUH
57g_ i 1,000 Tin
Z^ 720)1100 ALAS04.2W
16 -^ 4 1.0U0 in'
n § 7213100 CA)lA$U4)r>l>H
^ 4 i.nua fin
•< 7221100 CUH'A3fl4)26M
4 1.UB0 2)1
^Pfe 7220100 PEASO* «!n
ft*l 4 l(0k'f> 201
>®P 7247000 MMJASOIiflu
4 1 vIVIM 4 fkt
72Sa«00 NII 1*301 lain
4 ) ritffi ^>^>i
72bBd0H PuJltiOt)?
1.0U0 10 1,0H0 770
24.000 •1,406 .tfMie
1.000 10 1,000 770
59.140 •12.990 ,00V
1,006 10 1,000 '70
65,721 •21,290 ,000
1.000 240 1,000 10
70.660 -2S,«Ji) .000
2.000 10 2.0»0 770
.000 !.»96 ,000
4.000 770 -4,000 2
50,450 •14,460 .000
2.000 10 4,0*0 770
61,150 •10,»70 ,00U
2.000 10 4,000 770
15.610 5.160 ,000
2.000 2 1,000 1*0
21.TT0 16.920 .000
2.000 2 2.000 140
•14,110 2,601 2,»59
•6,000 2
•11.290 1,065 ,000
•6.000 2
-1.675 •4,155 ,00U
1.000 160 1,000 110
-62,690 60,971 ,000
1.000 710 1.000 110
•10.549 19,747 26.574
1.000 T10 2.000 110
5.405 «6,»99 .000
•1.000 2
,000 -6,291) ,000
•2.000 110 1.0U0 950
,000 •9,840 ,000
-2.000 110 1,000 160
5.600 -7,610 ,000
•2.000 110 1,000 600
,000 21,400 .000
1.000 560 1.000 110
.000 21,900 .000
1.000 560 1.000 110
.000 44,300 ,000
2,000 560
4.200 2,110 ,0H0
•1.000 130 >2.000 1
.000 •4,a00 .n0t)
1.000 61 2.000 2
,000 •28,100 .000
2.000 61 ' 4.0U0 2
,000 -6, IBB .000
2.M00 61 2,000 2
.004 -.400 .000
1.000 bl 2.0W0 2
.000 •I2.!)00 .Wk)U
2.000 bl 0.0U0 2
.000 •13,700 .000
2.000 bl «.0«tf *
.000 -b.BBB .0014
•4.000 1)0
,*)«*»
•4,000 110
,000
•10,004 310
,0t)0
1,000 7'0
,00*
•6,000 110
,B00
•6,000 110
.000
' •tt,000 110
,000
•8,000 110
1,940
•2,000 330
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•2,000 310
2, '26
1,021
,000
•1,000 2
46,004
• 6,«)U0 2
,000
1,000 1
•9,4f6
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2.000 99
.000
2,000 90
.000
2,000 90
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.000
.000
.000
.000
•1.000 110
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•0,000 3)0
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-6.000 110
,000
-1,000 110
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»6,0ttU 1)0
.at)*
-b.BHO 110
.000
•4,000 2
262.2250
•4,000 2
396.1110
511.6900
•10,000 310
. , 276.2110
160,1116
470,4414
4)4,4114
•2,000 2
221.1162
144,6716
195,6624
395,6824
4SS,614r
246,0154
106,9855
•1,000 2
229,6400
150.989)
196,0166
292,6091
150,9174
101,1691
611,5123
12,0640
165,9006
506,1700
576,5660
210.7967
' 566,7746
459.1707
699.4079
NEFfcHtNCE
7
7
tt
7
9
6
6
10
10
•MATED
HEACUON NUMBER
t
1
1
1
1
1
1
1
1
HC)
IIC)
1(0
1(M)
I(U
1(1)
»M».
1(1)
1(1)
111)
1(1)
497
I
496
499
500
501
466
266
314
361
194
374
t
175
402
489
490
491
492
493
494
49S
-------
TABLE A.3. (contd)
1
72*9*00
4
7218*88
1
2019*08
1
2019801
1
282a*B8
)
2046001
1
1021*01
4
1046001
4
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4
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s-n
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9
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66*001110
6
8641002
6
abijOMiJ
6
flblbMHb
k
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lNlAlO2.0U0 114
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•a, 000 114
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•a, 000 iin
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•a. 800 UK
CRYOLITE
|,00n Ulrt
HOUASTONlTt
•1,000 »«ia
•I,UV0 0H2
CA'OLlVINt
•4,000 lltf
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•4.000 1)4
CA13I09
•6,0U0 1)0
lONIICEULI't
•4,0u0 lie
AHEHMlNlTt
•1.000 0tf2
KAL4ILITE
•4,000 114
LEUCIIE
•2,0tl0 0H£
HICHOCllMf.
«4.(ll>0 UU2
H SANlOlNt
• 4.0VI0 Uni
NECMELI^t
•4,0UU llri
UtMLfllt
•IK.Bt'ti 11^
LtPIOUCHOCM
• l.^tfli 110
NA*MONTHnr)| 1
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H-NUslRUlllTt
-7,12k! Jl.l
CA-NONTNONlt
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MC-NOHTHOMll
>7,)2ti 111
2. 000
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2.80*
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2.808
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18,490
1.888
24, (46
U.M7
Ik, 119
1.888
78.S40
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1.800
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1,0*0
n.4«a
•2,888
21,84*
•2,800
1.80*
97,|)a
1.000
1,088
41,421
1,888
74.449
107,111
2,000
20,91*
1.800
22,889
•4.808
12,189
•4.888
J4.Z52
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11,204
1.0U0
tlk.l2S
2.0*0
a
I.0U0
0
-2.640
0
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f)
•2.690
n
-2. 680
kl -6
41 ' 2
41 ' «k
198 ' 1
•22,679
198 2
•11.447
228 . |
•21,41*
•27,}42
288 2
448 ' 2
•14.749
448 2
908 '• k
110 * '*!
•11.846
118 1
•17,64V
778 ~ 2
•11,14!
778 2
778 * 1
•10.272
778 1
•47,472
118 2
778 ' I
•!2.*)a
77« 1
•6(421
))8 2
•0(416
118 1
•1,062
118 1
•14,210
778 1
•96,422
010 1
•1,171
201 ' 2
14,^04
0i>2 B
ib,iW
82
0
B
tf
0
0
0
B
0
B.
0
0
0
0
0
0
0
0
U
0
*
u
0
It
K
1,670 770
1.670 770
1.670 770
J.b/B 7ffc
RtftKtNtC
1IIJ
1UJ
II
11
It
II
II
II
II
11
II
II
It
u
II
II
II
II
u
'll
II
11
11
II
11
11
II
11
II
HATC0
HEACTION NUMBER
416
941
------- |