EPA-600/3-78-024
February 1978
Ecological Research Series
             A   USER'S GUIDE  FOR REDEQL  •  EPA:
                 A  Computer Program  for Chemical
                      Equilibria  in  Aqueous  Systems
                                        Environmental Research Laboratory
                                       Office of Research and Development
                                      U.S. Environmental Protection Agency
                                             Corvallis, Oregon 97330

-------
RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, U.S. Environmental
Protection Agency, have been grouped into nine series. These nine broad cate-
gories were established to facilitate further development and application of en-
vironmental technology. Elimination of traditional grouping was consciously
planned to foster technology transfer and a maximum interface in related fields.
The nine series are:
1. Environmental Health Effects Research
2. Environmental Protection Technology
3. Ecological Research
4. Environmental Monitoring
5. Socioeconomic Environmental Studies
6. Scientific and Technical Assessment Reports (STAR)
7. Interagency Energy-Environment Research and Development
8. “Special” Reports
9. Miscellaneous Reports
This report has been assigned to the ECOLOGICAL RESEARCH series. This series
describes research on the effects of pollution on humans, plant and animal spe-
cies, and materials. Problems are assessed for their long- and short-term influ-
ences. Investigations include formation, transport, and pathway studies to deter-
mine the fate of pollutants and their effects. This work provides the technical basis
for setting standards to minimize undesirable changes in living organisms in the
aquatic, terrestrial, and atmospheric environments.
This document is available to the public through the National Technical Informa-
tion Service, Springfield, Virginia 22161.

-------
                                          EPA-600/3-78-024
                                          February 1978
       A USER'S  GUIDE  FOR  REDEQL.EPA
          A  Computer Program for
          Chemical  Equilibria in
              Aqueous Systems
                    by

               Sara E. Ingle
             Marcus D. Schuldt
             Donald W. Schults

   Marine and Freshwater Ecology Branch
Corvallis Environmental Research Laboratory
         Corvallis, Oregon  97330
CORVALLIS ENVIRONMENTAL RESEARCH LABORATORY
    OFFICE OF RESEARCH AND DEVELOPMENT
   U.S. ENVIRONMENTAL PROTECTION AGENCY
         CORVALLIS, OREGON  97330

-------
DISCLAIMER
This report has been reviewed by the Corvallis Environmental
Research Laboratory, U. S. Environmental Protection Agency, and approved
for publication. Mention of trade names or commercial products does not
constitute endorsement or recommendation for use.
11

-------
FOREWORD
Effective regulatory and enforcement actions by the Environmental
Protection Agency would be virtually impossible without sound scientific
data on pollutants and their impact on environmental stability and human
health. Responsibility for building this data base has been assigned to
EPA 1 s Office of Research and Development and its fifteen major field
installations, one of which is the Corvallis Environmental Research
Laboratory (CERL).
The primary mission of the Corvallis laboratory is research on the
effects of environmental pollutants on terrestrial, freshwater, and
marine ecosystems; the behavior, effects, and control of pollutants in
lake systems; and the development of predictive models on the movement
of pollutants in the biosphere.
This report describes a computer program (REDEQL.EPA) for deter-
mining aqueous chemical equilibria among metals and ligands under various
conditions of concentration, pH, and oxidation. It represents an update
of material presented at a users’ workshop at CERL in May, 1974.
A. F. Bartsch
Director, CERL
111

-------
ABSTRACT
This user’s guide explains the use of the computerized chemical
equilibrium program REDEQL.EPA. This program computes aqueous equilibria
for up to 20 metals and 30 ligands in a system. The metals and ligands
are selected from a list of 35 metals and 59 ligands for which thermo-
dynamic data for complexes and solids have been stored in a data file.
More data may be added by the user. The equilibria which the program
considers include coniplexation, precipitation, oxidation-reduction, and
pH-dependent phenomena.
This guide allows one to use the program without reference to the
FORTRAN program. The capabilities and limitations of the program are
discussed. The formats for input and explanation of output are given
with examples illustrating the various program options. Common user
errors are discussed.
This report covers a period from July, 1975 to July, 1977 and work
was completed as of September, 1977.
iv

-------
lexes for
• . . 111
• • • iv
• • . vi
• . . vi
• . . vii
.•.l
...2
.•.4
...5
.•.7
• . . 10
• . . 10
• . • 15
c data
• . • 15
21
• . . 22
• . 23
• . 24
• 25
• 26
• 26
• 31
• 35
• 35
• 40
• 41
• 44
• 45
• 59
CONTENTS
Foreword
Abstract
List of Figures
List of Tables
Acknowledgements
I. Introduction
A. Description of the program capabilities
B. A simple system
C. How to use this guide
II. Limitations of REDEQL.EPA
III. Data input and consequent output
A. Setting up a simple case
B. Running REDEQL.EPA on the EPA computer system
C. Ionic strength and correction of the thermodynami
for ionic strength
D. TOTH = zH - 0H
E. Solids: imposed and not allowed to precipitate
F. Gas phase, pCO 2
G. Redox computations
H. Mixed solids
i. Milligram/liter input and output
IV. Program output
A. Normal output
B. Error message output
V. Thermodynamic data
A. Thermodynamic data deck
B. Access to the thermodynamic data file
C. Preparation of data for solids and comp
ir .o the thermodynamic data file. . .
References
Tables
Computer printout figures
17
entry
V

-------
LIST OF FIGURES
LIST OF TABLES
1 Reference Numbers for Metals and Ligands
2 Redox Reactions: Reference number, type, and
equilibrium constant
3 Mixed Solids: Reference number, type, and
equilibirum constant
4 Program Input Cards: Card sequence, format, and
data required
5 Figure References for Output Routines
6 Thermodynamic Data Deck: Card sequence, format,
and data required
Number
Page
1 Calculation of the charge of a solution. . . .
9
2 Preparation of input data
10
3 Input data cards for sample case . .
.
11
4 Estimation of ionic strength
12
5 Estimation of TOTI -!
13
6 Output for a simple case
60
7 A case with fixed ionic strength
65
8 TOTH sample calculations
19
9 Three cases with fixed pH
66
10 A case with no solids allowed to precipitate
71
11 A case with one solid not allowed and one solid
imposed. . .
73
12 Four redox cases from oxidizing to reducing
76
13 A case with one mixed solid allowed
82
14 A case with milligram/liter input
84
15 Interaction capacities
86
16 A nonconvergent case
87
17 Examples of thermodynamic data cards
36
Number
Page
45
46
47
48
54
55
vi

-------
ACKNOWLEDGEMENTS
The authors wish to recognize Dr. James Morgan at California Insti-
tute of Technology who designed the REDEQL program and sent us updates
of thermodynamic data. We also acknowledge the efforts of Judy Carkin,
who helped maintain the program, and Dan Krawczyk and Joel McCrady for
their contributions in critically reviewing the manuscript. We also
gratefully appreciate the guidance of Dr. Donald Baumgartner who saw a
need for the user’s guide in the scientific community.
vii

-------
I. INTRODUCTION
The program described here, REDEQL.EPA, is a modification of REDEQL2
which was developed over a number of years at the California Institute
of Technology by Morgan, Morel, and McDuff under grants initially from
Gulf Oil Corporation, the Environmental Quality Laboratory of Cal Tech,
and the Rockefeller Foundation and, since 1972, under grants from the
Environmental Protection Agency. Some information in this guide is
taken from W. M. Keck Laboratories Technical Report EQ-73-02 by McDuff
and Morel (1).
The purpose of this guide is to make program use as simple as
possible. The program capabilities will be illustrated with a series of
examples. Emphasis is on defining program input and interpreting output
and on how the program can serve the user. No description of the FORTRAN
program is included. The method of computation for the program was
originally published by Morel and Morgan (2). For complete details of
the program consult references 1 and 2.
Applications of the program differ broadly, and there are many
unexplored areas to which the program might be applied. The impact of a
chemical spill on a water supply can be assessed. For example, what
happens when very acidic titanium wastes are dumped in the New York
Bight? What is the white material that precipitates? To answer these
questions the user needs the analytical concentrations in the dumped
material and analytical data for seawater. Total concentrations of
metals and ligands when one part of the dumped material is diluted with
100 parts seawater can be used with the computer program to determine
the resulting speciation of the chemicals. If solids precipitate, these
will be identified. Some other parameters, such as the final pH of the
mixture, will also be given. These results can rapidly be compared with
results for different dilution.
The program can serve as a quick check of laboratory measurements
or give a preview of what will happen in an experiment. Similar results
between the program output and laboratory analysis support the validity
of the program and the experimentalist’s technique. Differing results
raise questions such as: “Is what should be measured actually being

-------
measured?” and “If the experimental results are correct, what phenomenon
is occurring in solution that the program doesn’t take into account?”
While the limitations of the program are stressed in Section II,
page 7, it is important to consider why the program might be used in
preference to laboratory work. After some practice, using the program
is generally faster. It should involve fewer work hours than laboratory
work. When many similar situations are to be considered and the validity
of the program results for some of these situations has been confirmed
in the laboratory, the results for the rest of the situations could be
calculated by the program.
Suppose that the pH and mercury concentration in a river are known
and a chemical is spilled into that river. To determine the effects on
pH and mercury speciation, the program could be run for appropriate
mixtures of spilled chemical and river water. For a laboratory simulation
experiment, one would need unpreserved samples, but these would be
susceptible to mercury loss or pH changes. The program results, however,
are unbiased by contamination or loss.
REDEQL.EPA gives information that routine analytical work does not
reveal. For instance, it is easy to measure dissolved copper in seawater,
but it is difficult to measure that this copper is 68% free ion, 23%
chloride complexes, 7% a sulfate complex, and 2% a hydroxide complex.
One of these forms might vary greatly in toxicity from another, so that
their identity is important. This distribution might be very sensitive
to changes in other trace metal or ligand concentrations or pH. The
program can be used to vary such concentrations and pH and thus can
reveal which variables are most important in controlling the distribution
of copper in the aqueous system and need further study.
I-A. DESCRIPTION OF THE PROGRAM CAPABILITIES
This program is designed to compute chemical equilibria involving
solids, complexes, oxidation-reduction, and mixed solids in an aqueous
system. The adsorption scheme formerly used with REDEQL2 is still
intact but not described here because adsorption routines are being
modified. These modifications will be reported in a future publication.
2

-------
Ionic strength may be calculated or specified and formation constants
for solids and complexes are computed from the thermodynamic data for
infinite dilution and from ionic strength. Interaction capacities and
intensities as described by Morel etal. (3) can also be computed.
The primary inputs for the program are the total concentrations of
metals and ligands in the system, including quantities in solid and gas
phases if these are allowed to interact with the aqueous system. Con-
centration may be in molar units or milligrams/liter. The thermodynamic
data file contains thermodynamic data for metals, ligands, solids,
complexes, redox reactions, and mixed solids. It presently includes
thermodynamic data for 35 metals and 59 ligands which are listed in
Table 1, page 45. More can be added; see Section V-A, page 35. Up to
ten cases of different total concentrations for a set of metals and
ligands selected from those available can be treated by the program in
one run. A maximum of 20 metals and 30 ligands may be included in any
one system considered. The results of the program are the speciation of
the metals and ligands in various forms and combinations. A large
amount of complexation and solubility data is stored for up to three
solids and six complexes for each metal—ligand pair. It is possible to
allow for supersaturation with respect to any of the possible solids.
Data for 24 redox reactions from the thermodynamic data file are listed
in Table 2, page 46, and the user may specify which reactions will be
included in a particular run. Table 3, page 47, shows six mixed solids,
which contain more than one metal or ligand (not including or 0 1 - i).
A complete explanation of the thermodynamic data file and how it may be
modified is given in Section V-A, page 35. The mechanics of creating,
maintaining, and using one’s own thermodynamic data file are given in
Section V-B, page 40.
EPA research laboratories and regional offices are served by a
national computer services contract, frequently available to non-EPA
personnel working cooperatively with EPA. In August, 1977, REDEQL.EPA
was available on the COMNET IBM system of the Washington Computer Center.
If the system is changed under future contracts, this program will still
be available.
3

-------
The program may be used with either laboratory, field, or hypo-
thetical input data. The results of the program are based on thermo-
dynamic data, which have been previously measured in less complex systems,
applied to the input data. If the formation constant for a solid or
complex is not in the thermodynamic data file, that solid or complex
will not be predicted to form in the aqueous system being studied, even
though it may indeed be present. If a chemical (metal or ligand) present
in the system is omitted from the input data for the program, then the
results will be in error. If the pH of the system is not known or if
the redox potential is not known when oxidation or reduction might
occur, then results will be in error. pH is not required if the chemical
form of all species introduced to the system is known (see Section III-
D, page 17).
The program is useful for situations such as 1) mixing compounds
together in a beaker of water and predicting what would happen after
equilibrium is reached, 2) determining the fate of a chemical introduced
into a well-characterized body of water (assuming no further mixing or
dilution), 3) predicting removal of chemicals through precipitation
under varying conditions of pH, redox potential, and ionic strength, 4)
confirming laboratory results for pH or precipitation, 5) predicting pH
or metal concentration in aquatic media for biological experiments, 6)
examining mixing and dilution effects in sequential cases with varying
initial concentrations. There are many situations in which the program’s
use is limited and these are discussed in Section II, page 7.
I-B. A SIMPLE SYSTEM
A simple aqueous system might contain calcium, sodium, magnesium,
iron(III), carbonate, bicarbonate, and chloride ions and combinations
thereof. Any aqueous system also has some hydrogen ions, H+, and
hydroxide ions, OW. These ions do not exist independently of one
another but may form complexes or even solids.
Suppose that 0.5 mole NaCl (29 g), 0.1 mole CaCO 3 (10 g), 0.05
mole Mg(HCO 3 ) 2 (4.2g), and 0.01 mole FeCl 3 (1.6 g) are placed in a
4

-------
liter of water. Do all the species exist only as ions in solution or do
+
other things happen? Complexes such as CaHCO 3 may form. Solids such
as MgCO 3 or Fe(OH) 3 may precipitate from the solution. Fe might be
reduced to Fe2 . Dolomite, CaMg(C0 3 ) 2 , may precipitate. This system
will serve as an illustrative example for use of the program.
In Section III, page 10, this example will be used to demonstrate
the flexibility of the program, how the initial run is set up, and how
the output is interpreted. Variation of some of the input parameters
will show other facets of the program. How these changes affect the
output will be discussed and illustrated.
It should be stressed that the quantities used to describe an
aqueous system do not have to be chemical compounds, as in the example
above, but may be analytical concentrations of aqueous ions such as
those concentrations that might be available from field data. If analy-
tical data are used it is well to keep the constraint of electroneutrality
in mind (see Section II, page 7).
I-C. HOW TO USE THIS GUIDE
A brief overview of the scope of REDEQL.EPA has been given in the
introduction. The specific examples which are worked through in Section
III can be used as further demonstration of the scope of the program or
as models upon which to pattern one’s own input data. After reading
this introduction the user is advised to read Section II, page 7, on
the limitations of the program and to bear these limitations in mind
while using the program.
The thermodynamic data are essential to the program. How to obtain
a copy of those data is described in Section V-B, page 40. The form in
which equilibrium constants are expressed is outlined and exemplified in
Section V-C, page 41. The format for storage of these constants and
other metal-ligand data is discussed with examples in Section V-A, page
35, and is summarized in Table 6, page 55. All tables are near the end
of this guide. Section V-A also includes information on how the thermo-
dynamic data may be changed to include new or different data. The
mechanics of creating and using a modified thermodynamic file are given
in Section V-B, page 40.
5

-------
The FORTRAN version of the program is not given here. It may be
obtained, without documentation, by the following steps:
(log on to WCC)
PRINT CN.EPABDJ.CPR1 .REDEQL. EPA,ROUTE=REMOTENN
where 1*1 is the user’s terminal number.
In Section III, page 10, the input required by the program is de-
scribed and samples given. Table 4, page 48, should be examined in
conjunction with Section III. Sample outputs from the input data are
shown in figures in the computer printout section at the end of the
guide. In individual sections ionic strength, total hydrogen, solids,
gas phase, mixed solids, and oxidation-reduction are considered, and
particular problems that can arise from variation of parameters under
different situations are stressed. When different options are given by
the program, e.g. fixed or calculated pH, the description gives some
advice on where to use either option. The user should read all those
sections which pertain to his system and should not rely only on Table
4, which gives the input format. Some undesired results, e.g. changes
in imposed conditions, are difficult to detect without hints as to where
to check for them.
Section IV, page 26, is a more complete description of the formats
of the output from the program. References to various outputs are given
in Table 5, page 54.
6

-------
II. LIMITATIONS OF REDEQL.EPA
Some problems which arise in the use of REDEQL.EPA are enumerated
below. Some of them, such as poor analytical data, are the responsibility
of the user. Others such as kinetics of reactions were never intended
to be within the scope of the program. Still other limitations may be
lifted in the future by refinement of the program or afford no obstacle
now for well defined cases. The most serious limitations are:
1. The program is for equilibrium . Kinetics of dissolution, precipi-
tation and oxidation/reduction are not considered. Few natural
systems are truly at equilibrium because of slow chemical
processes, biological activity, and transport.
2. The program does not consider surface effects . Neither the varia-
tion of surface properties of solids from bulk properties nor
adsorption is included. Although the program may incorporate
adsorption on some solids in the near future, this will be
adsorption only for well-characterized surfaces such as
metal oxides.
3. The program is no better than the data used. If there are errors
in analytical or thermodynamic data these will be propagated
by the program. Many equilibrium constants are only known
accurately to an order of magnitude. Some species which exist
have never been measured. Other analytical data, such as pE
(redox potential), are extremely difficult to obtain.
4. The ionic strength corrections of equilibrium constants used in the
program are not accurate above approximately 0.1 M ionic
strength and should not be used above 1.0 M, although the
program frequently is used for more concentrated solutions
with diminished accuracy. At high ionic strength activity
coefficients re very difficult to determine and to represent
with a simple mathematical formula.
7

-------
5. The program can violate electroneutrality . Nowhere in the computa—
tional scheme of the program is the number of positive charges
in a unit volume required to equal the number of negative
charges although this is fundamental to the laws of chemistry.
Consequently it is possible to have a problem which is poorly
specified chemically but which will still undergo computation
satisfactorily. When a problem is being set up, the ionic
strength guessed or imposed should be approximately correct
for the final equilibrium state and the solution should be
nearly neutral. Often analytical concentrations do not result
in a neutral charge for the solution. If on close inspection
(see the example in the following paragraph) the final state
shows a great charge imbalance (positive charge not equal to
negative charge), the metal or ligand concentrations for the
initial input should be modified. The concentration of a non-
+
ion such as Na , NO 3 , or Cl
be a species of high concentra-
problem in seawater as it is in
precitipating, non—complexing
should be changed. It should
tion. This is not so great a
dilute solutions.
In order for results to be realistic, the absolute value
of the net charge should be at least two orders of magnitude
below the ionic strength; in actuality, it should be zero.
Consider the results from the sample case shown in Figure 6c
and d, pages 62 and 63. Only charged species of concentration
greater than 1 x lO 5 M need be considered. Calculation of the
net charge of the solution is shown in Figure 1. The net
charge is found to be -0.00560 on one liter. The calculated
ionic strength is 0.630 mole/liter so in this instance the
net charge is less than 1% of the ionic strength and the
solution is not far from realistic. Other examples might have
a much larger charge relative to the ionic strength.
8

-------
Figure 1
Calculation of the charge of a solution
Ion
Concentration
(mole/i)
Charge
Concentration
of charge
Ca2
2.55 x l0
+2
±0.00510
Mg2
3.693 x l02
+2
+0.07386
Na
5.0112 x l0’
±1
+0.50112
C0 3 2
4 x lO
-2
-0.00008
Cl
5.2481 x lO
-1
-0.52481
CaHCO 3
l0 .° = 9.1 x l0
±1
+0.00091
NaCO 3
7 x 1O
-1
-0.00007
HC0 3
lO1.21 = 6.163 x 102
-1
-0.06163
-0.00560
6. Very small concentrations in the output may be inaccurate ; see
problems in convergence (Section TV-B, page 31).
7. Atmospheric concentrations of CO 2 and N must be fixed and cannot
vary during a computation except to disappear entirely (see
Section Ill-F, page 22).
8. No temperature or pressure variation is allowed for the thermo-
dynamic data in the program which is given for 25°C and one
atmosphere.
9. At low concentrations, organic matter which is undetected and
uncharacterized may strongly affect equilibria .
9

-------
III. DATA INPUT AND CONSEQUENT OUTPUT
Ill-A. SETTING UP A SIMPLE CASE
Figure 2 shows preparation of the input data for metals and ligands
for the sample case in Section I-B, page 4. The format and sequence of
the cards for program input are shown in Table 4, page 48, and a copy of
the input cards for this case is shown in Figure 3.
The program header card (1) shows that this case contains 5 metals
(4 plus H ) and3 ligands (2 plus OW). (Note that HCO is just CO
combined with H ). Initially, one case will be run and, to keep it
simple, solids will not be imposed or disallowed. This means that if
the solution is supersaturated with respect to any solid, that solid
will precipitate. Since the pH of the solution has not been measured,
the program will compute pH (1 in field 7). Neither redox nor mixed
solids will be allowed and ionic strength will be calculated for this
case (1 in field 10). All of the normal output will be printed and
input concentrations will be in molar units as shown in Figure 2.
Figure 2
Preparation of input data
Solution
content
Ionic
content
Total ionic
content
Reference
number
from
Table 1
-log M
0.5 M NaCl
0.1 M CaCO 3
0.5 M Na
0.5 M C1
0.1 M Ca 2
0.1 M COç
Metals
Na 0.5 M
Ca2 0.1 M
Mg2 0.05 M
Fe 3 0.01 M
5
1
2
6
0.3
1.0
1.3
2.0
0.05 M Mg(HCO 3 ) 2
0.01 M FeC1 3
0.05 M Mg2
0.10 M HC0
0.01 M Fe
0.03 M Cl
Li g ands
CO3 0.20 M*
Cl 0.53 M
1
3
0.70
0.28
*ccor) is the sum of all CO in the system, C0 , HCO 3 and CO 2 . This
example assumed no CO 2 is dissolved in the solution water.
10

-------
Figure 3
Input data cards for sample case
Card
Type
5
Column Mu
10 15
mb
ers
20
25
30
(1)
5
3 1 0 0
0
1 0
0
1
(2)
l.l6E
0
(3)
1
2
5
6
1.0 1.0
1.3 1.3
0.3 0.3
2.0 2.0
(4)
1
3
0.1 0.7
0.28 0.28
(5)
8.0
(6)
0.1
(7)
0.0
The second card (2) calls for ionic strength, in this case a guess
because the program will be allowed to calculate the ionic strength.
Ionic strength is discussed in Section Ill-C, page 15, and calculation of
a guess for it for this case is shown in Figure 4.
The four cards following (2) are the metal cards (3). The metal
numbers come from Table 1, page 45, and the calculation of -log M for
each ion is shown in Figure 2. An initial guess for the free ion con-
centration for the first case is needed. Usually this can be taken to
be the same as the total concentration. This will cause problems only
if almost none of the total concentration (<0.001%) occurs as the free
ion. For example, the free concentration of C0 3 2 is very small at low
pH (0—5). In the case shown the total concentration is taken as the
guess, except for C0 where the free concentration is lower (1.0)
because it is known that some COç will be HC0 3 and not free. More
realistic guesses might make the program work more efficiently. For
successive cases the free ion concentration guess is the free ion concen-
tration from the preceding case.
The two ligand cards (4) are prepared just as the metal cards (3).
Card (5) requires a guess of pH and, since C0 3 2 and HC0 3 are
present, a guess of 8.0 might be made.
Card (6) is required because pH is being calculated. The concept
of TOTH is explained in Section III—D, page 17, and calculation of it
11

-------
Figure 4
Estimation of ionic strength
n
I = (1/2) E M.Z. 2
1=1 1 1
where n = number of metals + ligands including H+ and OW.
= concentration of species i
Z 1 = charge of species i
For the sample case in Figure 2,
I = (1/2)(0.5 x 12 + 0.1 x 22 + 0.05 x 22 + 0.01 x 32 + 0.10 x 22
(Na 4 ) (Ca2 4 ) (Mg2 ) (Fe 4 ) (C0 3 2 )
+ 0.10 12 + 0.53 x 12 + io x 12 + io x 12)
(Hc0 3 1 (Cl i (H 4 )* (0W)*
= (l/2)(.5 + .4 + .2 + .09 + . + .1 + .53)
= 1.11 M
*Sjnce H 2 0 was part of the solution (H+) = iOfl’ M for pure water
and (H 4 )(OW) = lO’ then (OW) = iO M and both are too small
to affect ionic strength in this example.
for this example is shown in Figure 5. It is entered as a molar
concentration .
Card (7) is required because ligand 1 (C0 3 2 1 is present. In our
case pCO 2 is set to 0.0 which means the water initially in the system is
C0 2 -free and no CO 2 enters the system from the atmosphere. If CO 2 did
enter (or leave) the system it would change both the total amount of
C0 3 2 and TOTH since CO 2 is considered a complex of H 4 and C0 3 2 and
contributes two H to TOTH (see Section III-D, page 17).
Cards (8), (9), and (11) are not needed because redox is not con-
sidered. Cards (10) and (12) are not required because no solids or
mixed solids are considered.
The data as shown in Figure 3 are punched and run as described in
Section Ill-B, page 15. All of the output (7 routines) is reproduced in
Figure 6, page 60. These routines are described in detail in Section IV-
A, page 26.
12

-------
Figure 5
Estimation of TOTH
TOTH = sum of the total conc ntration of all H containing species
times the number of H in the_species minus the sum of the
total concentration of all OH containing species times the
number of OH in the species.
or, stated in symbols,
TOTH = a C(H ) - b C(OH
i=l j=l
where the C(H ). and C(0W). are the total concentration of the
species that contain I-i and OW and the a. and b. are the number
+ _. . 1 3
of H and OH in those ions.
From the example
TOTH = 1 x 0.1 + 1 x 1O - 1 x io
(HCO 3 ) (Hf) (OW)
= 0.1 M
tFor further details see Section 111-0, page 17.
Figure 6a, page 60, shows the input data for verification. These are
the thermodynamic data that the program uses for the specified case and
are interpreted in the same way as the thermodynamic data deck card (5)
(Section V-A, page 35.) A line of solids and complexes is printed for
every possible combination of metal and ligand specified on cards (3) and
(4) whether or not they actually form any solids or complexes. 100 log K
has been corrected by the program to the guessed ionic strength (Section
Ill-C, page 15).
Figure 6b, page 61 , reproduces the input data giving the number of
metals and ligands entered, the ionic strength used, the fact that ionic
strength will be computed, the initial free ion concentration (-log M)
guess for each metal and ligand, and their total concentrations (-log M)
for each case. pH is unfixed but guessed to be 8 and TOTH is shown.
Figure 6c, page 62, shows the first case progress. The program
required a total of 51 iterations to converge to equilibrium (obtain
small enough remainders for each ion). After 36 iterations, the first
13

-------
solid listed in the thermodynamic date file between Fe and 0H (Fe(OH) 3
from data in Figure 6a, page 60) precipitated. After 39 iterations the
first solid between Ca2 and C0 3 2 precipitated (CaCO 3 from Figure 6a,
page 60). After 48 iterations, ionic strength corrections were made.
The REDEQL calculated ionic strength is 0.63 M. Notice that this
is very different from our estimation of l.liM. TOTH and the calculated
p 1-i, 6.41, are printed. The free concentrations of all metals and ligands
are given as M and -log M and their total concentrations (which are the
same as the input) are also shown as M and -log M. The remainders are
used by the program in determining how many iterations are necessary.
The amounts of two solids which precipitate are given and for CaCO 3
this is 0.0964 moles/i while all of the Fe precipitated as Fe(OH) 3 .
Figure 6d, page 63, shows the concentration of complexes. For
instance, the 1 1 0 complex of Ca2 and C0 3 2 (1 Ca2 , 1 C0 , 0 H ) has
a concentration of iO 5 3 moles/i while the concentration of the 1 1 1
complex of Ca2 and C0 3 2 (1 Ca2 , 1 C0 3 2 , 1 H ) is io ° or (CaHC0 3 )
= 103.03 mole/i. Generally, complexes with -log M greater than 8 are
of no interest but this depends on the total concentration of the species.
This output tells us that (HCO 3 1 = 101.21 M and (H 2 C0 3 ) = io’ M.
In the output for speciation of ions (Figure 6e, page 63) the free concen-
tration of each ion is given and the concentration of each ion that is
paired with another is listed. For example, there are 101.05 moles!
+ 2
liter of H and CO 3 complexes. They are (from the concentration of
complexes output) (HC0 3 ) = l01.21 M and (H 2 C0 3 ) = 10 ’ and their
total is i0’ ° M. This output is a combination of data from the
concentration of complexes output (Figure 6d, page 63) in a more con-
venient form. A row of stars signifies a number greater than 100 which
is a very small concentration.
The primary distribution of metals and ligands (Figure 6f, page 64)
shows all species which compose more than 0.5% of the total concentration
of a metal or ligand. For instance 48.3% of the C0 3 2 is precipitated
as CaCO 3 , 44.6% is complexed with H as HC0 3 and H 2 C0 3 , and 6.5% is
+ + 0 .
complexed with Mg 2 as Mgl-1C0 3 and MgCO 2 . The stoichiometry of the
complexes has been taken from the concentration of complexes output
(Figure 6d, page 63).
14

-------
Figure 6g, page 64, is the thermodynamic data used after ionic
strength corrections have been completed. Observe, that, for CaCO 3 (s),
(Ca2 )(CO 3 2i = lO ’•° at ionic strength of 0.63, while at ionic strength
of 1.11, this solubility product (the inverse of the formation constant)
was lO .’. From the thermodynamic data deck the solubility product at
zero ionic strength is found to be 108.3. Further examples of input and
output will be given in the following sections.
1 1 1-B. RUNNING REDEQL.EPA ON THE EPA COMPUTER SYSTEM
The input cards described in Section Ill-A, page 10, and Table 4,
page 48, are placed within a set of control cards in order to run the
program on COMNET at the Washington Computer Center (WCC), Washington,
D.C. The program is run from a load module and also requires the thermo-
dynamic deck MREHT or another data deck as described in Section V-B,
page 40.
The following control cards are required:
//(Job Card ),TIME=2,
Ii REGION=25 K,MSGLEVEL=( ,Ø)
/1 EXEC PGM=SARRUN
//STEPLIB DD DSN=CN.EPABDJ.CPR1 .HUNS,DISP=SHR,UNIT=333Ø-l
//FTØ5FØØ1 DD DDNAME=SYSIN
//FTØ6F Øl DD SYSOUT=A
//FT1ØFØØ1 DD DSN=CN.EPABDJ.CPR1 .MREHT,
/1 DISP=SHR,UNIT=333Ø-l ,VOL SER=USER6
//GO.SYSIN DD *
(Insert input cards here)
1*
Ill-C. IONIC STRENGTH AND CORRECTION OF THE THERMODYNAMIC DATA FOR
IONIC STRENGTH.
Ionic strength (I) is defined by
n
I = (1/2) E M Z 2
i =1
15

-------
where is the molarity (molar concentration) of ion i and is the
charge on that ion. The ionic strength is unaffected by uncharged
species in solution but depends on all ions including complex ions in
solution. IOfliC strength for the program can be estimated from the
input concentrations of ions, but complexation and precipitation among
reactants will reduce ionic strength. Normally one would want the
program to calculate ionic strength, unless working in a solution of very
constant ionic strength (such as seawater), because ionic strength is
not easy to estimate accurately.
Ionic strength is required by the program to adjust thermodynamic
data to the solution considered. The thermodynamic data on file are for
infinite dilution. For each computation the program makes, the data are
corrected with either an imposed ionic strength or an ionic strength
computed by the program from the equilibrium concentrations of ions and
complexes present as described above. The extension of the program to
seawater and other solutions of high ionic strength is limited by the
accuracy of the thermodynamic data at 25°C corrected with activity
coefficients y calculated from the Davies (5) equation:
‘I-
-log y(IZI) = 0.509 Z 2 ( - 0.2 I) (2)
vT+ 1
where Z is the absolute value of the charge and I is the ionic strength.
This equation is used to find the log of the activity coefficients for
all ions with charge Z except whose value is taken as 1/2 log y(l).
K 1 (K corrected to ionic strength I), is related to K at infinite
dilution through the activity coefficients. For example, for
Fe + 2 C1 = FeCl 2 , (3)
(FeCl 2 ) K i(3)i(l)2
K 1 = + K y(3)y(l). (4)
(Fe 3 )(C11 2 (l)
K is listed in the thermodynamic deck, the y(!ZI) are calculated from
the Davies equation, and then K 1 is calculated according to equation (4).
16

-------
It has been shown in Section Ill-A, page 10, how ionic strength
corrections affect the thermodynamic data. Figure 7, page 65, shows
the same deck as Figure 3, page 11, but this time without ionic strength
calculations. The thermodynamic input for verification (not shown) is
exactly as that first listed in Figure 6a, page 60, but the case progress
is different and of course the free ion concentrations are different.
Ionic strength is not listed after each case because it is fixed in the
input data. Notice that the program converged after 48 iterations
because it did not make ionic strength corrections (compare with Figure 6c,
page 62).
III-D. TOTH = EH - E0H
TOTH is a way of counting one more species (like a metal or a
ligand) in all of its combined and uncombined forms. The species is
and like any other species it can be free or combined. pH is a measure
of the amount of free H , pH = -log (Hf), and if pH is fixed (given) the
program can use all the thermodynamic constants to determine how much
combined H exists, and the sum of free and combined H is TOTH. If pH
isn’t fixed, the program does the opposite calculation, using the value
for total H supplied as TOTH and the thermodynamic constants to calculate
free H (pH).
Unlike other species in the program, TOTH may have a negative
concentration because from the total H+ one must subtract total 0H since
every OW has the potential of annihilating one H in the reaction:
H + OW = H 2 0 KHO = (H )(0W) = l0’ (5)
At pH greater than 7, there is more free Oi-i than H ; TOTH may or may
not be negative, however, because TOTH includes combined H+.
TOTH is readily calculated if one knows the concentrations of the
compounds being put into solution. One simply adds the concentrations
of H+ and subtracts the concentrations of OW (written as -Hf) in
solution. Remember that some species, namely nonmetal oxides, form
acids (H+ donors) in water. For example,
CO 2 + H 2 0 = H 2 C0 3 (6)
so each mole of CO 2 in solution will provide two moles of H+. (Remember,
17

-------
too, that even if CO 2 is not put in solution, it may diffuse in from the
atmosphere, especially if the solution is of high pH.) Other species,
metal oxides in particular, react with water to give bases (0H donors).
For example,
A1 2 0 3 + 3H 2 0 = 2 Al (OH) 3 (1)
so that each mole of A1 2 0 3 is providing six moles of 0H.
Notice that, for both metal and nonmetal oxides, a whole water
molecule is added, not split. Na 2 CO 3 gives a basic solution in water
because of the reaction
CO 3 2 + H O = HCO 3 + OW. (8)
The solution is basic because there is more free OW than H , but 10TH
is zero because Na 2 CO 3 contains neither H+ nor OW and even after reacting
with water there is an equal amount of HC0 3 , which adds to TOTH because
of the H in it, as the amount of OW which subtracts from TOTH.
Some examples (Figure 8) will illustrate the TOTI-I concept for
solutions made from stock chemicals. Consider the classification of
compounds below as acids (H+ donors) and bases (OW donors).
Acids (H+ donors) Bases (OW donors)
CO 2 or H 2 C0 3 NaOH, Na 2 0, KOH
NaHCO 3 , H 3 PO , NaH 2 PO 1 , Na 2 HPO CaO,Ca(OH) 2 , Mg(OH) 2
HC1, H 2 SO , NaHSO 4 Fe(OH) 3 , Fe 2 0 3
NH . Cl, CH 3 COOH, RCOOH Al(OH) 3 , A1 2 0 3
H 2 SiO 3 , Si0 2 ZnO, Pb0 2 , CuO
H 2 5
H L*
m
*L = ligand
**M = metal
18

-------
Figure 8
TOTH sample calculations
1. A system made up of 2 mole NaHCO 3 , 0.5 mole Na 2 CO 3 , 0.2 mole
NH Cl, 0.8 mole NaH 2 PO,f, 1.0 mole Ca(OH) 2 , and 0.5 mole Fe(OH) 3 in one
liter of solution.
chemical
concentr
(M)
ation
+
moles H mole
÷
moles H /liter
NaHC O 3
Na 2 CO 3
NH Ci (NH 3 .HC1)
NaH 2 P0
Ca(OH) 2
Fe(OH) 3
2.0
0.5
0.2
0.8
1.0
0.5
1
0
1
2
-2
-3
2.0
0
0.2
1.6
-2.0
-1.5
TOTH = 0.3
2. A system with
10’M CU 2 ,
10 M
NaHCO 3 ,
10’M
CaO,
and 10’M CaCO 3 .
CO 2 (H 2 C0 )
NaHCO 3
CaO (Ca(OH) 2 )
CaCO 3
1 x
1 x
1 x
1 x
10_i
l0’
l0
10 1
2
1
-2
0
TOTH
2 x 10’
1 x 10 ’
-2 x l0
0
= 1 x 10’
3. A system with
1 x 10 2 M
Al (OH) 3
and 1 x l0 2 M
SO 3
Al(OH) 3 1 X 102 -3 3 x lO
so 3 (H S0 ) 1 x 1O2 2 2 x l02
TOTH = -l x lO
An estimate of TOTH is difficult to make for solutions for which
one has only analytical data. A measure of C0 3 2 , for example, generally
includes total CO and HCO 3 , but for TOTH only HC0 3 and H 2 C0 3 are
counted and H 2 C0 3 counts twice because it can donate 2 H+. One must
calculate from an estimated pH how much of the C0 3 2 exists in complexes,
as H 2 C0 3 , as free HC0 3 , or in HC0 3 complexes. The thermodynamic data
for acid dissociation complexes can be used from the thermodynamic data
deck, so that knowing K and Kc for such things as:
(HC0 3 ) (CaHCO 3 )
K and K = + ( )
(H )(COF) c (Ca 2 )(HCO 3 )
where all concentrations are free, one can estimate total HC0 3 concen-
tration with the restriction that
(CO3 2 )ana1ytica1 = (CO3 2 )tota1 + (HCO3 )total (10)
19

-------
(excluding H 2 C0 3 in this case). HC0 3 , if present, will probably be the
most important species in estimating TOTH, but any other incompletely
dissociated acids or bases will also contain H or OW. Possibilities
for a particular system will be found by scanning the thermodynamic data
+ -
for metal-ligand-H (OH ) complexes, metal complexes w th ligand 99, or
metal 50 (H )-Ugand complexes.
At pH less than 7 the amount of free OW is negligible and the free
concentration is determined by
+
pH = -log (H ).
Above pH 7, is negligible and free OW is given by
-log(OI-i) = 14 - pH
It is not a good idea to estimate TOTH from a guessed pH because
the program will regenerate the guessed pH unless the calculations used
to get TOTH from the guessed pH were inaccurate.
A sample calculation with TOTH given and pH calculated has been
shown in Figures 3, page 11, and 6, page 60. Figure 9, page 66, shows
three cases with fixed pH. Notice the TOTH card (6) is not used.
Fixing pH negates the assumption that the system initially had 0.1 mole
of C0 3 2 and 0.1 mole of HC0 3 although in the first case the total
C0 3 2 concentration is specified in solution as 0.2 M. In the second
and third case this is no longer true. Removal of the constraint that
pCO 2 = 0 allows the solution to equilibrate with atmospheric CO 2 (see
also Section Il l—F, page 22). Some of the 0.2 moles/liter C0 3 2 may then
be in the atmosphere as CO 2 and not in the solution at all. This will
riot change pCO 2 . In the second case 51.7% of the C0 3 2 is CO 2 and
essentially all of it is CO 2 in the third case. Note that CO 2 is denoted
a solid formed from two H and C0 3 2 . It is treated as a solid by the
computational scheme and appears in the thermodynamic data for solids
under metal 50, ligand 1. pCO 2 has been included in the value of K for
formation of H 2 C0 3 . Notice also that TOTH in the first case is smaller
than the fixed TOTH used previously while TOTH for the second and third
cases is larger. The increase is due to the increase in CO 2 in the
second and third cases.
The output routine which prints the input data records pCO 2 for
the third case as 0.0 while it is intended to be 3.5. However, as with
20

-------
the input cards, this 0.0 will’ be replaced by the preceding case when
the program runs, and, in checking the progress for case 3 output, page
69, this is found to be true.
III-E. SOLIDS: IMPOSED AND NOT ALLOWED TO PRECIPITATE
All or any combination of solids (up to 13) can be allowed to
supersaturate the solution. To do this, the program removes the solid
from the data file. This option might be used, for instance, when
seawater is known to be supersaturated with respect to CaCO 3 .
As an example in which no solids are allowed, consider the output
from the data deck shown in Figure lOa, page 71. The thermodynamic data
show no solids and the free concentrations in the case progress are
different from those in Figure 6c, page 62, where solids were allowed to
precipitate. The distribution of species is also modified. This solution
is now supersaturated with respect to CaCO 3 and Fe(OH) 3 but there is no
way to determine this from the output in Figure 10, page 71. It must be
compared to the output in Figure 6e, page 63.
Solids can also be assumed to be present (imposed), although they
will dissolve if the solution is not saturated with respect to them.
One might use this option if the solution in question were known to be
in contact with a solid or if one is quite sure a solid will precipitate.
In Figure 11, page 73, one solid, CaCO 3 is not allowed and MgCO 3 is
imposed. These solids are identified on card (10) by their metal, ligand
and solid number. A positive solid number imposes the solid for the
first case; a negative solid number disallows it for all cases. Notice
that in the thermodynamic input data for verification the value for log
K of CaCO 3 has been removed, so CaCO 3 will not precipitate and that the
imposed solid is listed at the end of the input data output routine. Be
sure, by checking the case progress, that the imposed solid does not
dissolve because, if it does, the assumption of contact of the solid
with the solution is wrong. The program will give the same results
whether or not a solid is imposed, so long as a number which is too
large or too small is not generated in the computational process. If a
solid phase is to remain in contact with the solution, be sure to allow
an excess of the ions it contains.
21

-------
In general, for small systems it is easier not to impose solids.
For larger systems the program will converge more rapidly if correct
solids are imposed, but convergence is even harder to obtain if in-
correct solids are imposed.
I ll-F. GAS PHASE, pCO 2
If the solution is in equilibirum with a gas phase (for example,
air), partial pressures for CO 2 and/or N 2 are required for each case.
Typical atmospheric values are —log CO 2 3.5 and -log N 2 = 0.1. C0 2 (g)
and N 2 (g) are treated as solids in the computer system since they are a
phase other than the aqueous phase. CO 2 will be listed as a solid
containing 2 H and 1 C0 3 2 . N 2 is listed as a solid containing 2 N0 3
and 12 H+ when redox is allowed and N0 3 is present. These gases will
be listed under these stoichiometries in the thermodynamic input data
for verification, in case progress, and in the primary distribution of
species.
When an atmospheric value of CO 2 is given for an equilibrium system,
it sets, through all possible equilibria, the amount of CO 2 in every
other possible form because of the reactions diagrammed below.
-H 2 0 H H
CO 2 - H 2 CO 3 - HC0 3 - C0 3 2
K 5 K 1 K
(Nat) (Ca2 )
K
NaI-1C0 3 CaCO 3
Many more complexes are formed than the two shown above. Details of
carbonate chemistry may be found in texts such as that of Stumm and
Morgan (4). The amount of each species will depend upon pCO 2 , the
constants, and free concentrations of H+, Na+, and Ca2+ for the example
given. When pCO 2 is not given, the total C0 3 2 for the case is divided
according to the thermodynamic constants among all possible forms. When
pCO 2 is given, the total C0 3 2 given must be greater than the sum of all
C0 3 2 species in equilibrium with that pCO 2 . This means excess CO 2 will
22

-------
just escape from the system. The imposed atmospheric pCO 2 is unaffected
by “precipitation of GO 2 ’ because the atmosphere is assumed large enough
and sufficiently mixed that CO 2 added to the atmosphere from the solution
does not change the pCO 2 .
However, if H 2 C0 3 dissolves when the program begins iterations, it
means that no CO 2 remains in the atmosphere because the system was not
given sufficient total C0 3 2 to be in equilibrium with the atmospheric
CO 2 . The solution is undersaturated and “CO 2 dissolves” leaving no CO 2
in the atmosphere but not increasing total CO 3 2 . This obviously is not
what one would expect to happen in a system in equilibrium with CO 2 in
the atmosphere. To avoid this situation total CO 3 2 should be given as
about 0.1 M or even larger at high pH.
III-G. REDOX COMPUTATIONS
When redox reactions are considered, be sure that all metals and
ligands (as listed in Table 1, page 45) in the reactions specified on
card (11) have been included in the metal and ligand cards, (3) and (4),
and determine a value for pE, -log (electron activity), in the system.
Typical values of pE in aqueous solutions range from -4 (reducing) to 12
(oxidizing). For elaboration of the concept of pE see Chapter 7 of the
text by Stumm and Morgan (4).
Judicious selection of redox equations is essential for proper
functioning of the program. If the pH and pE of the computation are
such that the concentration of a redox species is less than 10’°M or a
ratio of concentration of species linked by redox is less than l0 or
greater than l0 , species involved should be put in the program as the
dominant form and redox should not be considered. For example, put all
iron in as Fe2+ below pE = 6. Above pE = 6 put the total concentration
of iron in as Fe2+, Fe3+, or some combination of the two and include
redox reaction 1 . N0 3 may be reduced to NH 3 or NH 3 may be oxidized to
N0 2 . This can depend on pH as well as pE. For example, at pE = 6,
nitrogen should be considered as NO 3 above pH 8, as NH 3 below pH 4, and
as a mixture of the with the redox reaction allowed between pH 4 and
8.
23

-------
It is recommended in using redox reactions to introduce only one
reaction at a time and not to vary pE and pH greatly between cases. In
this way it is easier to trace which reaction is causing a problem such
as non-convergence (see Section IV-B, page 31) should it occur.
Caution must be exercised in using the redox reactions because the
kinetics of some are very slow, particularly the nitrogen reactions and
those involving oxidation of solids. If one is interested in short-term
effects, some redox reactions might not be included because of their
slow rates of reaction or because biological activity maintains the
concentrations which are not at equilibrium chemically. As an example,
consider that NH 3 and NO often occur simultaneously in aquatic systems
where their coexistence is not predicted by the program. Whether this
is caused by slow interchange (redox) or constant supply of one of them
doesn’t really matter. The user would want to leave both in the system
and not use a redox equation.
Use of a redox reaction is illustrated in Figure 12, page 76. This
computation is the same as Figures 3, page 11, and 6, page 60, but now
also includes a redox reaction so a pE card (8) and a redox card (11)
are needed. A pN 2 card is not needed as N0 3 (ligand 57) is not included.
Four cases from pE 12 to pE -4 are considered. The redox reaction
considered is 1 and, since Fe2+ is not part of the input, a metal card
(3) must be added for it. The concentration of Fe2+ is made very small
so as not to change the total iron concentration and since the first
case is oxidizing, the free ion concentration of Fe2+ will probably be
low. The first thermodynamic input data for verification output is
shown along with the four case progresses.
Ill-H. MIXED SOLIDS
Mixed solids and clays are treated just as solids in Section III-E,
page 21. Once mixed solids are specified by a 1 in field 9 of the pro-
gram header card, all mixed solids are allowed to precipitate when the
solution is saturated with respect to them unless a mixed solid is
imposed (postive) or not allowed (negative) on the mixed solid card
(12). An example in which dolomite is allowed to precipitate but no
24

-------
other mixed solids may precipitate because they are not allowed and also
because some of their components are missing in the solution is shown in
Figure 13, page 82. The thermodynamic input data for verification, the
case progress, and the primary distribution of species outputs are
shown.
I ll-I. MILLIGRAM/LITER INPUT AND OUTPUT
An option for mg/i input data is available by placing a 1 in field
17 of the program header card (1). This option has been introduced
because field data is more often available in this form than in moles/i.
Input data in this form produce the normal output routines except that
the input data reproduced will be in mg/i and the case progress gives
concentrations of all species in mg/i. The concentration of complexes
and speciation of metals output routines will have concentrations in
moles/i. Examples of input cards, input data output, and case progress
are shown in Figure 14, page 84.
25

-------
IV. PROGRAM OUTPUT
This section of the guide contains descriptions of both standard
output and undesired problem output.
tv-A. NORMAL OUTPUT
The output for the program if only zeros are placed in fields 11-16
of the program header card (1) appears in six printed formats. A seventh
showing interaction capacity and intensity is available by placing 1, 2,
or 3 in field 11 of the program header card. These seven outputs are
described in order of appearance below. See Table 5, page 54, for
references to examples of each of these outputs.
1. Thermodynamic input for verification
The first page of output is labeled input data for verification.
It is the input thermodynamic data corrected to the ionic strength given
on input card (2) (see Section Ill-C, page 15). This data format is
identical to that described in the thermodynamic data cards (5) in Table
6, page 55, except more widely spaced and the numbers given are 100 log
K rather than 10 log K. A line is shown for every possible metal-ligand
pair from those specified in the program input cards (3) and (4). In
any line the first number is the metal reference number, the second the
ligand reference number, and these are followed by nine groupings of
numbers, three for solids and six for complexes. Within each grouping
the first number is 100 log K and this is followed by the stoichiometric
coefficients of the metal, ligand, and H (O r - i if negative) respectively.
The log K values are not the same as the thermodynamic data because they
have been corrected for ionic strength. If a solid is not allowed, it
will not be listed in these data.
If mixed solids are considered, mixed solids data for those solids
whose components are included in the metal and ligand input cards will
be listed below the data for solids and complexes, unless the mixed
solid is not allowed. The mixed solid number from Table 3, page 47, is
26

-------
given first. The number preceding the M (or L) is the stoichiometric
coefficient of that metal (or ligand) whose reference number from Table
1, page 45, is within the parentheses. The number of hydrogens in the
solid is shown and is followed by 10 log K corrected for ionic strength.
Redox data are recorded but are identified neither by reaction
number nor name so they are hard to identify. The names of the re-
actions are listed in the next output routine of the input data. In the
thermodynamic input data for verification routine, the type of redox
reaction is printed (KRED), then the two species (MREDOX and LREDOX)
which are involved in the reaction (metal—metal, ligand-ligand, or
inetal-ligand), identified by their position (first, second, third, etc.)
among the input metals and ligands for the particular run, are printed.
The number of electrons produced (NELEC) and consumed (NHRED) are
also shown, along with 100 log K (REDCST) corrected for ionic strength.
This output is repeated after each case when ionic strength correc-
tions are being made by the program. The output after each case (but
not initially) may be suppressed by placing a 1 in field 16 of the
program header card. Only in the printout of this output after each
case will H 2 C0 3 (s) (C0 2 ) or H 12 (N0 3 ) 2 (s) (N 2 ) appear.
2. Input data for the program calculation
The second page of output describes the input data from the cards
read into the computer. The first line tells how many metals and ligands
were used and how many solid and complex equilibria were used. The
second line is the ionic strength as shown on input card (2). If ionic
strength is to be calculated and corrections performed on the constants,
this is stated. The number of cases considered is listed. After this,
the metal and ligand data are blocked out exactly as on the input cards
but with the metals and ligands labeled. After the blocked out data, a
line tells whether pH is fixed or not, the pH values for fixed pH or the
pH guess for the first case followed by all values of TOTH if pH is to
be computed.
27

-------
If any CO 2 pressures are on the pCO 2 input card (7), pCO 2 values
for all cases will be listed. A zero following a non-zero value for
pCO 2 will be treated as the non-zero value.
The redox potential, pE, will be listed in each case if redox is
considered.
All solids which are imposed are listed by metal, ligand, and place
(first, second, or third) in the thermodynamic data list, and mixed
solids imposed are listed by number (from Table 3) and components.
Redox reactions considered are listed by the name given them in
columns 46-53 of the redox reaction cards (7) from the thermodynamic
data deck.
3. Case progress for each case
The output routine for the first case progress will follow the two
routines above. After it prints all the following routines, the program
will print case progress for the second case, the following routines,
case progress for the third case, etc.
The case progress routine gives a brief outline of what is happening
during successive program iterations for the case in question. The
final free concentrations (not complexed or in solids) of all species
are given as well as the “concentration” of solids and gases. i.e., how
much of the solid or gas precipitated from one liter of the initial
solution. Each time the program determines that the solution is super-
saturated with respect to a solid which could precipitate or undersatu-
rated with respect to a solid with which it is in contact, the solid
which precipitates or dissolves is printed under the number of iterations
done up to that point. The number of iterations with no other notation
is also printed every time the ionic strength is recalculated. The last
number of iterations is the number required to obtain convergence. The
smaller the number of iterations, the more efficiently the program ran
because of a simple case or good guesses of free concentrations, pH,
ionic strength, imposed solids, etc.
The ionic strength is printed if calculated. TOTH and pH are
printed. pE is printed if redox is included. The free concentrations
28

-------
and total concentrations are printed in mole/i or mg/l. The total
concentrations should agree with the input data unless two species are
linked by redox (see Section III-G, page 23) in which case the sum of
their total concentrations may appear under one or the other. A remainder
is the difference between the total concentration of a metal or ligand
and the sum of concentrations calculated for that species in all of its
forms. It must be less than 0.01% of the total concentration for con-
vergence.
The total amounts of solids and mixed solids in contact with one
liter of solution are given. The solids are identified by their metal,
ligand, and solid number 1, 2, or 3 representing whether it is the
first, second, or third solid listed in the thermodynamic data.
This output can be suppressed by a 1 in field 12 of the program
header card.
4. Concentration of complexes
The concentration of complexes output, unless suppressed by a 1 in
field 13 of the program header card, follows case progress for each
case. For each metal and ligand which form a complex the metal, the
ligand, -log M for the complex, and the stoichiometric coefficients of
the metal, ligand, and H (OW if negative) are given.
5. Speciation of the metals and ligands
Speciation of the metals and ligands is given after the concentra-
tion of complexes output unless suppressed by a 1 in field 14 of the
program header card. The output is blocked out in a matrix of metals
and ligands. The free concentration of each metal and ligand is given
as -log M and the sum of all concentrations of all complexes of a given
metal and a given ligand is given as -log M. The free concentrations
are the same as those shown in the case progress output. The individual
complexes which sum to the total complex concentration can be found in
the preceding complex concentration output.
29

-------
6. Primary distribution of metals and ligands
The output for the primary distribution of metals and ligands,
unless suppressed by a 1 in field 15 of the program header card, shows
the form (free, bound or complexed with some other species, or in solid
form with another species) and percentage of any fraction of a metal or
ligand which comprises more than 0.5% of the total concentration of that
metal or ligand.
7. Interaction capacities and/or intensities
Interaction capacity and intensity are measures of how strongly the
concentration of one species is affected by a change in concentration of
another species. In the output and for the following, the X component
is listed vertically and the Y component is listed horizontally and they
are both all the metals and ligands used in the case shown.
Capacity, is defined by
p(X ) l4
X,Y aTOTY
Where p(X) is -log of the free concentration of the X component and TOTY
is the total concentration of the V component.
Intensity, SXY is defined by
= ap(X ) 15
X,Y p(T0TY)
where p(X) is as above and p(TOTY) is -log of the total concentration of
the V component.
X,H is always printed instead of because the latter cannot
be defined in general since TOTH can be zero or negative. For a complete
explanation of the corcept of interaction capacities and intensities see
Morel etal. (3). This output appears only when 1 (capacities), 2 (in-
tensities), or 3 (both) is entered in column 33 of the program header
card.
30

-------
A portion of an interaction capacity output is shown in Figure 15,
page 86. In the first column -195 indicates that a small change in the
total Ca2+ ‘-.oncentration sharply decreases the free Mg2+ concentration
while -0.0003 indicates the free K concentration is relatively unaffected
by changes in the total Ca2+ concentration.
IV-B. ERROR MESSAGE OUTPUT
Both program- and system-generated error messages are considered to
be problem output. Actually any output that gives an undesired result
is problem output. Four program-generated error messages may occur:
1. Be careful - no convergence
This message is generated in the case progress output when 200
iterations have been made. An example is shown in Figure 16, page 87.
Two possible reasons why convergence might riot be obtained are:
(a) If a large solid set is generated or for very large computa-
tions, the system may be converging although more iterations are required.
In this case the remainders will be smaller than the total concentrations
shown on the case progress. To correct, run again using the free concen-
trations shown on the case progress and imposing the solids listed there
and no others.
(b) If the system has diverged, the values of the remainders will be
larger than the respective total concentrations for some species. Thus
by comparison of the remainders and total concentrations the problem
areas of the computation may be identified. Also, ridiculous concentra-
tions may be apparent such as that shown for free Ca2+ and CaCO 3 (s) in
Figure 16, page 87. This particular output was obtained when pE was
varied from case to case. A slight change in total or guessed concen-
trations might remove the problem. Further information can be obtained
from the listing of complex concentrations. By hand calculation of a
small subsystem in which the problem is suspected to originate, better
31

-------
guesses can be made as to free concentration and imposed solids and then
the program run again with these guesses. As mentioned before, be
especially careful when considering redox reactions and varying pE and
pH.
Two particularly bad cases for obtaining convergence are:
(1) If both a metal M and a ligand L are nearly all bound in a
strong complex C, i.e., K = (C)/(M)(L) is very large and the total
concentration of the metal is approximately the same as the total con-
centration of the ligand, e.g., K = 1020, (C) l02, total concentra-
tion of metal = total concentration of ligand = 102, then (M) = CL) =
10’’ but the equation is also satisfied within the precision of the
program when (M) = 1013 and (L) = lO .
(2) If a solid with small K is computed from a large equation,
e.g., the total concentration of Ca2+ = 101 and the total concentration
of PO 3 = 108, and Ca 5 (P0 ) 3 0H is present, very small changes in the
concentration of either Ca2+ or P0 3 can give very different solubility
results because of the large stoichiometric coefficients.
2. Error return from GAUSSL - Diagonal term reduced to zero
This message is generated if one of the terms on the diagonal of a
computational matrix becomes zero. This is highly unlikely for a properly
specified system . To correct this situation carefully check the condi-
tions of the problem specified. The input cards for metals and ligands
have probably been prepared incorrectly (see Section Ill-A, page 10).
3. Gibbs phase rule violated in subsystem
This message is generated when a solid set is imposed which is
inconsistent with Gibbs phase rule. Gibbs phase rule is a limitation on
the number of solid, liquid, and gas phases that can coexist. This is a
physical limitation not a program limitation and is similar to the
reason why ice, water, and water vapor do not coexist in equilibrium at
32

-------
25°C and one atmosphere pressure. This program allows at most one gas
and one liquid phase, but each solid is a different solid phase. When
too many solids are imposed initially, Gibbs phase rule will be violated.
To correct this situation, restart the computation with a set of imposed
solids consistent with the phase rule (fewer solids).
The fact that the preceding case is used as a guess for the next
case may also cause phase rule problems when the preceding case pre-
cipitated solids because those solids are imposed on the next case and,
if pE, pH or some other parameter is radically different between the
cases, those solids probably should not be imposed. A much less likely
cause for violation of Gibbs phase rule is that the program did not
generate the set of solids for the case correctly. A better guess of
the solids to impose should be made in this instance.
4. Repeated precipitation-dissolution
Under some circumstances the program will precipitate a solid phase
and then dissolve it, repeatedly. It is likely in this case that another
solid (possibly in the same row of thermodynamic data) should be pre-
cipitated instead. To correct, restart the computation with the suspected
correct solid imposed.
System generated program errors which are likely to occur are shown
below.
5. 1HN208 Underflow - this message has been suppressed but the error
is generated as the result of computation of a number too small in
magnitude for the computing system, e.g., a species with a concentration
of 10b00 M. This error can be ignored, but the number of times it
occurred is printed at the end of the program output.
6. 1HN217 End of data on unit 5
7. 1HN205 Illegal decimal character - These messages (6 and 7) are
generated by any of the input routines as the result of incorrect input
data cards. The input cards should be carefully checked against the
33

-------
sequence, formats, and total number of cards specified in Table 4, page
48, and Section III, page 10.
8. 1HN207 Overflow - This message may be generated as the result of
computations of very large numbers (10+72). Such a condition normally
will not allow the program to converge, and the computation will be
terminated by default after ten of these errors occur. This situation
will usually be caused by the computations of redox systems over a wide
range of pE. Care should be taken in performing such computations so
that redox species at extremely small concentrations are not included in
the chemical system (see Section III-G, page 23).
9. 1HN209 Divide check - This message is generated when division by
zero occurs. It may be caused by a total concentration set to zero
unintentionally. Particularly in the first case of mg/liter total
concentration input, be sure to make the total concentration > l01 +
mg/i.
10. 1HN253 Argument of a log is equal to or less than zero - This
error usually occurs when other errors described above have been made.
34

-------
V. THERMODYNAMIC DATA
Formation (stability) constants at infinite dilution are required
by the program. All reactions are written in terms of metals, ligands,
protons, and electrons. The constants used with the program were se-
lected mainly from the compilations of Sillen and Martell, Garrels and
Christ, and Ringbom (6-9). One can use these constants corrected to a
given ionic strength (e.g., O.5M) or ionic strength corrections can be
made on the constants continuously while the program is running. The
program now uses the Davies (5) equation to make ionic strength correc-
tions; see Section Ill—C, page 15.
Equilibrium constants are stored as log K where K is the formation
constant for a given solid or complex at infinite dilution. For solids,
the log of the formation constant is the negative log of the solubility
product. All formation reactions are written in terms of free metal
ions, free ligands, and protons (H+). Calculations of formation con-
stants to use in the thermodynamic data are illustrated in Section V-C,
page 41. The program design allows for a maximum of three solids and
six complexes of a given metal-ligand combination. For example Ca 5 (PO 4 )OH,
Ca H(POi ) 3 and CaHPO are three solids of Ca2 and POr currently listed
and six complexes of Ni and NH 3 are Ni(NH 3 ) , Ni(NH 3 ) , Ni(NH 3 Y
Ni(NH) 3 ) , Ni(NH 3 ) and Ni(NH 3 ) .
V-A. THERMODYNAMIC DATA DECK
The format and variables for the thermodynamic data deck are listed
and defined in Table 6, page 55. Examples of data lines from this deck
are shown in Figure 17, page 36, and the following text explains the
deck and how to modify it. It is recommended that users examine the
thermodynamic deck before using the program to determine whether complexes,
solids, redox reactions, etc., in which they are interested are included
in the data. Users are encouraged to create their own data files to
suit their own needs. The process of listing, copying, and using an
independent data deck is described in Section V-B, page 40.
35

-------
Figure 7. Examples of thermodynamic data cards.
Within each card group
Column numbers ore in the first line,
Sample cords are in the intermediate line(s),
Field numbers are in the last line.
I 2 3 56 1213 21
(3) 09-03 1.00 94.980
I 2 3 4
56 lOll 5
(4) 803:4.0 180.0
2 3
23 4 5 8 9 0111213 6718 192021 24(2526272829 323 34353637 4( 4Il4 434445 48 )49) 5i 5253 56 7i58(596C 6l 64)65)66)676869 72173 174757
l5 99377320 0000 0000 16011 1213)1)12 I I I ) I
9 9 9 - 8 3 I 0 - 2 0 0 0 0 0 0 0 0 - 7 9 I 0 - I o )olo 0 0(010 0 0 0)0) 0 010 01 0 0)0)0 0
I 2 3 4 5 6 7 8 9 0 II 213 4 5 1617 8 9 C 2I 22 23 (24125 26 27 5129) 30 31 (323 34 35 (3 3 38
(6) 1 2 4
I 56 lOll 1516 202! 2526 303! 3536 404! 4546 53
01 06 07 —10 - l 0 130 0 OFE2/FE3
02 08 99 -2 2 —4—0420 I OMNO2
04 4 99 03 —2 0000307 2 0862+2
09 7 57 0 8 —9—1100 0 0N 83/N03
2 3 4 5 6 7 8 9 0
I 4
(8) 06
I 4 5 8 9 1213 1617 202! 2425 2829 3233 3637 40W! 44)45 5051 5354 5657 6485 71
2 I 2 4 50 50 5 12 —020 13874 46 70 ILL! TE 7678.21
5 0 5 20 09 3 5 0 3 I 804 PBPO4CL 356.83
2 3 4 5 6 7 8 9 10 II 12 13 14 5 16
COLUMN NUMBERS
5 0 5 20 25 30 35 40
I 34 6
(I I 35 59
I 2
23 56
(2) 23002
I 2
1213
.35
3
2!
9.102
4
45 50 55 60 65 70 75

-------
1. Metals and ligands
Examples of the metal-ligand header card (1), a metal card (2), and
a ligand card (3) are shown in Figure 17, page 36. Card (1) says the
thermodynamic deck includes information on 35 metals and 59 ligands.
Card (2) says metal 23 (Be2 from Table 1, page 45) has a charge of +2,
an ionic radius of 0.35 A, and an atomic weight of 9.102 grams/mole.
Sample card (3) says ligand 9 (P0 3 ) has a charge equal to -3, ionic
radius of 1.0 A (if ionic radius is unknown assume 1.0 A) and a molecular
weight of 94.98 grams/mole.
If the user wishes to add more metals or ligands to the deck, this
may be done by increasing the numbers on the header card and adding
cards for metals 35 to 49 and ligands 59 to 89. Metals and ligands
should not be renumbered or rearranged in the data file or they will be
labeled incorrectly in the program output. Added metals and ligands
will be labeled only as, for example, M37 and L69 in the output unless
the program is modified.
2. Complexes and solids
The next card (4) in Figure 17, page 36, after the metal and ligand
cards gives the total number of data lines to follow for solids and
complexes between the available metals and ligands, the negative log of
the ionization constant for water, and 10 log K for the reaction:
+
2H + C0 = C0 2 (g) + H 2 0 (16)
specifically, card (4) in Figure 17 says:
803 lines of data exist for complexes and solids,
K = (H )(0H) = l0’ , and (17)
PCO 2 / (H )2(C0 ) = 1018 (18)
The solid and complex cards tell what solids and complexes can
exist between a given metal and ligand. These solids and complexes are
identified in the program by the metal and the ligand they contain and
their order in the line of data for that metal-ligand pair, i.e. as 1,
37

-------
2, or 3 for the first, second, or third possible solid and as 1 through
6 for the first through sixth complexes. The stoichiometry of the
solids and complexes is given in the thermodynamic data and in some of
the program outputs.
Two examples of card (5) are shown. The first of these cards
reads: metal 9 (CU2 ) and ligand 9 (P0 3 ) form a solid with log K =
+37.7 (log = -37.7) containing 3 CU2 4 , 2 P0 3 , and no H or 0H.
Thus
3 Cu + 2 P0 3 Cu 3 (P0 ) 2 (s) K = iO (19)
+
Cu 2 and P0 3 also form two complexes as follows:
CU2 + + = CuHP0 K = 1016.0 (20)
Cu2 + P0 3 + 2 H CuH 2 P0 K = 1021.3 (21)
The second data card says metal 9 (CU2 ) and ligand 99 (OH1 form a
solid with 1 CU2 and 2 OW with log K = -8.3. This reaction is not
written with OW so,
CU2 4 + 2 H 0 Cu(OH)o (s) + 2 H K 108.3 (22)
Similarly for the complex,
Cu2 + H 2 0 = Cu0H + H K = IQ (23)
See Section V-C, page 41, for further detail regarding K.
In these solid and complex cards (5), additions, deletions, or
modifications may be made on any card with no other changes in the data
deck. Also a line of data may be deleted or added and in that instance
the total number of solid and complex lines in the data deck must be
corrected on the header card (4).
3. Redox equations
The number of redox reactions available follows the solid and
complex data and is given on card (6). Each of these reactions is
described on a redox card (7). The redox reactions currently on file
are given in Table 2, page 46.
For example, card (6) in Figure 17, page 36, says 24 redox reac-
tions are on file. Four examples of redox reactions are shown as card
38

-------
(7), one for each type as given in field 4. The first card (7) specifies
that the first redox reaction (field 1) is of type -10 (field 4),
oxidation or reduction, with metal 6 (Fe ) (field 2) transformed to
metal 7 (Fe2 ) (field 3), with consumption of 1 electron (field 5) and
no H (field 6). Log K is 13 (field 7).
Fe + e = Fe2 K = (Fe2 )/(Fe3±)(e) = l0’ (24)
In the second card (7) reaction 2 is of type -2, metal 8 (Mn2 ) and
ligand 99 (0H) form a solid, 2 electrons, and 4 H . The solid contains
1 Mn and no 0H (fields 8 and 9) so 0H is not really involved. The
reaction is:
Mn2 + 2H 2 0 = Mn0 2 (s) + 4 H + 2 e K = l0 2 .0 (25)
In the third card (7) reaction 4 is of type 3 so metal 14 (Hg ) and
ligand 99 form a complex consuming 2 electrons and unaffected by H+.
Two Hg2+ are involved and 0H is again not used. Thus,
2 Hg2 + 2 e = Hg 2 2 K = io ° (26)
In the final redox reaction card shown reaction 9 is of type 10, so
ligand 7 (NH 3 ) is oxidized to ligand 57 (N0 3 ) producing 8 electrons and
9 H :
NH 3 + 3H 2 0 = N0 3 + 8 e + 9 H K = (27)
More reactions may be added up to a total of 30. The total number
must be corrected on card (6).
4. Mixed Solids
The final data stored in the thermodynamic deck are for mixed
solids. Each mixed solid is assigned a number and the total number is
recorded on card (8). One card follows for each solid and this card
includes the composition, stoichionietry, formation constant, and mole-
cular weight of the solid.
Card (8) in Figure 17, page 36, says 6 mixed solids are available
to the program. Cards (9) are two examples of mixed solids available to
the program. Mixed solid 2 (field 1) illite is of type 1 (field 2), (an
aluminosilicate or clay) and contains 5 (field 7) metal 2, Mg2 (field
39

-------
3), 12 (field 8) metal 4, K (field 4), no other metals (only 50 in
fields 5 and 6), 20 0 1 -i (field 11), 46 Al (field 13) and 70 Si0 2 (OH) 2 2
field 14). Thus the mixed solid is Mg 5 K 12 A1Lf 6 (Si0 2 (OH) 2 ) 70 (OH) 20 , or
1/20 of this as shown in Table 3, and the molecular weight is 7678.40
and log K = 1387.4. The second mixed solid shown (5, field 1), is of
type 0 (field 2) and contains 5 (field 7) metal 15, Pb2 (field 3), 3
(field 9) ligand 9, P0 3 — (field 5), and 1 (field 10) ligand 3, Cl
(field 6). This solid is Pb 5 (PO 1 ) 3 Cl. The formation constant is l080.
and its molecular weight is 1356.83 grams/mole.
More mixed solid cards may be added to a total of 20. The mixed
solid header card (8) must be changed if other mixed solids are added.
V-B. ACCESS TO THE THERMODYNAMIC DATA FILE
All users should obtain a listing of the thermodynamic data file,
MREHT. This can be done by the following step:
(log on to WCC)
PRINT CN.EPABDJ.CPR1 .MREHT,ROUTE=REMOTENN
where NN is the user’s terminal number.
Some users will want to modify the thermodynamic data as described
in Section V-A, page 35. To create a different thermodynamic file for
personal use the following steps can be taken:
(log on to WCC)
LOAD CN.EPABDJ.CPR1 .MREHT
(modify data file as desired)
PRINT *,ROUTEREMOTE fl
SAVE . NEWNAME
where NEWNAME is a name assigned to the newly created file.
In order to use the new data file with REDEQL.EPA replace
DSN=CN.EPABDJ.CPR1 .MREHT
with DSNCN.EPAIII.AAAA.NEWNAME,
where III = customer identification
AAAA = account number
in the seventh control card shown in Section Ill-B, page 15.
40

-------
V—C. PREPARATION OF DATA FOR SOLIDS AND COMPLEXES FOR ENTRY INTO THE
THERMODYNAMIC DATA FILE.
To enter a solid or complex into the thermodynamic data file one
must know the metal and ligand composition of the solid or complex and
be certain these are given in cards (2) and (3) of the thermodynamic
deck. The formation reaction for the solid or complex must be written
and K (the equilibrium constant) for that reaction must be ascertained.
Often, K for the formation reaction is not known, so it must be deter-
mined from some related parameter. OH can not be
but must be replaced by H 2 0 and H+, because H+ and
pendent species but are related by the ion product
Consider the complex CdOH . For this complex
is written:
Cd2 + H 2 O CdOH + H (28)
Any of the following data might be known for the species CdOH
(c) i G° for the reaction (28) above, where G° is the free
energy of reaction.
(d) G°’ for the reaction (29) above.
(e) G°f for CdOH , the free energy of formation of C OH
which is the change in free energy when CdOH is
formed from elements in their standard states:
Cd(s) + 1/2 0 2 (g) + 1/2 H 2 (g) CdOH + e (30)
the program needs log K. The other quantities, (b) through (e) can be
readily converted to K. The equations relating each of these to K are
shown below.
For (b), K = K’KW where K. = (H )(OH) (31)
= lO1’+
used in any reaction
OW are not inde-
of water, K .
the formation reaction
( CdOH ) (Hf )
(a) K = ___________
(Cd2 )
(CdOH )
(b) K’ = ___________
(Cd2 ) (OW)’
the equilibrium constant for the
formation reaction required by the
program at infinite dilution.
the equilibrium constant for the
forqjation reaction including 0 1- I
Cd 2 + a l- i = Cd OH (29)
41

-------
For (c) log K = - 2 303RT where R = 1.987 cal/mole-deg (32)
T = 298.16°K
For (d), log K’ = - 2.303RT where R andl are as above. (33)
and
log K = log K’ + log K (34)
For Ce) either G° or G°’ can be calculated provided L G is known,
where is the change in free energy when CdOH+ or any other species
is formed from elements in their standard states (equation 30). For any
reaction, G° is the sum of the free energies of formation of the
products minus the sum of the free energies of formation of the reactants.
Thus for the reaction shown in equation (28), the change in free energy
is:
= G CdOH+ + L G H+ - L G Cd2+ - where AG H+ 0 (35)
and the values for reactants are obtained from tables (e.g., refer-
ences 10 and 11). Then determine K from equation (32).
As a second example of free energy of reaction G°’ for reaction
(29) is determined by equation (36),
- txGf cd2 - f,0H (36)
where the values for reactants are obtained as above. Then deter-
mine K using equations (33) and (34).
Any equation written in reverse from those given here will have the
opposite sign for the change in free energy and K will be the reciprocal
of that required by the program.
1. A reference might give
= -62.4 kcal/mole
Proceeding as in Ce) above, reaction (28) may be written. From a
tabulation (10, 11)
= -18.54
f,H 2 0 = -56.69
= 0
42

-------
Subtraction of the free energy of formation of the reactants from the
energy of the product (equation 35)
= -62.4 + 0 - (-18.54) - (-56.69)
= 12.83 kcal/mole
12830 cal/mole
and then from equation (32)
1 K— 12830
og — - (2.303)(l.987)(298. 16)
log K = -9.4
2. Or some reference might give K’ for reaction (29) then
proceeding as for (b) above using equation (31)
K =
K 1O
and
log K = -9.4 as in the first example.
After log K has been determined, the data can be inserted in the
thermodynamic data file according to the format in Table 6, page 55.
Data for solids are similarly treated. Solubility products are
often given and these are the reciprocal of formation constants.
43

-------
REFERENCES
1. McDuff, R. E. and F. M. Morel, Technical Report EQ-73-02: Description
and use of the Chemical Equilibrium Program REDEQL2 . W. M. Keck
Laboratory of Environmental Engineering Science, California Institute
of Technology, Pasadena, 1975.
2. Morel, F. and J. J. Morgan, “A Numerical Method for Computing Equili-
bria in Aqueous Chemical Systems,” Environ. Sd. Tech. , 6:58-67, 1972.
3. Morel, F. and R. E. McDuff and J. J. Morgan, “Interactions and chemo-
stasis in Aquatic Chemical Systems--the role of pH, pE, solubility
and complexation,” in P. C. Singer (ed.), Trace Metals and Metal-
Organic Interactions in Natural Waters , Ann Arbor Science Publishers,
Ann Arbor, 1973.
4. Stumm, W. and J. J. Morgan, Aquatic Chemistry , Wiley-Interscience,
New York, 1970.
5. Davies, C. W., Electrochemistry , Philosophical Library, London, 1967.
6. Sillen, L. G. and A. E. Martell, Stability Constants , Special Publica-
tion 17, The Chemical Society (London), 1964.
7. Sillen, L. G. and A. E. Martell, Stability Constants--Supplement #1 ,
Special Publication 25, The Chemical Society (London), 1971.
8. Garrels, R. M. and C. L. Christ, Solutions, Minerals and Equilibria ,
Harper and Row, New York, 1965.
9. Ringbom, A. Complexation in Analytical Chemistry , Wiley-Inter-science,
New York, 1963.
10. Handbook of Chemistry and Physics 53rd Edition, CRC Press, Cleveland,
1973.
11. Lewis, G. N., M. Randall, K. S. Pitzer, and L. Brewer, Thermodynamics ,
McGraw-Hill, New York, 1961.
44

-------
= acetate
ACAC = acetylacetate
CIT = citrate
OX = oxalate
SAL = salicylate
TART = tartrate
EN = ethyl enedi aol ne
DIP = dipyridyl
SUSAL = sulfosalicylate
GLY = g lycine
GLUT = glutamate
PIG = picolinate
NTA = nitrilotriacetate
EDTA = ethylenediarninetetraacetate
DCTA = 1 ,2-diaminocyclohexane-tetracetate
CYST = cysteine
NOC = nocardamine (desferri-ferrioxaniine)
PHTH = phthalate
ARG = arginine
ORN = ornithine
LYS = lysine
HIS = histidine
DTPA = diethyl enetriami nepentaacetate
a s par tate
serine
alani ne
tyros I ne
methioni ne
val I ne
threoni ne
phenylal ani ne
i sol euci ne
leucine
prol me
Table 1 . Reference Numbers for Metals and Li gands
Metals
1.
Ca2
8.
Mn
15.
Pb2
22.
Li
29.
Ce
2.
Mg
9.
Cu
15.
Co
23.
Be2
30.
Au
3.
Sr
10.
Ba
17.
Co
24.
Sc
31.
Th
4.
K
11.
Cd
10.
Ag
25.
Ti0
32.
UO
5.
Na
12.
Zn
19.
Cr
26.
Sn2
33.
Cu
6.
Fe
13.
Ni
20.
Al
27.
34.
CH 3 Hg
7.
Fe
14.
Hg
21.
Cs
28.
La
50.
H
Ligands*
1.
C0
13.
SO
25.
GLL’T 2
37.
ASP
49.
S0f
2.
S0’
la.
CN
26.
PIC
38.
SER
50.
SCN
3.
C1
15.
AC
27.
NTA 3
39.
ALA
51.
NHOH
4.
F
16.
ACAC
28.
EDTA
40.
TYR
52.
MoO
5.
Br
17.
CIT
29.
DCTA
41.
MET
53.
W0
6.
I
18.
OX -
30.
CYST 2
42.
VAC
54.
As0
7.
NH
19.
SAL-U
31.
NUC
43.
THR
55.
HVU
S.
S
20.
TART-
32.
PHTH-
44.
PHE
56.
Se0
9.
P0
21.
EN 2
33.
ARG
45.
1S0
57.
N0
10.
P0
22.
DIP
34.
URN
46.
LEU
58.
DTPA
11.
P 0
23.
SUSAL
35.
LYS
47.
PRO
99.
0H
12.
Si0(0H)
24.
GLY
36.
HIS
48.
B(UH)I
ASP =
SER =
ALA =
TYR =
MET =
VAL =
THR =
PHE =
ISO =
LEU =
PRO =
45

-------
Table 2. Redox Reactions: Reference number, type, and equilibrium constant
Reference
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Reaction
Type
-10
—2
—2
3
—2
-10
3
10
10
1
-10
-2
—2
—3
—1
4
5
6
—1
3
4
-10
—1
—1
13.0
-42.0
28.7
30.7
-49.2
-31 .6
13.2
20.0
-110.0
-60.1
-5.1
45.3
6.4
-61.7
—25.7
-135.2
-68.4
-74.9
16.2
71.6
87.1
-2.6
8.8
208.9
Reaction
+ 2+
Fe 3 + e- - Fe
Mn2 + 2H 2 0 Mn0 2 (s) + 4H + 2e-
+
Hg 2 + 2e- - Hg(liq)
+ +
2Hg 2 + 2e- -* Hg (aq)
p52k + 2H 2 0 Pb0 2 (s) + 4H + 2e-
0+
Co -# Co + e-
C0 + 6H + 4e- - CH 2 O(aq) + 2H 2 0
S0 + 8H + 8e- S 2 + 4H 2 0
NH 3 (aq) + 3H 2 0 -* N0 + 9H + Be-
2N 2 0 - H 2 0 2 + 2H + 2e-
Sfl2+ Sn + 2e-
Fe2 + 2S 2 - FeS 2 (s) + 2e—
3Fe + 4H 2 0 + e- -* Fe 3 0 (s) + 8H
3Mn2 + 4H 2 0 - Mn 3 0 (s) + 8H + 2e-
Mn2 + 2H 2 0 MnO(OH)(s) + 3H + e-
2Cr + 7F1 2 0 - Cr 2 0 + 14 + 6e-
Cr + 4H 2 0 - HCr0 + 7H + 3e-
Cr + 4H 2 0 Cr0 + 811k + 3e-
S 2 - S(s) + 2e-
4S 2 - S + 6e-
5S 2 - S + 8e-
Cu+ - CU2+ + e-
Cu+ + e- - Cu(s)
2N0 + 12H + lOe- N 2 (g) + 6H 2 0
46

-------
Table 3. Mixed Solids: Reference number, type, and equilibrium constant
Reference Reaction
Number Type Reaction
1 1 5Mg2 +2Al3 +3Si0 +9H 2 O
Mg 5 A1 2 Si 3 0 10 (OH)s + 10 H -4.9
2 1 5Mg2 +l2K +46Al3 +70Si0 +
30 H 2 0 20(K. 5 Mg. 25 A1 2 . 3 Si 3 . 5 0 10 (OH) 2 )
+ 20 H 1387.4
3 1 + A1 + 3 Si0 + 2 H - KAlSi 3 O 8
+ H 2 0 67.1
4 1 Na + 7 Al + 11 Si0 + 3H 2 0
3(Na. 33 A1 2 • 33 Si 3 . 67 0 10 (OH) 2 ) 232.3
5 0 Ca2 + Mg2 + 2 C0 -* CaMg(C0 ) ’ 19.7
6 0 5 Pb + 3 PO + C1 Pb 5 (P0L) C1 80.4
NAME OF MIXED SOLIDS
Reference
Number Name As Appears on Printout
1 CHLORITE CHLORITE
2 ILLITE ILLITE
3 MICROCLINE MICCLINE
4 NA-MONTMORILLONITE NA-MONT
5 DOLOMITE DOLOMITE
6 Pb 5 (POL ) 3 C1 PBPO4CL
47

-------
Table 4
Program Input Cards:
Card sequence, format, and data required
Card Card
type Field columns Description
(1) Program header card: 1 card, Format 1713. All blanks are read as
zeros.
1 1-3 Number of metals including H . (< 20).
2 4-6 Number of ligands including OW. (< 30).
3 7-9 Number of cases to be considered. f< 10).
A case consists of total concentrations for
a group of metals and ligands and pH or TOTH
for that set of concentrations. Different
pCO 2 , pE, and pM 2 , may also be specified. One
or more of the above parameters may be varied
from case to case. The number of metals or
ligands cannot be changed although concentra-
tions may be vanishingly small.
4 10-12 Solid phases to consider (see Section III-E, page 21).
-l means no solids may precipitate even when the
solution is supersaturated.
0 means no solids are imposed (assumed to be in
contact with the solution) but any solid may
precipitate if the solution is saturated with
respect to it.
N, where 0 < N < 13, is the sum of those solids
imposed and those not allowed to precipitate.
If N in field 4, card (10) is required.
5 13-15 Blank
6 16-18 Blank
7 19-21 pH, calculated or fixed?
0 means ph is specified for each case.
1 means the program will compute pH for each case.
Note: If this field is 1, TOTH data card (6)
is required.
8 22-24 Redox reactions.
0 means no redox reactions considered.
1 means the program will include redox reactions.
Note: If this field is 1, an electron activity
card (8) and a redox reaction card (11) are_re-
quired and a pM 2 card (9) is required if NO 3 is
present.
9 25-27 Mixed solids.
0 means no mixed solids considered.
1 means some mixed solids considered.
Note: If this field is 1, a mixed solids card
(12) is required.
10 28-30 Ionic strength.
0 means the user specifies the ionic strength for
the computer run (same value for all cases).
I means the program will compute the ionic strength
for each case.
48

-------
Card Card
type Field columns Description
Fields 11 thru 16 merely suppress or increase output. They are
generally 0 or left blank. See Section IV, page 26, for a de-
scription of the output routines.
11 31—33 Selects interaction intensity and/or capacity
output routine.
0 means no output.
1 means interaction capacities computed and
printed.
2 means interaction intensities computed and
printed.
3 means both are printed.
12 34—36 0 means output routine for case progress is used.
1 means suppressed.
13 37-39 0 means output routine for complex concentrations
is used.
1 means suppressed.
14 40-42 0 means output routine for speciation of the
ions is used.
1 means suppressed.
15 43-45 0 means output routine for primary distribution
of species is used.
1 means suppressed.
16 46-48 0 means output routine for verification of
thermodynamic data is used after each case
when ionic strength is calculated.
1 means suppressed after each case.
17 49—51 Concentration units.
0 means the input data concentration will be
expressed as -log 10 (molar concentration) or
-log M.
1 means the input data will be expressed in mg/i
(approximately ppm). These units will also be
used in the output routines for input data
verification and case progress.
(2) Ionic strength card: 1 card, Format [ 7.2
1 1-7 Fixed or guessed ionic strength in molar units,
(moles/l). See Section Ill-C, page 15, and field
10 in program header card.
(3) Metal Cards: car s = # metals on the header card minus one. No
card required for H . Format is 12,2X,ll(lX,F5.2) for molar concen-
tration. Format is 12,2X,llE6.2 for mg/l concentrations. Column
numbers enclosed in parenthesis indicate mg/i format.
1 1-2 Reference number of metal. See Table 1, page 45.
49

-------
Card Card
type Field Columns Description
2 Guess of the free concentration of the metal for
the first case. (See discussion in Section Ill—A,
page 10.)
6-10 Use —log M for molar concentration. If 0, program
assumes a value of 8. -
(5-10) Use mg/i for concentration. Must be > 10 ‘ .
The following fields are for the total concentration of the metals
for up to ten cases. All cases must be in the same units.
3 12-16 First case. Use -log M for molar concentration.
If the first case is 0, program assumes 1M
total concentration. If any subsequent value
is 0, the value from the previous case is used.
(11—16) First case. Use mg/l for total concentration.
Value for the first case must be > 10 ‘ . If
any subsequent value is 0, the value from the
previous case is used.
4 18-22 Second case. Description for this case and the
(17-22) remaining cases is the same as for
5 24-28 Third case. the first case.
(23-28)
6 30-34 Fourth case.
(29-34)
7 36-40 Fifth case.
(35-40)
8 42-46 Sixth case.
(41 -46)
9 48-52 Seventh case.
(47—52)
10 54-58 Eight case.
(53—58)
11 60-64 Ninth case.
(59-64)
12 66—70 Tenth case.
(65—70)
(4) Ligand cards: # cards = # ligands on the header card minus one. No
card required for OFI. Format 12,2X,11(lX,F5.2) is for molar con-
centration. Format 12,2X,11E6.2 is for mg/i concentrations. Column
numbers enclosed in parenthesis indicate mg/i format.
1 1-2 Reference number of ligand. See Table 1, page 45.
Field, column, and Description identical to card (3) except for
case numbers the ligand instead of metal concentrations.
same as card (3).
50

-------
Card
____ Field Columns ___________
(5) pH card: 1 required, Format 4X,l0(1X,F5.2)
1 6-10
2 12-16
3 18-22
4 24-28
5 30-34
6 36-40
7 42-46
8 48-52
9 54-58
10 60-64
(6) TOTH card:
header card
If pH is imposed (0 in field 7 of program
header card), give pH for each case. If
pH is calculated (1 in field 7), give a
guess of pH for each case. If first case
is 0, program assumes a value of 8. If
any subsequent case is 0, the value from
the previous case is used.
1 card, used oniy if pH calculated (field 7 of the program
= 1), Format 10E7.2
1 1-7
2 8-14
3 15—21
4 22-28
5 29—35
6 36-42
7 43-49
8 50-56
9 57-63
10 64-70
Case
1 TOTH = zH - zOH. See Section III-D,
2 page 17, for calculation. A value must
3 be given for each case , as a molar con-
4 centratio Tnot -log M). A zero or blank
5 means zero value for that case.
6
8
9
(7) Partial pressure of CO 2 card: 1 card used only if ligand
is included, Format 10F5.2.
1, C0 ,
Partial pressure of C0 2 , pCO 2 , is given as
—log (pressure in atmospheres). If 0 for
the first case, no partial pressure is
allowed. If any subsequent value is 0,
value from the preceding case is used.
(Normal partial pressure is 10 atm.)
Caution: See discussion in Section Ill-F,
page 22.
Card
type
Description
Case
1
2
3
4
5
6
7
8
9
10
7
10
1 1-5
2 6-10
3 11-15
4 16-20
5 21-25
6 26-30
7 31-35
8 36-40
9 41-45
10 46-50
Case
1
2
3
4
5
6
7
8
9
10
51

-------
Card Card
type Field Columns Description
(8) Electron activity card: 1 card used only if redox reactions considered
(field 8 of the program header card = lJ Format 10F5.2.
Case
1 1-5 1 -log (electron activity), p , must be given
for each case . 0 means 0. Typical values
Field, column, and range from -4 (reducing) to 12 (oxidizing).
case numbers the
same as for card (7)
(9) Partial pressure of N 2 card: 1 card used only if redox reactions
considered (field 8 of the program header card = 1) and if N0
(ligand 57) is included, Format 10F5.2
Case
1 1-5 1 -log (partial pressure of N 2 ), pN 2 , where
the pressure is in atmospheres and is given
Field, column, and for each case. If 0 for the first case, no
case numbers the partial pressure is allowed. If any sub-
same as for card (7) sequent value is 0, value from previous case
is used. (Normal partial pressure is o• 1
atm.)
(10) Solids card: 1 card used only if solids are imposed and/or not
allowed to precipitate (field 4 of the program header card > 0),
Format 3912
1 1-2 Reference number of metal in solid A. See Table 1,
page 45.
2 3-4 Reference number of ligand in solid A. See Table 1.
3 5-6 1, 2, or 3 depending on whether A is the first,
second or third solid listed in the thermodynamic
data file. If this number is positive, the solid is
imposed. If this number is negative, the solid is
not allowed to precipitate.
7-8 Same set of 3 parameters in six columns for up to
13 solids.
5 9-10 Solid B.
6 11-12
7 13-14
8 15-16 Solid C.
9 17—18
Etc.
52

-------
Card Card
Field column Description
(11) Redox reaction card: 1 card used only if redox reactions considered,
(field 8 of program header card = 1), Format 2012
1 1-2 First redox reaction considered. Enter reaction
reference number from Table 2, page 46, or from
the thermodynamic data file. Up to 20 reactions,
two columns/reaction.
2 3-4 Second redox reaction.
3 5-6
4
Etc.
(12) Mixed solids card: 1 card used only if mixed solids considered (field
9 of the program header card = 1), may be blank, Format 2014
1 1-4 Mixed solid reference number from Table 3, page 47,
or from the thermodynamic data file. If the number
is positive the solid is imposed. If the number is
negative the solid is not allowed to precipitate.
A mixed solid whose number is not given is allowed
to precipitate . Up to 20 solids, 4 columns/solid
2 5-8 Second mixed solid.
3 9—12
4
Etc.
53

-------
Table 5
Figure References for Output Routines
Text Routine
number name Figure
1 Thermodynamic input 6a, 6g, 9g, lOb, lib, 12b, 13b
data for verification
2 Input data 6b, 9b, lic, 12c, 14b
3 Case progress 6c, 7b, 9c, 9e, 9h, lOc, lid, 12d,
12e, 12f, 12g, 13c, 14c
4 Concentration 6d
of complexes
5 Speciation of 6e
metals and ligands
6 Primary distribution 6f, 9d, 9f, 9i, lOd, lie, 13d
of metals and ligands
54

-------
Table 6
Thermodynamic Data Deck:
Card sequence, format, and data required
Card Card
type Field columns Description
(1) Metal and ligand header card: 1 card, Format 213
1 1—3 The number of metals including hydrogen for
which data are available to the program.
2 4—6 The number of ligands including hydroxide for
which data are available to the program.
(2) Metal cards: # cards = # metals given on header card, (1),
Format 12,13,F7.2,F9.3
1 1-2 Reference number of metal. See Table 1, page 45.
2 3-5 Charge of the metal.
3 6—12 Ionic radius of metal in ngstroms. Used only
in adsorption, use 1.0 if unknown.
4 13-21 Molecular weight of metal in grams/mole.
(3) Ligand cards: # cards = # ligands given on header card, (1),
Format 12,13,F7.2,F9.3
1 1—2 Reference number of ligand. See Table 1, page 45.
2 3-5 Charge of ligand, including sign.
3 6—12 Ionic radius of ligand in ngstroms. Used only
in adsorption, use 1.0 if unknown.
4 13—21 Molecular weight of ligand in grams/mole.
(4) Solid and complex header card: 1 card, Format 15,F5.2,F5.l
1 1-5 Number of metal-ligand solid/complex cards to
follow.
2 6-10 -log of the ionization constant of water = 14
at 0 ionic strength, T = 25°C.
3 11-15 10 log K of t e equi’ibrium constant for the
reaction: 2H + C0 -* C0 2 (g) + H 2 0
(5) Solid and complex cards: # cards = # given on header card (4),
Format 212,9(14,211,12)
1 1-2 Reference number of metal.
2 3-4 Reference number of ligand combined with above
metal.
3 5-8 10 log K where K is the formation constant of a
solid formed from the above metal, ligand, and
hydrogen or hydroxide.
4 9 Stoichiometric coefficient of the metal in the
first solid.
55

-------
Card Card
type Field columns Description
5 10 Stoichiometric coefficient of the ligand in the
first solid.
6 11-12 Stoichiometric coefficient of hydrogen (negative
if hydroxide) in the first solid. Zero if
neither present.
7 13-16
8 17 Same as Fields 3 thru 6, except for second solid.
9 18
10 19-20
11 21—24
12 25 Same as Fields 3 thru 6, except for third solid.
13 26
14 27-28
15 29-32 10 log K where K is the formation constant of a
complex from the metal and ligand given in
combination with hydrogen or hydroxide.
16 33 Stoichiometric coefficient of the metal in the
first complex
17 34 Stoichiometric coefficient of the ligand in the
first complex.
18 35-36 Stoichiometric coefficient of hydrogen (negative
if hydroxide) in the first complex. Zero if
neither present.
19 37-40
20 41 Same as Fields 15 thru 18, except for a second
21 42 complex.
22 43-44
23 45-48
24 49 Same as Fields 15 thru 18, except for a third
25 50 complex.
26 51-52
27 53-56
28 57 Same as Fields 15 thru 18, except for a fourth
29 58 complex.
30 59-60
31 61-64
32 65 Same as Fields 15 thru 18, except for a fifth
33 66 complex.
34 67-68
35 69—72
36 73 Same as Fields 15 thru 18, except for a sixth
37 74 complex.
38 75-76
56

-------
Card
____ Field columns Description
(6) Redox reaction header card: 1 card, Format 15
1-5 Number of redox reactions (<30)
(7) Redox reaction cards: # cards = # given on header card (6), Format 915,A8
Arbitrary sequential number assigned to the redox
reaction. See Table 2, page 46. The last reaction
number mus$ be assigned to:
2N0 + l2H -* N 2 (g) + 6H 7 0 - lOe ________________________
Reference # of:
Reference of: ______________ __________________________
Reaction type: _______________ _________________________
ea
cting
metal
Lme
tal pro
duced
-10
metal
ligand
reacti
ligand
ng ligand
produced
-9 to
-l
10
1 to9 I
-10 is a metal oxidized/reduced to another metal ± e-.
-9 to -l is a metal + ligand forming a solid ± e-.
1 to 9 is a metal + ligand forming a complex ± e-.
10 is a ligand oxidized/reduced to another ligand ± e-.
Number of e+ produced (negative if consumed).
Number of H consumed (negative if produced).
10 log K for the reaction as written.
Stoichiometric coefficient of ion given in field 2.
Zero if reaction type ± 10 or metal 50.
Stoichiometric coefficient of ion given in field 3.
Zero if reaction type ± 10 or ligand 99.
Name of the reaction, up to 8 alphanumeric characters.
(8) Mixed solid header card: 1 card, Format 14
2 metals
or OH
4 metals
Card
type
1
1 1-5
2 6-10
3 11-15
4 16-20
5 21-35
6 26-30
7 31-35
8 36-40
9 41-45
10 46-53
1 1-4
Number of mixed solids for which data are available
to the program (< 20).
(9) Mixed solid cards: # cards = # given on header card (8),
Format 1l14,16,213,A8,F7.2
1 1-4
2 5-8
3 9-12
4 13—16
5 17—20
number assigned to the mixed
page 47.
Arbitrary sequential
solid. See Table 3,
Reaction type:
0 if solid contains up t
addition to possible H
1 if olid contains up to
Al 3 and SiO 2 (0H)
Reference number of first metal.
number of second metal.
and 2 ligands in
in addition to
50 if no second
Reference
metal.
Reference number of third metal for reaction type 1.
Reference number of first ligand for reaction type 0.
50 if no third metal.
57

-------
Card Card
type Field column Description
6 21-24 Reference number of fourth metal for reaction type 1.
Reference number of second ligand for reaction type 0.
50 if no fourth metal.
99 if no second ligand.
7 25-28 Stoichiometric coefficient for ion in field 3.
8 29-32 Stoichiometric coefficient for ion in field 4.
Zero if no second metal.
9 33-36 Stoichiometric coefficient for ion in field 5.
Zero if no third metal.
10 37-40 Stoichiometric coefficient for ion in field 6.
Zero if no fourth metal or second ligand.
11 41-44 Number of hydrogens in the solid (ne 9 ative if
hydroxide present). Do not count OH of SiO 2 (OH)
12 45-50 10 log K where K is the formation constant of the
reaction as written. See Table 3.
13 51-53 Number of Al 3 ions for type 1 reaction.
Zero for type 0 reaction.
14 54-56 Number of Si0 2 (OH) ions for type 1 reaction.
Zero for type 0 reaction.
15 57-64 Name of the mixed solid.
16 65-71 Molecular weight of the mixed solid in grams/mole.
58

-------
COMPUTER PRINTOUT
59

-------
Figure 6
Output for a simple case
6a.
INPUT DATA FOR VERIFICATION
THERMObYNAMIC CONSTANTS CORRECTED TO IONIC STRENGTM LAST USED
MET LIG • SOLID *
COMPLEXES
I
1 1 711 1 1 0
3 _0 0 00
1 99 —2?34 1 0—2
2
0 0 0 0
0_ 0 _0
0
0
3
0 0 0
000
1
181 1 1 0
0_ OO
2
1048 1 1 1
0000
3
0 0 0 0
0000
0
0
4
0 0 0
000
5
0 0 0 0
0000
6
0 0 0 0
0_0 Q_Q_
0 0 0 0
0
0 0 0
—1257 1 0—1
0 0 0 0
0 0 0 0
0
0 0 0
0 0 0 0
0 0 0 0
2 1 421 1 1 0
I o_ 000
2 99 —1684 1 0—2
0 0 0 0
0
0 0 0
201 1 1 0
1048 1 1 1
0 0 0 0
0
0 0 0
0 0 0 0
0 000____
000 0
0 0 0 0
Q 0_Q_0_
0 0 0 0
0_P_0 0
0 0 0 0
0
0
0 Q0
0 0 0
00
—1157 1 0—1
0 Q_0 0
o 0 0
0 0 00
0 0 0 0
0
0
0 _0
0 0 0
5 1 0000
0000
0
000
60110
0000
0000
0
000
0000
0000
Q_0Q_Q
599 0000
000 0
0
0 0 0
0000
0 0 00
00 9_Q
0
0 0 0
Q_ _09
0.__0_0••_
0000
0
000
0000
0000
0000
0
000
0000
0000
6 1 0000
3 0 0 00
6 99 —401 1 0—3
0000
0
000
0000
000
0000
0
000
0000
0000
Q _0 0
0 0 0 0
0
0
0 0 0
0 0 0
51 1 1_C
—286 1 0—1
61 1 2 0
—723 1 0—2
—47 1 3 0
—2408 1 0—4
0
—304
0 0 0
2 0—2
0 00 0
0 0 0 0
0000
0 0 0 0
50 1 —4012
0000
0
000
968 011
1575 012
0000
0
000
0000
0000
50._3__Q_0_Q_0_
5099 0000
0_0_ 0
0
0 0 0
0 0 0 0
0 0 0 0
0
0 0 0
0 0 0 0
0 0 0 0
0000
0
000
0000
0000
0000
0
000
0000
0000

-------
6b.
T iPtIT r rr
THESE COMPUTALIONS INVOLVE 5 4ETALS, LIGANDS, 16 COMPLEXES AND 6 POSSIBLE SOLIDS.
IONIC STRrNGTH= o.1110000E_01
IONIC STRENGTH CORRECTIONS WILL BE PERFORMED
1 DIFFERENT CASES ARE TREATED
THE CONDITIONS FOR THLDIFFERENT CASES ARE _
METAL vINMAT GUESS 101CC 1 TOTCC
CA 1. 1.000 1.000
MG 2 1.300 1.300
NA 5 0.300 0.300
FE3 6 2.000 2.000
LIGAND INMAT GUESS TOTCC TOTCC
C03— 1 1.000 0.700
CL 3 0.280 0.280
PH GUESS ‘1 8.000 ___________
TOT H
0.1OE 00

-------
6c.
CASE NUMBER
CASE PROGRESS
NUMBER OF ITERATIONS 36
SOLID FE3 OH 1 PRECIPITATES
NUMPI R OF ITERATIONS 39
SOLID CA CO)— 1 PRECIPITATES
NUMBER OF ITERATIQNS 48
NUMBER OF ITERATIONS 51
IONIC STRENGTH 6.3052237E—O1
FIXED TOTH= 0.9999996E—O1 COMPUTED PH
6.410
FREE CONC —LOG FREE CONC
TOT CONC
—LOG
TOT CONC
REMAINDER
CA 2.678157 1E—03 2.57216
MG 3.7081733E02 1.43084
NA 5.0112247E—0l 0.30006
1.0000002E—01
5.0118871E—02
5.01lt3738E—0I
1.00000
1.30000
0.30000
—1.2338161E—0
1.4649195E—0
—2.9700459E—O
FE) 7.4247097E—16 15.12932
C03— J.7339152E—05 4.42784
1.0000009E—02
1.9952637E—01
2.00000
0.70000
0.0
0.0
5 ?48015j Q1 0.28000
TOTH 3.8924327E—07 6.40978
5.?480757E—0l
9.9999964E02
0.28000
2,36113B4E—1
1.5623868E_0c
SOLID MOLES PER LITER OF SOLUTION
CA C03— 1 9.6370697E—02
FE3 OH 1 1. 00 0 00 0SE—02
—

-------
6d.
CONCENTRATIONS OF COMPLEXES
COMPLEX (—LOG M) FOLLOWED BY
THE COMPI FX fflEJfl’ .J_1G Nf). HYnPfl(Wr fl
1 1 0 3.03 1 1 1
1 0—
1n
1
CONCENTRATION OF
SXnTcJQNFTPY OF
CA C03— 5.30
CA OH 8.76
M(. (1)1—
.
1.89 1 1 1
MG
OH 6.62 1 0—1
NA
C03— ‘+.19 1 1 0
FE3
CL 14.98 1 1 0
15.21 1 2 0 16.59 1
3 0
FE3
OH 11.63 1 0—1
9.63 1 0—2 13.64 1
0—4
20.49
2
0—2
H
C03— 1.21 0 1 1
1.57 0 1 2
6e.
SPECIATION OF METALS
AND LIGANDS
OF CONCENTRATION
OF ALL SPECIES AS —LOG(M)
FREE MET
C03— CL OH
FREE LIG
4.43 0.28 7.35
2.57
3.03 8.76
MG 1.43
1.88 6.62
.
NA 0,30
4.19
.
FE3 15.13
14.77 9.63
HYDROGEN 6.41
1.05

-------
6f.
PRIMARY DISTRIBUTION OF METALS AND LIGANDS
SPECIES OVER 0.05% SHOWNI BOUND SIGNIFIES COMPLEXED
2.7 PERCENT
0.9 P RCENT
C03—/ 96.4
as
CA
AS A FREE METAL/
bDUND_W . .LIJt..CQ1 L
IN SOLID FORM WITH
PERCENT
AS A FREE MFTAL/
BOUND WITH CO3—/
74.0
26.0
PERCENT
PERCENT
NA
AS A FREE METAL/
100.0
PERCENT
FE 3
IN SOLID FOkM WITH
ON
/ 100.0
PERCENT
C03—
IN SOLID FORM WITH
CA
/ 48.3
PERCENT
MG /
6.5
PERCENT
.
8OUND WITH H /
44.6
PERCENT
CL
AS A FREE LIGAND/ 100.0 PERCENT
6g.
INPUT
DATA FOR VERIFICATION
THERMODYNAMIC CONSTANTS CORRECTED
TO IONIC STRENGTH LAST USED
COMPLEXES
METLIG
SOLID
*
6
1 2
3 1
2
3
0 0 0
0 0 0 0
1 1
70fl 1 1 0 0 0 0 0
0 0 0 0 170 1 1 0
1038 1 1 1
0 0 0 0
0 0 0 0
0000
00_ .0 .. 0___
1 99
Q_000
0000 0000
0000
0 0_0_0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
—2237 1 0—2 0 0 0 0
0 0 0 0 —1260 1 0—1
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
2 1
3
2 99
410 1 1 0 0 0 0 0
- 0.._Q_0 .0 O. .0 .0 0
—16R7 1 0—2 0 0 0 0
0 0 0 0 190 1 1 0
0_ 0Q 0 Q Q_0
1038 1 1 1

0 0
0 Q_Q0
0 000
0 0 0 0
Q_0 .0_
0 0 0 0
0000
Q .00_O_
0 0 0 0
0000
0 0 0 0 —1160 1 0—1
0 0 0 0
0 0
0000
5 1
0000 0000
0000 54110
0000
0000
O_0 0_0
O_0 Q9_
3__ ...3
0 Q..O_Q 0_O ....O 0
0 OJ_O 0_O . .P
PJL Q 0
0 Q_Q.0
Q_0O_0
0000
0000
0_ .0_Q 0
—305 2 0—2
0 0 0 0
0000
0000
0000
Q_._0 ._0_0
0 0 0 0
0 0 0 0
0000
0000
0000
0_O_0 9_
0 0 0 0
0 0 0 0
0000
0000
599
6 1
6 3_ _
b 99
50 1
50
0000 0000
0000 0000
0.0.00
—410 1 0—) 0 0 0 0
—10 0 1 2 0 0 0 0
0000 0000
0000 0000
0.000 0000
0_L .Q_Q ‘+L1i._0
0000
0000
48_1_2 0
—732 1 0—2
1568 0 1 2
0000
000.0
—6 _j_3_0
—2415 1 0—4
0 0 0 0
0000
0 0 0 0 —291 1 0—1
0 0 0 0 963 0 1 1
0000 0000
5099
0000 0000
0000 0000
0000
0000
0000
0000

-------
Figure 7
A case with fixed ionic strength
7b.
(1) 5 3
(2) 0
(3) 1 1.0
2 1.3
5 0,3
6 2.0
(4) 1 1.0
3 0.28
(5)
(6) 0.1
(7) 0.0
0001000
1.0
1.3
0.3
2.0
0.7
0.28
CA
‘16
NA
FE)
CoD-
CL . -
TOTH
2.3719610E—03
3.6191728E—02
5.01 l2206 —01
5. 88410 28E—16
3. 27260 50 E—05
5 I24 807 51E— 0 1 .
3. 8597 256E—07
2. 62489
1.44139
15.23333
4.48511
6.41344
1 .0000002E—01
5.01 1887 1E—02
5.0118738E—0 1
1 .0000009E—02.
I .9952637E—01
5 4 LQL57 0 L
9 • 9999964E—02
1.00000
1. 30000
0. 30000
2. 0 0000
0.70000
0.28000
1. 1920929E—07
—4.6641730E—09
—3. 8082362E—08
0.0
0.0
2. 40 6 12 86E— 15
—1.60 18748E—07
MOLES PER LITER OF SOLUTION
9.671 8252E—02
1. 000 00 0 9E— 02
CASE NUMBER
I
ASF PROCPFSS
NUMBER OF ITERATIONS= 36
7a. Input cards
SOLID FED
hIUMBEft OF
OH 1 PRECIPITATES
IJERATIONS= 39
g SOL1D CA
CD )— 1 PRECIPITATES
NUHBE OF
ITERATIONS 4R
Fj J flj O.9999996E 01 CQ! fUTED PH 6.413
8.0
FREE CONC —LOG FREE CONC TOT CONC -LOG TOT CONC REMAINDEk
SOLID
CA
FE)
C03— 1
OH i

-------
Figure 9
Three cases with fixed pH
9b.
INPUT DATA
ECOMPUTATIONS INVOLVE 5 METALS, 3 LIGANDS, 16 COMPLEXES AND 6 POSSIBLE SOLIDS .
TONIC STRFNGTH= 0.I110000E 01 ________________________________
9a. Input cards
___________________________________________________________ (1) 5 3 3
(2) 1,11E 0
(3) 1.0
__________________________________________________________________ 2 1.3
5 0.3
6 2.0
_____ ___________________________________________________________________ 1 1.0
3 0.28
8..0
0.0 3.5
IONIC STRENGTH CORRECTIONS WILL BE PERFORMED
3 DIFFERENT CASES ARE
a. ’
° ‘ THE CONDITIONS FOR THE
TREATED
DIFFERENT
CASES ARE
METAL #INMAT GUESS
TOTCC 1 TOTCC
2
TOTCC
3
TOTCC
CA 1 1.000
1.000
1.000
1.000
M C , 2 1.300
1.300
1.300
1.300
NA 5 0.300
0.300
0.300
0.300
FED 6 2.000
2.000
2.000
2.000
LIGANO ,INMAT GUESS
TOTCC 1 TOTCC
2
TOTCC
3
TOTCC
1 1.000
0.700
0.700
0.700
00
i.e
1.3
0.3
2.0
0.7
0.28
8.0
(4)
(5)
(7)
0000
4.0
COD—
CL 3
F I _ E 1) P H
C02 PRESSURE
0 • 280
0.280 0.280 0.280
8.000 8.000 4.000
0.0
3.500 0.0

-------
9d.
PRIMARY DISTRIBUTION OF METALS AND LIGANDS
SPECIES OVER O.O5 SHOWN; BOUND SIGNIFIES COMPLEXED
9c.
CASE NUMBER 1
CASE PROGRESS
NUMBER OF ITERATIONS: 14
SOLID
NUMBER
FE)
OF
OH I PRECIPITATES
ITERATIONS: 15
SOLID
CA
C03— 1 PRECIPITATES
NUMBER
OF
ITERATIONS: 21
NUMBER
OF
ITERATIONS: 24
IONIC
STR
ENGTN 6.2531871E—01
FIXED PH= .00O
COMPUTED TOTH 0.. lO9280E—fl1
CA
IN SOLID FORM WITH
C03—/
99.9
PERCENT
MG
AS A FREE METAL/
HOUND WITH C03-/
63.8
36.2
PERCENT
PERCENT
NA
AS A FREE HETAL/
BOUND WITH C03—/
99.4
0.6
PERCENT
PERCENT
FED
IN SOLID FORM WITH
OH /
100.0
PERCENT
CO 3—
AS A FREE LIGAND/
IN SOLID FORM WITH
BOUND WITH HG /
BOUND WITH NA /
BOUND WITH H /
0.9
CA /
9.1
1.5
38.4
PERCENT
50.1
PERCENT
PERCENT
PERCENT
PERCENT
CL
AS A FREE LIGAND/ 100.0 PERCENT
FREE CONC —COG FREE CONC
TOT CONC
—LOG TOT CONC
REMAINDER
CA
5.6309786E—05
4.24942
1.0000002E—01
1.00000
0.0
MG
3. 1977393E— 02
1.49516
S.0118871E—02
1.30000
5.6554200E—08
NA
4,48 12 007E—01
0.30267
5.0118738E—0l
0.30000
—4. 47O6S3E—Oa
FE)
1.258’Th60E—20
19.89999
1.0000009E—02
2.00000
0.0
C03—
1.7758941E—03
2.75058
1.9952 637E—01
0.70000
5 .9604645E—08
CL
0 .28000
5.24,80757E—01
0.28000
4.0037377E—20
SOLID
MOLES PER LITER
OF SOLUTION
CA
C03—
1
9.9914610E—02
FED
tiM
1
1.00 00009E—02

-------
9e.
CASE NUMBER 2
NUMBER OF ITERATIONS 26
IONIC STRENGTtI= 6.2296730E—01
FIXED PH R.000 COMPUTED TOTft 0 .i774696E
00
-03
a
cx
FREE CONC —LOG FREE CONC
TOT CONC
—LOG
TOT CONC
REMAINDER
CA 4.8976541E—03 2.31C01
1.0000002E—01
1.00000
0.0
MG 4.9781822E—02 1.30293
5.0118871E02
1.3QQOO
2.2828317E—08_.
NA 5.0115186E—01 0.30003
S.0118738E—O1
0.30000
—4.4325134E—08
FE3 1.2589660E—20 19.89999
1.0000009E—02
2b00000
0.0
C03— 2.04iAQ25 05 4. 8999
1.9952637E—01
0.70000
0.0
CL 5.2480757E—O1 0.28000
5.2480757E—O1
0.28000
4.0037377E—20
SOLID MOLES PER LITER OF SOLUTION
CA C03— I 9.5073104E—02
FE3 OH I 1.0000009E—02
H C03— 1 1.0316283E—01

-------
9f.
PRIMARY DISTRIBUTION OF METALS AND LIGANDS
SPECIES OVER 0.05% SHOWN; BOUND SIGNIFIES COMPLEXED
CA
AS A FREE METAL/
IN SOLID FORM WITH
4.9
C03—/
PERCENT
95.1
PERCENT
MG
A FREE METAL/
99.3
PERCENT
HOUND WITH C03—/
0.6
PERCENT
NA
AS A FREE METAL/
100.0
PERCENT.
F(3
IN SOLID FORM WITH
OH /
100.0
PERCENT
IN SOLID FOMM WITH
IN SOLID FO*i WITH
CA /
H /
47.6
51.7
PERCENT
PERCENT
CL
9g.
AS A FREE LIGAND/ 100.0 PERCENT
INPUT DATA FOR VERIFICATION
THERMODYNAMIC CONSTANTS CORRECTED TO IONIC STRENGTH LAST USED
METLIG
SOLID
* COMPLEXES
1 1
i
- 1
700 110
.o
0
o
2
000
0 .o
0
a.
3
000

1
170 110
o Q Q__ A
1038
2 3
111 0000
QQ Q 0 Q
4
0000 0

5
000

6
0000
- PQQ
1 99
—2?37 1 0—2
0
0 0 0
0
0 0 0
1260 1 0—1
0
0 0 0 0 0 0 0
0 0 0 0 0
0 0 0
0 0 0 0
2 1
410 1 1 0
0
0 0 0
0
0 0 0
190 1 1 0
1038
1 1 1 0 0 0 0
0 0 0 0 0
0 0 0
0 0 0 0
1
0.00 0
I
00 0 _____
O O_0
Q 0 Q
Q Q Q ___ Q
Q 0 Q
Q 01Q
2 99
1687 1 0—2
0
0 0 0
0
0 0 0
—1160 1 0—1
0
0 0 0 0 0 0 0
0 0 0 0 0
0 0 0
0 0 0 0
5 1
0000
0
000
0
000
54110
0
000 0000
0000 0
000
0000
5 1
0 00 0.
0 I Q__
L0 Q.
QIQ 0__
P Q __
Q Q
599
0000
0
000
0
000
0000
0
000 0000
0000 0
000
0000
6 1
0000
0
000
0
000
0000
0
000 0000
0000 0
000
0000
63
0
000
0
003
43110
48
120 —62 130
0_ 00 0
000
0 00_Q
6 99
—410 1 0—3
0
0 0 0
0
o 0 0
—291 1 0—1
—732
1 0—2 —2415 1 0—4
—305 2 0—2 0
0 0 0
0 0 0 0
50 1
S 3
2069 012
Q 000
0
0
000
000
0
0
000
000
963 011
0000
1568
0
012 0000
000 0000
0000 0
0000 0
000
000
0000
0000
5099
0000
0
000
0
000
0000
0
000 0000
0000 0
000
0000

-------
gi.
PRIMARY DISTRIBUTION OF METALS AND LIGANDS
9h.
CASE NUMBER 3
COMPUTED TOTHs O.369152 E 00
METAL/ 100.0 PERCENT
AS A FREE LIGAND/ 100.0 PERCENT
PCO2= 0.3?14697E—03
FREE CONC —LOG FREE CONC
TOT CONC
—LOG TOT CONC
REMAINDER
CA_________
MG
9.9999964E—0
5.Q11RR’.5E-02
1.000002E01
i.ooooo
—1 o E—Q8_.
—2.405U394E i0
1.30000
1.30000
5.0118871E—02
NA
5.0118738E—01
0.30000
5.0118738E—01
0.30000
3.5482202E—13
FF1
1.2022765E—08
7.9?000
1.0000009E—02
2.00000
0.0
CO)—
1.9952974E—13
12.70000
1.9952637E—01
0.70000
0.0
CL
5.2480751E—01
0.28000
5.2480757E—01
0.28000
—1.9912246E—08
SOLID
MOLES PER LITER
OF SOLUTION
FEIOH
I
9.9997409E—03
H C03—
1
1.9951636E—01
CA
AS A FREE
PECICS OVER 0.05% SMOWNI BOUND SIGNIFIES COMPLEXED
PROGRESS_______________________________
MG
AS A FREE METAL/ 100.0 PERCENT
NUMBER OF ITERATIONS= 28
NA
AS A FREE METAL/ 100.0 PERCENT
SOLID CA C03— 1 DISSOLVES
____NUMRFR OF_TTFRATTONS= 12
—4
C)
__NUMBER OF_IT!RATIONS 33
__1ON1 JRC2Pi 8. 1328493E—01
FIXED PH 4.000
FE3
IN SOLID FORM WITH OH / 100.0 PERCENT
CO 3—
IN SOLID FORM WITH H / 100.0 PERCENT
CL

-------
Figure 10
A case with
no solids allowed to precipitate
l0a. Input cards
(1) 5 3
(2) 1.11E 0
(3) 1 1.0
2 1.3
5 0.3
6 2.0
(4) 1 1.0
3 0.28
8.0
—1 0 0 1 0 0
1.0
1.3
0.3
2.0
0.7
0.28
INPUT DATA FOR VERIFICATION
1
(5
(6 0 1
(7) 0.0
1 Ob.
Ti-i Rp lODYN4MIC CONSTANTS CORRECTED
MET LIG * SQL 10
TO IONIC STRENGTH LAST USED
*
COMPLEXES
1
2
3
1
2
3
4
S
6
1 1 0 0 0 0
0 0 0 0
0 0 0 0
181 1 1 0
1048 1 1 1
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0000
0000
0000
0000
0000
0__9 0 _0
0000
0000
1 99 0 0 0 0
0 0 0 0
0 0 0 0
—1257 1 01
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
2 1 0 0 0 0
0 0 0 ,O
0 0 0 0
201 1 1 0
1048 1 1 1
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
2 1 - 0 00
2 99 0 0 0 0
Q 0 0
0Q 0 0
0000
0 0 0 0
0_0_0_O
0 0 0 0
0000
0 0 0 0
0 0 0 0
0 0 0 0
—1157 1 0—1
0 0 0 0
0 0 0 0
5 1 0000
0000
0000
60 110
0000
0000
0000
0000
0000
5_3______O__0 0__0
00 0 0
p 0 0 0
0000
0 0 0 0
0 0 0 0
0000
0000
0 000
599 0000
0000
0000
0000
0000
0000
0000
0000
0000
6 1 0000
0000
0000
0000
0000
0000
0000
0000
0000
6 3
6 99 0 0 0 0
0 Q_P...0
.
0 0 Q
51 1 1_0
61_I 2 0
—47 1 3 0
0 0 0 0
0 0_ _0
0 000
0 0 0 0
0 0 0 0
—286 1 0—1
—723 1 0—2
—2408 1 0—4
—304 2 0—2
0 0 0 0
0 0 0 0
SC) 1 0000
0000
0000
968 011
1575 012
0000
0000
0000
0000
53 3 0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
5099 0000
0000
0000
0000
0000
0000
0000
0000
0

-------
1 Od.
1 Oc.
CASE
PRIMARY DISTRIBUTION OF METALS AND LIGANOS
NUMBER 1
CASE PROGRESS
J
N)
NUMBER
0F
ITERATIONS
36
NUMBER
OF
ITERATIONS
39
NUMBER
OF
ITERATIONS=
41
SPECIES OVER 0.05%
SHoWN; BOUND SIGNIFIES COMPLEXED
CA
AS A FREE METAL/
BOIJND WITH C03—/
49.7 PERCENT
50.3 PERCENT
HG
dOUND WITH C03—/
43.& E2CENT
56.3 PERCENT
NA
AS A FREE METAL/
BOUND WITH C03—/
96.8 PERCENT
3.2 PERCENT
FE3
BOUND WITH OH /
100.0 PERCENT

C03—
AS A FREE LIGANO/
Bt QJJ_ft A /
4.7 PERCENT
25.2 PERCENT
BOUND WITH MG /
BOUND WITH NA /
BOUNO WITH H /
14.2 PERCENT
8.0 PERCENT
48.0 PERCENT
IONIC STRENGTH= 7.4154127E—01
CL
AS A FREE LIGAND/
100.0 PERCENT
FIXED TOTH= 0.9999996E—01
COMPUTED P11=
8.619
FREE CONC
—LOG FREE CONC
TOT CONC
—LOG
TOT CONC
REMAINDER
CA
6.9670812E—02
1.30390
1.0000002E—O1
1.00000
—2.6781890E—08
MG
2.1857675E—02
1.66040
5.0118871E—02
1.30000
—1.6822014E—08
NA
4.8519003E01
0.31409
5.0118738E—O1
0.30000
—4.4703484E—08
FE3
3.3079458E—13
12.48044
1.0000009E—02
2.00000
—9.6823101E—08
92? 3E L3
2.03 187
1.9952637E—01
0.70000
—8.7311491E—08
CL
5.2480757E—01
0.28000
5.2480757E—01
0.28000
1.0535964E—12
TOTH
2.4070772E—09
8.61851
9.9999964E—02
4.8102811E—07

-------
Figure 11
A case with
1 solid not allowed and 1 solid imposed
ha. Input cards
(1) 5 3
(2) 1.11E 0
(3) 1 1.0
2 1.3
5 0.3
6 2.0
(4) 1 1.0
3 0.28
8.0
1.0
1.3
0.3
2.0
0.7
0.28
INPUT DATA FOR vERIFIcATIoN
2001001
(5)
(6) 0.1
(7) 0.0
(10) 0101—10201 1
lib.
THERMODYNAMIC CONSTANTS CORRECTED TO IONIC STRENGT 1 LAST USED
MET LIG * SOLID
COMPLEXES
I I
1
1) 0 0 0
2
0 0 0 0
p 0_op
0
0
3
0 0 0
000
181
0
1
1 1 0
000
2
1048 1 1 1
0000
0
0
3
0 0 0
000
4 5
0 0 0 0 0 0 0 0
0 Q 0 0000
6
0 0 0 0
Q_p_00
1 99
—2234 1 0—2
0 0 0 0
0
0 0 0
—1257
1 0—1
0 0 0 0
0
0 0 0
0 0 0 0 0 0 0 0
0 0 0 0
2 1
.23
2 99
4?i 1 1 0
16R4 1 0—?
0 0 0 0
0_0 0 _0
0 0 0 0
0
0
0 0 0
000
201
()
1 1 0
000
1048 1 1 1
0000
0
0
0 0 0
000
0 0 0 0 0 0 0 0
0000 0Q_0_0
0 0 0 0 0 0 0 0
0 0 0 0
O_ Q0_Q_ .
0 0 0 0
0
0 0 0
—1157
1 0—1
0 0 0 0
0
0 0 0
5 1
0000
0000
0
000
60
110
0000
0
000
0000 0000
0000
.5 3
0 0
0_ 000
0
000
p
Q Q
0000
0
000
0 0
0000 0000
00_oP
599
0000
0000
0
000
0
000
0000
0
000
0000
6 1
0000
0000
0
000
0
000
0000
0
000
0000 0000
0000
6 99
J J1
—401 1 0—3
0 0_0 0
0
0 0_0
51
110
±L1 ._J 20
—47
130
_O 0 0 000
0000
0 0 0 0
0
0 0 0
—286
1 0—1
—723 1 0—2
—2408
1 0—4
—304 2 0—2 0 0 0 0
0 0 0 0
50 1
— . 012
0000
0
000
968
011
1575 012
0
000
0000 0000
0000
S0 _ L______ _Q_ _o
5099 0000
0 0 0 0
0
0 0 0
0
0 0 0
0 0 0 0
0
0 0 0
0 0.0 0 0 000
0 0 0 0
0000
0
000
0
000
0000
0
000
0000 0000
0000

-------
lic.
INPUT DATA
THESE COMPUTATIONS INVOLVE 5 METALS, 3 LIGANDS, 16 COMPLEXES AND 5 POSSIBLE SOLIDS.
IONIC STRENGTH O.1110000E 0
IONIC STRENGTH CORRECTIONS WILL BE PERFORMED
I DIFFERENT CASES ARE TREATED
THE CONDITIONS FOR THE DIFFERENT CASES ARE
METAL vINMAT GUESS TOTCC 1 TOTCC
CA 1 1.000 1.000
MG 2 1.300 1.300
NA 5 0.300 0.300
FE3 6 2.000 2.000
LIGAND rINMAT GUESS TOTCC I TOTCC
COD— 1 1.000 0.700
CL 3 0.280 0.280
PH GUESS 1 8.000
10TH
THE FOLLOWING I SOLIDS
METAL LIGAND
—--—
0.1OE 00
ARE IMPOSED AT THE START OF THE COMPUTATION
C03— 1

-------
lie.
PRIMARY DISTRIBUTION OF METALS AND LIGANDS
SPECIES OVER 0.05% SHOWN; BOUND SIGNIFIES COMPLEXED
lid.
CASE NUM EP 1
- CASE..YROGRESS_
NUMBER OF ITCRATIONS 31
SOLID FE OH
I PRECIPITATES
(T I NUMBEO 1TERAIIQN 3
___NUM BESLOF_IIERALLQNSaL
.._NUM8ER . 0. ITEF ATiQNS 38
____I
FIXED TOTH= O.9999996E—0L
COMPUTED PH 8.486
CA
AS A FREE HETAL/
BOUND WITH C03—/
53.1 PERCENT
46.9 PERCENT
MG
A FREE METAL/
BOUND WITH C03—/
IN SOLID FORM WITH
24.7 PERCENT
C03—/ 52.5
22.7_PERCENT_____________________
PERCENT
.
NA
AS A FREE METAL/
BOUN JTH C03—/
97.6 PERCENT
2 4 PERCENT
FE)
OH / 100.0
IN SOLID FORM WITH
PERCENT
CD)-
A FREE LIGAND/
SOUND WITH CA /
BOUND wITH MG /
SOLID_FORM_WITH_MG
BOUND WITH NA /
BOUND WITH H /
3.4 PERCENT
23.5 PERCENT
6.2 PERCENT
/
5.9 PERCENT
47e7 PERCENT
13.2_PERCENT
AS A FREE LIGAND/
100.0 PERCENT
FREE CONC —LOG FREE CONC TOT CONC —LOG TOT CONC REMAINDER
____CA __________ 5.3096762E—Q2_
MG 1.1388279E—02
NA 4.8935264E-01
____FE) 4.?789M7SE—22
C03— 6.8162009E—03
CL 5.2480757E—01
TOTt4 - .2ll6iL—J1 .9
1.94354
0.31038
21.36667
2.16646
6.28000

I .0000002E—01
5.01 18871E—02
5.01 18738E—01
1. 00000 09E—02
1 .9952637E—01
5.2480757E—O 1
9. 9999964E—02 .
1.00000
1. 30000
0.30000
2.00000
0 • 70000
0.28000
1 .0258900E—06
—3. 851950 2E—06
1 .5646219E—07
0.0
0.0
1 .3628932E—21
. 1 q? 37E—o6
2. 63300 Ô IE—02
1 • 0000009E—02
____SOLID
MG
FE3
CO 3—
OH
1
MCILFS PER LTTFP OF SOLUTION
1

-------
(1) 6 3 4
(2) 1. 1IE 0
(3) 1 1.0
2 1.3
5 0.3
6 2.0
7 8.0
(4) 1 1.0
3 0.28
8.0
1.0
1.3
0.3
2.0
8.0
0.7
0.28
THERMODYNAMIC CONSTANTS CORRECTED
MET LIG • SOLID
TO IONIC STRENGTh LAST USED
COMPLEXES
REDOX DATA
Figure 12
Four redox cases from oxidizing
12a. Input cards
to reducing
0001101
(5)
(6)
(7)
(8)
(11)
0.1 0.1 0.1 0.1
0,.0
12.0 8.0 0.0 •0
01
2b.
INPUT DATA FOR VERIFICATION
1
1 1 711 1 1 (1
1 3_ — 0 0 0
I 99 —?234 1 0—2
2
0 0 0 0
3
0 0 0 0
QQ..._Q_0
1 2
181 1 1 0 1048 1 1 1
0 0 0 0 0 0 0 0
3
0 0 0 0
0 0 0 0
4
0 0 0 0
0 0 0 0
5
0 0 0 0
0__ 0
6
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
—1257 1 0—1 0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
2 1 4?1 I 1 0
0 0 0 0
0 0 0 0
201 1 1 0 1048 1 1 1
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
2 3. 0 .0 0
2 99 —1684 1 0—?
0 0 0 0
Q 00_O
0 .. 0_0QQ__Q_Q0
0_Q_Q 0
0Q P
Q .p_0
0 0 0 0
0 0 0 0
1157 1 0—1 0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
5 1 0000
0000
0000
60110 0000
0000
0000
0000
0000
3 0 0 0 Q
599 0000
0_Q Q_Q_________
0j 1_QQ
Q_O_0Q
0000
O__0 _.__Q_q__
0000
0000
0000
0000 0000
0000
0000
6 1 000(1
6 3 0 00
6 99 —401 1 0—3
0000
0 0 0 0
0000
0000 0000
0000
0000
0000
0000
Q_ _0_Q
0 0 0 0
SJiiO 61 1 2Q
—286 1 0—1 —723 1 0—2
—47 1 3_0
—2408 1 0—4
0Q Q0
—304 2 0—2
0000.
0 0 0 0
0000
0 0 0 0
7 1 QOl 110
0000
0000
0000 0000
0000
0000
0000
0000
j7_o.0_Q_0
7 99 —j314 1 0—2
0000
0_11Q 0000
0 00.0
0000
0000
0 000_
0 0 0 0
0 0 0 0
—897 1 0—1 0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
50 1 —4012
50. 3 __Q _0_0 Q
5099 0000
0000
Q_Q OQ_
0000
0000
968 011 1575 012
0000
0000
0000
0000
0 0 0 0
0000
0_O 0 0 0 0 0 0
0000 0000
0 0 0 0
0000
0 0 0 0
0000
0 0 0 0
0000
0 0 0 0
0000
KRED
—10
MREDOX LREOOX NELEC NMREO REDCST
4 S —1 0 1225

-------
1 2c.
INPUT DATA
THESE COMPUTATIONS INVOLVE 6 METALS, 3LIGANDS, 18 COMPLEXES
AND 8 POSSIBLE SOLIDS.
IONIC STRENGTH= 0.1110000E 01
IONIC STRENGTH CORRECTIONS WILL HE PERFORMED
4 DIFFERENT CASES ARE TREATED
THE CONDITIONS FOR THE DIFFERENT CASES ARE
-. J

METAL wINMAT GUESS TOTCC 1 101CC 2 TOTCC 3 TOTCC 4
TOTCC
CA 1 1.000 1.000 1.000 1.000 1.000
MG 2 1.300 1.300 1.300 1.300 1.300
NA 5 0.300 0.300 0.300 0.300 0.300
FE) 6 2.000 2.000 2.000 2.000 2.000
FE2 7 8.000 8.000 8.000 8.000 8.000
LIGAND WINMAT GUESS TOTCC 1 TOTCC 2 101CC 3 TOTCC 4
TOTCC
C03— 1 1.000 0.700 0.700 0.700 0.700
CL 3 0.280 0.280 0.280 0.280 0.280
PH GUESS 1 8.000
10TH 0.IOE 00 O .1QE 00 0.1OE 00 0.1OE
00
REDOX POTENTIAL 12.000 8.000 0.0 —4.000
THE FOLLOWING REDOX REACTIONS ARE CONSIDERED
FE2/FE3

-------
12th
CASE NUMRUP
PROC,RE5S .
NUMBER OF ITERATIONS 37
SOLID
FE3 OH I PRECIPITATES
-
NI)MBEB
SOLID
QF1TERAT1Or _k0_
CA C03— 1 PRECIPITATES
NUMBER
OF tTERATIONS 49
NUMBER
OF ITERATIONS 52
IONIC STPFNGTH 6.3052249E01
COMPUTED PH 6.410
PE= 12.00
FREE CONC -LOG FREE CONC TOT CONC —LOG TOT CONC REMAINDER
CA 2.6781587E—03 2.57216 1.000o002E- 01 1.00000 —1.2636185E—05
1.4984471F—06
MG 3.7081730E—02 1.43084 5.0118871E—02
NA 5.012 ’.7E—01 0.3000 5 01187E01 Q 300_0Q — ,97O0459E 08____
FF3 7.4247097E—16 15.12932 1.0000017E02 2.00000 2.1515789E15
2.1515789E15
FF2 1.1237857E—15 14.94933 0.0
.C03_ 3,7339 52E:05 4,42j 84 1,9952637E—01 p.7Q 00 0,0
3.3860445E—15
CL 5.2480757E01 0.28000 5.2480757E01 0.28000
1.6041100E—05
10TH 3.8924’06E—07 6.40978 9.9999964E—02
SOLID MOLES PER LITER OF SOLUTION
CA C03— I 9.6370399E—02
FE3 OH 1 I.0000013E— 02

-------
1 2e.
CASE NUMBER 2
—— CASLE ROGRESS___________
NUM’ ER OF ITERATIONS 60
IONIC STPENGTH 6.3051867E—01
FIXED TOTH=
0.9999996E—01 COMPUTED PH
6.410
PE=6.Q
- J
FREE CONC —LOG FREE CONC
TOT CONC
—LOG TOT CONC
REMAINDER
CA
2.6784043E—03 2.57212
1.0000002E—01
1.00000
0.0
3.7081737E—02 1.43384
5.0118871E—02
1.30000
1.5787066E—08
NA
5.0112247E—01 0.30006
5. 0118738€—01
0.30000
—3.5695848E—08
FE)
7.4242565E—16 15.12936
1.0000017E—02
2.00000
2.1514179E—11
1.1fl7022E—11 10.94936
0.0
2.1514179E—I1
COl—
3.7335747E—05 4.42788
1.9952637E—01
0.70000
0.0
CL
5.2480757E—01 0.28000
5.2480757E—01
0.28000
1.0250661E11
3 93 iE—07 6.40979
9.9999964E—02
1.1175871E—08
SOLID
MOLES PER LITER OF SOLUTION
CA C03— 1 9.6382797E—02
FC3 OH 1 1.0000013E—02

-------
1 2f.
CASE NUM 3 [ R 3
CASC. P.RO( RCSS _____________
NUMBER OF ITERATIONS 67
SOLID FTP CO)— 1 PRECIPITATES
_NUMBEP OF _1iERkT1 t45 81
SOLID FE3 OM
1 DISSOLVES
NUMBER OF ITERATIONS 85
IONIC STPENGTH 6.2756062E—O1
F1XLO.JQTH O 99996E. 0l COM UIED PH
6.875
PE= 0.0
FREE CONC —LOG FREE CONC
TOT CONC
—LOG TOT CONC
REMAINDER
CA 8.5869664E—04 3.06f ’16
1.0000002E—01
1.00000
—1.7881393E—07
MG 3,62624?7E—02 1.44054
5.0118871E—02
1.30000
3.055419 0E—08
NA 0.30018
5.0118738E—01
0.30000
2.00000
—2.6921043E—09
—3.72S 903t—09
1.0000017E—02
FE3 7.J426095E—18 17.14615
FE2 1.08103 5E—05 ‘..96616
0.0
—3..7252903E—09
3 93384
CL 5.2479768E—01 0.28001
1,7 Q1
QL7QQQQ
—47o 4a4E—08_
5.24807 57E—01
0.28000
— .5329322E—08
TOTH 1.3346596E—07 6.87463
9.9999964E—02
1.1920929E—07
SOLID MOLES PER LITER OF SOLUTION
C03—i 9.8 315858E—Q2
.
FE2 CO3— 1 9.9792629E—03
cc

-------
12g.
CASE NUMBER ‘4
PROGRESS _____
NUMBER OF ITERATIOMS 93
IONIC STRENGTI1= 6.2756062E—O1
FIXED TOTti= O.9999996E—01 COMPUTED PH=
6.875
_ ._Q0
FREE CONC —LOG FREE CONG
TOT CONG
—LOG TOT CONC
REMAINDER
CA 8.5870270E-04 3.06616
1.0000002E—O1
1.00000
—2.9802322E—07
MG 1,k 54
NA 5.0 098509E—01 0.30018
5.0118871E02
1.30000
3.8000223E—08
5.0118738E—01
0.30000
—3.8417056E—09
FE) 7.1429227E—22 21.14613
1.0000017E—02
2.00000
—3.7252903E—09
4.96 j6
0.0
—3.7252903E—09
C03— 1.16 ’ 45503E—04 3.93384
1.9952637E—01
0.70000
—4.4703484E—08
CL 5.2479768E—01 0.28001
5.2480757E—01
0.28000
—3.5262929E—08
TOT 1 __i, 87E—07 6.87463
9.9999964E02
2.4586916E—07
SOLID MOLES PER LITER OF SOLUTION
CA CO)— I 9.8815739E—02
FE2 CO)— I 9.9792629E—03

-------
Figure 13
A case with one mixed solid allowed
13a. Input cards
(1) 5 3 1
(2) 1.L1 0
(3) 1 1.0
2 1.3
5 0.3
6 2.0
(4) 1 1.0
3 0.28
8.0
1 3b.
INPUT DATA FOR VERIFICATION
____THER Onm t1C.. QNSIANTS C QRRF T Ff1
MET LIG • SOLID
0001011
I.0
1.3
0.3
2.0
0.7
0.28
(5)
(6) 0.1
(7) 0.0
(12)
—2 —3 —4 —6
TQ tQ !C TRF GTM LAd USFO
COMPLEXES
1
2
3
1
2
3
4
6
1 1 711 1 1 0
0 0 0 0
0 0 0 0
181
1 1 0
1048
1 1 1 0
0 0 0
0
0 0 0 0 0 0 0
0 0 0 0
3 3 0000
0000
0000
0
000
0
000 0
000
0
000 0000
0000
_ 1 —723k La—?
2 1 421 1 1 0
0_0_0 0
0 0 0 0
Q0 0 0
0 0 0 0
—1257
201
1 0—1
1 1 0
0
1048
0 0 0 0
1 1 1 0
0 0 0
0
0
0 0 Q. __Q_0_Q
0 0 0 0 0 0 0
OqJ Q_
0 0 0 0
2 3 0000
0000
0000
0
000
0
000 0
000
0
000 0000
0000
2 _99 _ J6.S 4_L1 2
0_00.. P
0 0 Q
—1157
1 0—1
0
Q_0 - 0 0
0 0 0
0
0 0 0 0QQ
0 0_0 0_.
S 1 6000
0000
0000
60
210
0
000 0
000
0
000 0000
0000
5 3 0000
0000
000
0000
fl 000
0
0
000
000
0
p
000 0
ooa a
000
n oo
0
a
000 0000
pop a ooo
0000
o_a_ _o_
6 1 0000
0000
0000
0
000
0
000 0
000
0
000 0000
0000
b 3 0 0 0 0
0 0 0 0
0 0 0 0
51
1 1 0
61
1 2 0 —47
1 3 0
0
0 0 0 0 0 0 0
0 0 0 0
— 6 __99 1 0—1
0 0 0fl
P 0 0_Q
—786
1 0—1
—723
1 0—2 —2408
1 0—4
—304
2 0—2 00 0 0
0 0 0_D
50 1 —4012
0000
0000
968
011
1575
012 0
000
0
000 0000
0000
50 3 0000
0000
0000
0
000
0
000 0
000
0
000 0000
0000
t 000
0000
0000
0
000
0
000 0
000
0
000 0000
000_O
DATA
5 iNC 1)_
1M( 2)_ 2L( 1)_ 0LC99)._ OH CONSTANT—
173

-------
13c. 13d.
CASE NUMBER I PRIMARY DISTRIBUTION OF METALS AND LIGANDS
CASE PROGRESS SPECIES OVER 0.05 SHOWN BOUND SIGNIFIES COMPLEXED
NUMBER OF ITERATIONS 36 CA ____________
AS A FkEE METAL/ 26.8 PERCENT
. K1X!O SOLTfl c PRC.PTATFS: BOUND WITH C03/ 4.0 PERCENT
I 5QUD FORM WITH C03-/ 19.1 PERCENT
NUMBER OF ITERATIONS 47 IN SOLID FORM IN MIXED SOLID ’ 5/ 50.1 PERCENT
SOLID FE) OH 1 PRECIPITATES
IN SOLID FORM IN MIXED SOLIOW 5/ 99.9 PERCENT
NU14&.ROF TTFRATIONS= 52
NA
SOLID CA C03— 1 PRECIPITATES AS A FREE METAL/ 100.0 PERCENT
NUMBER OF ITERATIONS 57 FED
IN SOLID FORM WITH OH / 100.0 PERCENT
NUMBER OF ITERATIONS
eOUND WITH CA / 2.0 PERCENT
_____ —_____________________________________________________ IN SOLID FORM WITH CA / 9.6 PERCENT
IONIC STRENGTH 5.8201408E—01 H / 38.2 PERCENT
IN SOLID FORM IN MIXED SOLID’ 5/ 50.2 PERCENT
FIXE LIQ1H O.9999996E—O1 COMEUTED p -j= 777
CL
AS A FREE LIGAND/ 100.0 PERCENT
—LOG TOT CONC
REMAINDER
FREE CONC —LOG FREE CONC
TOT CONC
—5.7369471C07
CA
2.6840061E— 02 1,57122
1.0000 002E01
5.0118871E—02
1.00000
1.30000
0.0
MG
2.6840120E—O5 4.5712?
O.3 0 030
5. o 118oa9E- u1 O.J00 0L
2.00000
0.0
FE)
5. 8620209E—14 13,231 .96
1.00 000 09E02
0.70000
0.0
COD—
3.725786flE-06 5.4287R
1.9952637E—01
5.24E 0757EO1
0.28000
CL
5.Z 811E .QJ 0.2i3O O0
1.147389 EO6
10TH
1.6698559E—O& 5,77732
9,9999964E02
SOLID
MOLES PER LITER OF SOLUTION
CA
C03— I
1.9060493E—02
t 1 1.00
M XCD
5 CA
SOLID
MG
MOLES PER LITRE OF SOLUTION
COD— OH 5, 0 08 8 011E— 02

-------
14a. Input cards
(1) 5 3 1
(2) 1.11E 0
(3) 01 401E 3401E 3
02 122E 3122E 3
05 115E 4115C 4
06 559E 2559C 2
01 60E 4120E 4
03 188E 4188E 4
8.0
0.1
0.0
Figure 14
A case with milligram/liter input
1 4b.
It .PUT DATA
THESE
COMPUTATIONS iNVOLVE
5 METALS, 3 LIGANDS , 16 COMPLEAES AND 6 POSSIBLE SOLIDS.
IONIC
$TRENGTH o.1110000E
01
IONIC STRENGTH COk ECTIONS WILL BE PERFORMED
— 1--D-I -EFER [ NT CASES ARE T EATEO
Co
THE CONDITIONS FOk THE DIFFERENT CASES ARE
METAL sINMAT
CA
GUESS
,.,4 1E 04
TOTCC 1
401E D4
TOTCC
MG 2
.122E 0’,
.122E 04
MA S
.11SE 05
.115E 5
FE3 6
5S9 03
.559E 0-3
LIGAND jINMAT
GUESS
TOTCC 1
101CC
COD— I
.600E 04
.120E C5
CL 3
.188E 0 5
.188E—1 5
PH GUESS 1
TgTH
8.000
0.IOE
( o
1 1
(4)
(5)
(6)
(7)

-------
1 4c.
CASE NUM 3ER
1
CASE PROGRESS
41JM13ER OF ITERATIONS 37
SOLID FE3 OH 1 RECIPI1ATES
NUMBER OF ITERATIONS= 40
SOLID CA C03— 1 PRECIPITATES
NUMBER OF ITERATIONS 4
MUM EP O ITE ?ATInNS 51
cx
0 1
ICThIIC STPE GTH= 6 33RpO7cE01
‘
FIXED TOTH= fl ,9999996E—01
COMPUTED PH
6,287
FkEE C(NC
—LflG FREE C NC
TOT CUN
—LflG TOT CONC
REMAINDER
MG/L
MG/L
1,f 2 f It cF fl2
—2.2U OP
4.O1flflfl29E fl3
— -60 14
.-3. 0339694E—O]
MG 9.3337964E 02
NA 1.!499016E 04

—2,97006
—4.(J 6066
1 p pi 51 g
1.220002UE 03
1.IS00000E 04
,cgpppg8E 02
—3.08636
—4.06070
—2-74741
2.0031713E—0
—8.3871256E—0’
0.0
C03— 1.528t3792E 00
CL 1. 3800000E 04
TOTH I 2 ggF— i7
—0.18437
—4.27416
6.28741
1.2000004E 04
1.8800000E 04
9.9999 i4E—O2
—4.07918
—4.27416
0.0
1.9816851E—1(
1.0203570E—0
SOt If) MC PER LTTFP OF cot UT TON
CA
C03—
1
q,6723945
03
FE)
OH
I
1.0696985E
03

-------
Figure 15
INTERACTION CAPACITIES:
CA MG
NA FE3
FE2 MN AL
CA —9.18E+03 —1.95E O2
-‘2.99E—04
—7.96E—o1 -2,45E O4
—2.45E O4 —7.ô6E O2 —2.28E+O’i ?,63E.03
—l.Q5E±O2_ 9-.-9-5E+O3
—8.c6E O3_—2
19E—O2 .33E+O2
—4. 3E±O2 —1.t 7E+O’I —4,fl3E±O2 1.77E±02
K —2.99E—04 —8.56E—03
-I.O7E O4
—1.99E—04 —7.24E—04
—7.24E—04 —6.18E—03 —6.74E-04 2.63E—04
NA —7.96E—Ol —2.19E—02
—l.99E—04
—l.69E O3 —2.95E.OO
—2.95E+OO —7.04E—02 —2.74E.OO 1.31E+OO
S32.45E±O4_ 4..13E+O2
—7,24E-04
-2. cF+pp -9. E Q4
- ,oaE±o 3jE±U3&. 5E±M4 2,&3E+04
FE2 —2.45E,04 —4.33E.02
7.2LiE Q4
—2.95E+OO —9,08E+04
-9.O8E+04 -2.O1E+O3 —8.45E’04 2.83E.04
MN—7.66E+02 —1.67E Ol
—6.18E—03
—7.04E—02 —2.OlE O3
—2.OlE O3 —2.68E O5 -‘1.87E.03 6.52E.02
—?,?RF+fl4 — .OW+O2
—674E—04
—2.74E+clQ —P .45Ei-t)4
— 4SE+O4 —1.H7F+t)3 —F .1RE+O4 2 63E+O4
C03— 7.bJE+03 1.77E 2
2.63E—04
1.31E OO 2.83E+04
2.83E+04 6.52E+02 2.63E+04 —l.26E+04
SO ’. 2.89E+OO 8.26E+O1
4.82E+OO
l.92E OO 6.99E+OO
6.99E+OO 5.96E Ol 6.51E.OO —2.54E+OO
LL.2IE O? 2 1 66E—04
9.8flE—OR
1..12E—06 3.19E—02
3 19E—O2 4.2Sf.±QO ?.97E—O? —1 1 03E—02
P04 l.26E+04 2.76E O2
4.19E—04
9.98E—O1 3.08E+04
3.08E+04 1.05E+03 2.86E.04 —9.57E+03
S103 l.46E+04 2.59E+02
4.33E—04
1.7 E OO 5.43E+04
5.43E O4 l.20E+03 5.36E’04 —1.69E+04
j_ _ 7F+p —1..44E+O?
—? 41E—p4
—9_F 3E—p1 —hO3E+fl4
—3.03E+04 —t .71E+O2 —2..E 2E.O4 ?.42E+O3
0 ,
C.)

-------
Figure 16
A nonconvergent case
CASE NUMBER 3
NUMBER OF ITERATZONSS 38
SO Jfl FE4 OH 1 PRFCIPTTATFc
.*..e***o**ee*aa*e*********
°BE CAREFUL NO CONVERGENCE
* **************************
.
SOLID FE2 C03— I DISSOLVES
6.27C23 4E—Ol
FIXED TOTH 0.1000000E+OO COMPUTED PH
3.051
PE 8.00
FREECQNC —LOG FREE CONC
TOT CONC
—LOG TOT CONC
REMAINDER
CA 1.0e Q75 E 01 —1.03666
1.0O000Q2 Q1
1.0QP_0O
0 .0
MG 4.1905552E—02 1.37773
5.0118778E—02
1.30000
—1.4779989E—08
NA 5.O}18726E—01 0,30C 00
S.0118732E—01
0.30000
—4.3632799E—08
8, 42 i E—06 5.05334
1.00000J1 —0?
2d1 QQ0
. 3 5E 01
F f 22 1.3698083E—01 0. 3 334
0.0
2.4635345E.01
C03— 9.1909129E—09 8,03665
1.9952637E—O1
0.70000
Z.4635345E .01
CL 4.2388’41 5E -Q1 p ,37275
5.2480757E—01
0.28000
2.384185B 07
10TH 8.8896835E—04 3.05111
1.00 00002E—01
1.3732910E—04
SOLID MOLES PER LITER OF SOLUTION
CA C03- 1 —1.2913297Ee01
FE OH 1 24407425E+O1

-------
TECHNICAL REPORT DATA
(Please read Instructions on the reverse before cotnplethzg
2. 3. RECIPIENT’S ACCESSIOF+NO.
5. REPORT DATE
February 1978
Chemical Equilibria in 6. PERFORMING ORGANIZATION CODE
8. PERFORMING ORGANIZATION REPORT NO.
Schuldt and Donald W. Schults
ADDRESS 10. PROGRAM ELEMENT NO.
Laboratory 1BA608
Development 11.CONTRACT/GRANTNO.
Agency
Corvallis, OR 97330
ADDRESS 13. TYPE OF REPORT AND PERIOD COVERED
Laboratory In-House July 1975-July 1977
Development 14.SPONSORINGAGENCYCODE
Agency EPA/600/O2
Corvallis, OR 97330
the use of the computerized chemical equilibrium
program computes aqueous equilibria for up to 20
system. The metals and ligands are selected from
ligands for which thermodynamic data for complexes
in a data file. More data may be added by the
the program considers include complexation, pre-
and pH-dependent phenomena.
use the program without reference to the FORTRAN
and limitations of the program are discussed. The
explanation of output are given with examples illustrating
Common user errors are discussed.
KEY WORDS AND DOCUMENT ANALYSIS
b.IDENTIFIERS!OPEN ENDED TERMS
C. COSATI Field Group
oxidation—reduction
chemical precipitation
chemical complexation
aquatic equilibria
07/B,C,D.
08/H
19. SECURITY CLASS (Tills Report)
21. NO. OF PAGES
unclassified
20, SECURITY CLASS (This page)
j unclassified
96
22. PRICE
EPA Form 2220-1 (9-73)
88
u S Q\\ .\•r R ’N1ING O iC0 5— 0o-250 ‘O ROGLON 0

-------