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. 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