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Introduction to COPLOT

Worked examples
The following examples are intended to introduce the features of COPLOT by reference to problems of industrial significance. 
The iron-oxygen-sulphur system
At high temperature the corrosion of iron based alloys is generally accelerated if conditions favour the formation of sulphides. If a sulphur bearing gas, such as sulphur dioxide is able to penetrate along cracks, the oxygen potential defined by the coexistence of metal and oxide is often low enough to break down the sulphur carrier and cause sulphides to form. The  sulphides do not confer protection against further  corrosion because metal ions diffuse through them relatively easily. Moreover, they have low melting points.
Predominance area diagrams produced by COPLOT enable the conditions for oxide and sulphide formation to be explored conveniently.
A datafile can be prepared in advance using ACCESS or, generated from within CPOLOT by defining the system as in the following example for the iron-oxygen-sulphur system. 
define data 'Fe,O,S' source sub !
list system phases substances !
Data are retrieved from the SGTE pure substance database. The phases and compounds that belong to this systems are listed. FeO should be omitted as it is not a stable compound in the Fe-O system. 

classify absent 23 !
set temperature 1000 n(Fe) 1 !
Setting a high amount of iron (1 mole) relative to the default volume of the gas phase (see futher below) ensures that only condensed compounds of iron will feature in the diagram. Note that in setting the amount of a type 1 component the chemical formula without a phase label is used. This is because it is indeed the amount of the component that is being set and not the amount of any substance.
range lgt_pressure(O2<gas>) -30 2 l_p(SO2<gas>) -30 2 !
This entry sets the range of the first variable, log10 p(O2), as -30 to 2. The pressure, being divided by the pressure of one atmosphere is dimensionless. The first range is assigned to the abscissa (x-axis). Similarly log10 p(SO2) is assigned to the ordinate. A still shorter way of setting the ranges would have been.
ra l_p(8) -30 2 l_p(11) -30 2 !

In setting and establishing ranges of activities it is necessary to relate these to particular substances. Therefore either substance formulae with phase lables or the equivalent substance numbers can be used.

comp lgt_p_max 2 !   

Within the compute command it is possible to alter the maximum pressure limit, which in this case is set to 100 atm. This is an unrealistically hugh pressure, which can be justified only because it enables trends near the edge of the diagram to be made more evident. After the compute command has been executed, a further carriage return will be needed to cause the diagram below to be plotted. The heavily and partly indecipherably marked eare to the top left is a region where many gaseous species would form with a pressure in exces of 100 atm. This region has therefore been excluded from further consideration. The gaseous species involved are S, S2, S3, S4, S5, S6, S7, S8, S2O and SO. The extreme top right of the diagram is similarly over-constrained by high pressures of SO3. If these species are classified as absent, as in the following command, the over-constraint would disappear.
classify absent sub(7,8,10-15,27) ! comp !

The diagram is cleaned up but the warning  of the overconstraint is lost. A better method of controlling the indication and exclusion of overconstrained regions is provided within the zero pass options of the COMPUTE command, which also includes a facility for suppressing labelling. A better way of achieving this same effect as illustrated in the next figure is to inhibit the operation of the zero pass using the following option in compute.

comp zero_pass none !

Among other things the diagrams show that at the  interface between iron and wuestite, Fe0.947O, partial pressures of SO2 as low as 10-10 could result in sulphide formation. The conditions for formation of the sulphides, wuestite, magnetite, haematite and the sulphates are shown. Note that, as implied here, the atmosphere that is important in corrosion is often the microenvironment within the corrosion layer. The composition of the gas in this micro environment is determined by a complex interplay with the crystalline phases present. Hence the disctinction between the dependent and independent variables in predominance area diagrams in often blurred.


In common with other modules the command laser is used to obtain hard copy of the current plot.out file, where diagrams are stored.

In  general, the environments involved in corrosion are usually more complex than can be represented by sulphur dioxide and oxygen potentials. For example, the alloys use in combusters  are  exposed to systems containing carbon, hydrogen, oxygen, sulphur, chlorine,  nitrogen and their compounds.
COPLOT includes the ability to deal with some of the problems raised by this extra complexity. It achieves this by assigning an amount to the Type 1 element or elements of which the chemical behaviour in the environment is under scrutiny. 

 COPLOT OPTION ? define system 'Fe,O,S' source sub !

 sub_sgte        - SGTE Substance Database version 12.1 - June 2009
 sub_sgte        - SGTE Substance Database version 12.1 - June 2009

 ******                 GOOD DATAFILE CREATED                 ******

 Date and time of run  5-JUL-2010  15:12:49
 * DATAFILE = D:\MTDATA\handbook\def.mpi -  CREATED 15:12:49  5-JUL-2010
 * SYSTEM = Fe,O,S,/-,
 COPLOT OPTION ? list system phases substances !

 NUMBER    PHASE                   STATUS      MODEL
    1      Fe                      NORMAL      PURE SUBSTANCE
    2      GAS                     NORMAL      IDEAL GAS
    3      WUSTITE                 NORMAL      PURE SUBSTANCE
    4      FeO                     NORMAL      PURE SUBSTANCE
    5      FE2O3_GAMMA             NORMAL      PURE SUBSTANCE
    6      FE2O3_HEMATITE          NORMAL      PURE SUBSTANCE
    7      MAGNETITE               NORMAL      PURE SUBSTANCE
    8      FeO4S                   NORMAL      PURE SUBSTANCE
    9      Fe2O12S3                NORMAL      PURE SUBSTANCE
   10      PYRRHOTITE              NORMAL      PURE SUBSTANCE
   12      TROILITE                NORMAL      PURE SUBSTANCE
   13      MARCASITE               NORMAL      PURE SUBSTANCE
   14      PYRITE                  NORMAL      PURE SUBSTANCE
   15      S                       NORMAL      PURE SUBSTANCE

    1      Fe                      NORMAL
    2      Fe<g>                   NORMAL
    3      Fe2<g>                  NORMAL
    4      FeO<g>                  NORMAL
    5      FeO2<g>                 NORMAL
    6      FeS<g>                  NORMAL
    7      O<g>                    NORMAL
    8      O2<g>                   NORMAL
    9      O3<g>                   NORMAL
   10      OS<g>                   NORMAL
   11      OS2<g>                  NORMAL
   12      O2S<g>                  NORMAL
   13      O3S<g>                  NORMAL
   14      S<g>                    NORMAL
   15      S2<g>                   NORMAL
   16      S3<g>                   NORMAL
   17      S4<g>                   NORMAL
   18      S5<g>                   NORMAL
   19      S6<g>                   NORMAL
   20      S7<g>                   NORMAL
   21      S8<g>                   NORMAL
   22      Fe0.947O<WUSTITE>       NORMAL
   23      FeO                     NORMAL
   24      Fe2O3<FE2O3_GAMMA>      NORMAL
   25      Fe2O3<FE2O3_HEMATITE    NORMAL
   26      Fe3O4<MAGNETITE>        NORMAL
   27      FeO4S                   NORMAL
   28      Fe2O12S3                NORMAL
   29      Fe0.875S<PYRRHOTITE>    NORMAL
   31      FeS<TROILITE>           NORMAL
   32      FeS2<MARCASITE>         NORMAL
   33      FeS2<PYRITE>            NORMAL
   34      S                       NORMAL

 COPLOT OPTION ? classify absent 23 !
 COPLOT OPTION ? set temperature 1000 n(Fe) 1 !
 COPLOT OPTION ? range lgt_pressure(O2<gas>) -30 2 l_p(SO2<gas>) -30 2 !
 COPLOT OPTION ? comp lgt_p_max 2 !

Fe-O-S system at 1000 K

Diagram for the Fe-O-S system at 1000 K. The top left corner of the diagram is over-constrained as discussed in the text.

 COPLOT OPTION ? classify absent s(10,11,14-21) !
 COPLOT OPTION ? comp zero_pass none !

Zero pass diagram

Diagram as above but without the zero pass that indicates over-constrained regions


The iron-hydrogen-sulphur-oxygen-chlorine system
The  possibility should be considered that when transition metals are exposed to atmospheres bearing chlorine, volatile chlorides might form. The chlorine will be present almost exclusively as hydrogen chloride. The behaviour of sulphur, as indicated by the overconstrained regions of the first figure above, is not uniform over the diagram. For this reason it is preferable to fix sulphur by amount rather than by activity. 

In the following figure the amount of H2 is set at 1 mol (equivalent to 1 atmosphere pressure) and S is set to 0.01 mol (equivalent to 1.0% impurity in the hydrogen). Iron is assigned an amount of 10-6 mol in order that the formation of volatile species can  be investigated. The  oxygen and hydrogen chloride potentials vary along the abscissa and  ordinate. The computation of a diagram can be set up very easily.
def sys 'Fe,H,Cl,O,S' source sub ! lis sy subs !
set n(Fe) 1E-6 n(H2) 1 n(S) 0.01 te 1000 !
ran l_p(O2<gas>) -30 2 l_p(HCl<gas>) -10 2 ! comp !     

The resultant diagram has no overconstrained regions, indicating a good choice of axis variables. The greatest interest lies in the behaviour of iron but, before examining this, it is worthwhile to look at what happens to the hydrogen and sulphur. The hydrogen shows two regions (separated by lines composed of widely spaced dots) marked 31, H2<gas> and 34, H2O<gas>. The sulphur forms three regions (separated  by lines composed of closely spaced dots) occupied from left to right by 42, H2S<gas>; 49, SO2<gas> and 50, SO3<gas>. The existence of these regions has apparently no effect on the coexistence lines of the iron diagram (solid lines) except that the region for FeS<TROILITE>, 78, exists only because of the presence of sulphur. If the sulphur amount is reduced, as caused by the following entry, the diagram shows that  sulphides are no longer formed and that the boundary between  FeCl2<gas> and wuestite is sensitive to the conversion of hydrogen to water.
set n(S) 0.0001 ! comp !
The simplicity in COPLOT of changing some conditions, whilst leaving others fixed, makes it possible to explore the many variables of the five component system.
The coexistence lines between the condensed products of iron in these two figures can readily be correlated with those in the very first figure. The boundaries between the condensed phases and the two gaseous chlorides FeCl2 and FeCl3 move as the amount of iron is changed.
The volume of the system defaults to the volume occupied by one mol of ideal gas and, because FeCl2 and FeCl3 each contain only one atom of iron, the partial pressures of iron gaseous species are numerically equal to the amount of iron at the boundary between gaseous and condensed compounds. Thus by superimposing a number of diagrams with varying amounts of iron, a contour map of partial pressures of volatile species can be obtained. Note that if a dimeric molecule such as Fe2Cl6 became dominant, in order to preserve equivalence in the amount of iron, its pressure would be only half that of the monomeric species.

 COPLOT OPTION ? def sys 'Fe,H,Cl,O,S' source sub ! lis sy sub !

 sub_sgte        - SGTE Substance Database version 12.1 - June 2009
 sub_sgte        - SGTE Substance Database version 12.1 - June 2009

 ******                 GOOD DATAFILE CREATED                 ******

 Date and time of run  5-JUL-2010  15:51:14
 * DATAFILE = D:\MTDATA\handbook\def.mpi -  CREATED 15:51:14  5-JUL-2010
 * SYSTEM = Fe,H,Cl,O,S,/-,

    1      Cl<g>                   NORMAL
    2      Cl2<g>                  NORMAL
    3      ClFe<g>                 NORMAL
    4      Cl2Fe<g>                NORMAL
    5      Cl3Fe<g>                NORMAL
    6      Cl4Fe2<g>               NORMAL
    7      Cl6Fe2<g>               NORMAL
    8      ClFeO<g>                NORMAL
    9      ClH<g>                  NORMAL
   10      ClHO<g>                 NORMAL
   11      ClHO3S<g>               NORMAL
   12      ClO<g>                  NORMAL
   13      ClO2<g>                 NORMAL
   14      Cl2O<g>                 NORMAL
   15      Cl2OS<g>                NORMAL
   16      Cl2O2S<g>               NORMAL
   17      ClS<g>                  NORMAL
   18      ClS2<g>                 NORMAL
   19      Cl2S<g>                 NORMAL
   20      Cl2S2<g>                NORMAL
   21      Fe<g>                   NORMAL
   22      Fe2<g>                  NORMAL
   23      FeH<g>                  NORMAL
   24      FeHO<g>                 NORMAL
   25      FeHO2<g>                NORMAL
   26      FeH2O2<g>               NORMAL
   27      FeO<g>                  NORMAL
   28      FeO2<g>                 NORMAL
   29      FeS<g>                  NORMAL
   30      H<g>                    NORMAL
   31      H2<g>                   NORMAL
   32      HO<g>                   NORMAL
   33      HO2<g>                  NORMAL
   34      H2O<g>                  NORMAL
   35      H2O2<g>                 NORMAL
   36      HOS_HSO<g>              NORMAL
   37      HOS_SOH<g>              NORMAL
   38      H2OS_H2SO<g>            NORMAL
   39      H2OS_HSOH<g>            NORMAL
   40      H2O4S<g>                NORMAL
   41      HS<g>                   NORMAL
   42      H2S<g>                  NORMAL
   43      H2S2<g>                 NORMAL
   44      O<g>                    NORMAL
   45      O2<g>                   NORMAL
   46      O3<g>                   NORMAL
   47      OS<g>                   NORMAL
   48      OS2<g>                  NORMAL
   49      O2S<g>                  NORMAL
   50      O3S<g>                  NORMAL
   51      S<g>                    NORMAL
   52      S2<g>                   NORMAL
   53      S3<g>                   NORMAL
   54      S4<g>                   NORMAL
   55      S5<g>                   NORMAL
   56      S6<g>                   NORMAL
   57      S7<g>                   NORMAL
   58      S8<g>                   NORMAL
   59      Cl2Fe                   NORMAL
   60      Cl3Fe                   NORMAL
   61      ClFeO                   NORMAL
   62      Cl2S<CL2S1_LIQUID>      NORMAL
   63      Cl2S2<CL2S2_LIQUID>     NORMAL
   64      Fe                      NORMAL
   65      FeHO2                   NORMAL
   66      FeH2O2                  NORMAL
   67      FeH3O3                  NORMAL
   68      Fe2H2O4                 NORMAL
   69      Fe0.947O<WUSTITE>       NORMAL
   70      FeO                     NORMAL
   71      Fe2O3<FE2O3_GAMMA>      NORMAL
   72      Fe2O3<FE2O3_HEMATITE    NORMAL
   73      Fe3O4<MAGNETITE>        NORMAL
   74      FeO4S                   NORMAL
   75      Fe2O12S3                NORMAL
   76      Fe0.875S<PYRRHOTITE>    NORMAL
   78      FeS<TROILITE>           NORMAL
   79      FeS2<MARCASITE>         NORMAL
   80      FeS2<PYRITE>            NORMAL
   81      H2O<H2O1_LIQUID>        NORMAL
   82      H2O2<H2O2_LIQUID>       NORMAL
   83      H2O4S<H2O4S1_LIQUID>    NORMAL
   84      H4O5S<H4O5S1_LIQUID>    NORMAL
   85      H6O6S<H6O6S1_LIQUID>    NORMAL
   86      H8O7S<H8O7S1_LIQUID>    NORMAL
   87      H10O8S<H10O8S1_LIQUI    NORMAL
   88      H15O10.5S<H15O10.5S1    NORMAL
   89      S                       NORMAL

 COPLOT OPTION ? set n(Fe) 1E-6 n(H2) 1 n(S) 0.01 te 1000 !
 COPLOT OPTION ? ran l_p(O2<gas>) -30 2 l_p(HCl<gas>) -10 2 ! comp !

Diagram for Fe-H-S-O-Cl system
Diagram for the Fe-H-S-O-Cl system, in which Fe, H and S are set by amount in a system of fixed volume of gas (equal to that which would be occupied at standard pressure by one mole of ideal gas). Because hydrogen is present in largest amount, its diagram is calculated first (dash-dort lines, large numbers), followed by the sulphut (dotted lines, medium numbers) and finally iron. Because the amount of iron is only 10-6 moles, it is entirely converted to gaseous chlorides at high pressure of HCl<gas>.

 COPLOT OPTION ? set n(S) 0.0001 ! comp !

Sulphur reduced to 0.0001 mole

Diagram for the Fe-H-S-O-Cl system for identical conditions to those of the previous figure except that the amount of suphur is reduced to 0.0001 mol. As a result no region of sulphide formation is found.

An example of a trimeric species, Mo3O9, is given below. The quantitative significance of these points is evident from an examination of the amounts of the various gaseous molybdenum oxides.
Because COPLOT and MUTIPHASE use datafiles of the same format, it is possible by use of MULTIPHASE to investigate in quantitative  detail features noticed in diagrams produced by COPLOT. In the description of MULTIPHASE results are given of a calculation relating to the four phase equilibrium between Fe, Fe0.947O, FeS and the gas phase. The amounts of all the gaseous iron species are given, whereas COPLOT allows only predominant species to be displayed.  
Aqueous systems
The  methods described in the above examples can also be used to prepare Pourbaix diagrams for aqueous systems. 

In the very first example above the influence of sulphur on the hot corrosion of iron was investigated. Systems of iron and sulphur are also important at low temperatures, both in aqueous corrosion and hydrometallurgy.

The system, to be studied has five components, one more than the number of elemental components, because charge has to be added to iron, sulphur, hydrogen and oxygen. The system could, of course, be defined in many ways but it is preferable to use as components element combinations that relate to reality or to the variable to be used in the calculations. For the copper water system a suitable choice might be 'Cu,/-,H2O,H'. If the system is to be open to charge, as is normal in COPLOT, one component, which should not be the last in the component list, must be charged.

It is usual tp plot Eh as the ordinate and pH as the abscissa. Eh is defined by:

where z = ionic charge (-1 for the electron), pE by analogy with pH is -log10(notional activity of the conventional aqueous electron) and F is the Faraday constant, 96485.3 C mol-1.  At 298.15 K the equation gives Eh = 0.05916 pE. The properties of the aqueous electron are obtained by making the enthalpy, entropy and heat capacity changes for the reaction

1/2 H2<g> = H/+<aq> + /-<aq>

all equal to zero. This choice makes the properties of the conventional aqueous electron very different from those that might be anticipated for the real aqueous electron. Purists may object to the use of half cell reactions. The justification lies in the fact that the final diagram can be used as a basis for understanding practical problems.

The reason for this digression os to explain how to select the axes variables, namely pH for the abscissa and Eh for the ordinate. These are the type 3 components. A suitable range for the pH is 0 to 14. For normal temperatures a useful range for Eh will be found to be -1.5 to 1.3. For temperatures over 500 K a range nearer -2.0 to 2.0 may be more suitable.

If data are to be retrived from databases, AQEXTRAS should be included in the list of sources. This makes data for the conventional electron available. It is not included on other databases because the convential electron is unreal and is needed only for use with COPLOT.

The Type 1 components, Fe and S, are set by amount. The activity of H2O<aq> is set to 1, making it a Type 2 component. In principle, fixing the activity of water to unity is thermodynamically unsound, since its mole fraction is bound to be reduced when anything dissolves in the water. MULTIPHASE does not allow the abuse of the laws of thermodynamics in this wat, but in drawing predominance are diagrams as in COPLOT, the simplification of breaking the rule is widely accepted. A warning is sent to the screen but can be ignored.

Unless corrosion is very fast the amount of iron in solution should be rather low. In the next fiigure the amounts of sulphur and iron are set to 0.01 and 10-5 mol respectively and the temperature is 573 K. The behaviour of the sulpur is determined in the first pass and that of the iron, being in the smaller amount, in the second pass. The behaviour of the iron is dependent on that of the sulphur as can be seen from the fact that regions of FeS, FeS2 and FeSO4 form and the fact that the slopes of the boundaries of these regions change as they cross boundaries in the sulphur water system.

By default the amount of water is set to be 1 kg. Unlike in MULTIPHASE this amount of water is not used up by evaporation or conversion into hydrogen and oxygen. It is in effect a space just like the volume assigned to the gas phase. Its activity should normally be set to unity, in which case, if the temperature exceeds 373.15 K, the pressure of H2O<g> will exceed 101325 Pa. At still higher temperatures the system will become over-constrained because the calculated partial pressure of H2O<g> will exceed the default limit. To avoid these problems it is simplest to classify H2O<gas> as absent. The substance H2O as distinct from H2O<ag> should also be made absent.

If H2<gas), O2<gas> and other compounds of hydrogen and oxygen are included in the data, it will be found that large regions of the diagram will be shown to be over-constrained. However, it is known that substantial over-potentials can develop, without formation of hydrogen and oxygen. In order ot be able to examine the equilibrium line between Fe and Fe3O4, for example, H2<aq>, and similarly O2<gas> and O2<ag> and other compounds of O and H can be classified as absent but this is not advised. Two other methods are available. The volume available to the gas phase can be reset to a very low value, for example 10-10 or the two options within the COMPUTE command to inhibit the exclusion or indication of over-constrained regions can be used.

It is sometimes desirable to investigate the partition of type 1 components between the gas and aqueous phases, in which case itis important to make an estimate of the free space for the gas and the mass of water in the practical situation. The volume V available to the gas should then be set to a value that will maintain the right ratio to the mass of liquid water, assumed by COPLOT to be 1 kg.

If you are concerned with aqueous corrosion in boilers or heat exchangers, some data are available for temperatures to 600 K. Be sure to begin with the appropriate datafile before exploring this interesting are of solution chemistry. These are the instructions needed to generate an appropriate diagram in COPLOT.

def sys 'Fe,S, /-,O,H' sou hotaq aqextras !
set n(Fe) 1e-5 n(S) .01 temperature 573 volume 1e-10 l_a(H2O<ag>) 0 !

Now we need to exclude H2O and H2O<g> from the list of substances.

li sy sub !
cl abs 35 41 !
range ph 0 14 Eh -2 2 !
co zero mark !

 COPLOT OPTION ? def sys 'Fe,S,/-,O,H' sou hotaq aqextras !

 hotaq           - Database for ideal aqueous system 'Fe,Cr,Ni,C,S,H,O,/-' - 26/3/93
 aqextras        - Data for CONVENTIONAL aqueous electron - (use only in COPLOT) - 29

 ******                 GOOD DATAFILE CREATED                 ******

 Date and time of run  5-JUL-2010  16:22:23
 * DATAFILE = D:\MTDATA\handbook\def.mpi -  CREATED 16:22:23  5-JUL-2010
 * SYSTEM = Fe,S,/-,O,H,
 COPLOT OPTION ? set n(Fe) 1e-5 n(S) .01 temperature 573 volume 1e-10 l_a(H2O<aq>) 0 !
 COPLOT OPTION ? lis sy sub !

    1      Fe                      NORMAL
    2      FeHO2                   NORMAL
    3      FeH2O2                  NORMAL
    4      H2O<aq>                 LGT_ACTIVITY(*) = 0
    5      FeH2O2<aq>              NORMAL
    6      FeH3O3<aq>              NORMAL
    7      FeHO/+2<aq>             NORMAL
    8      FeHO/+<aq>              NORMAL
    9      FeH2O2/+<aq>            NORMAL
   10      FeH3O3/-<aq>            NORMAL
   11      FeH4O4/-<aq>            NORMAL
   12      FeO4S<aq>               NORMAL
   13      FeO4S/+<aq>             NORMAL
   14      FeO4/-2<aq>             NORMAL
   15      Fe/+3<aq>               NORMAL
   16      Fe/+2<aq>               NORMAL
   17      HO4S/-<aq>              NORMAL
   18      HO/-<aq>                NORMAL
   19      H2S<aq>                 NORMAL
   20      HS/-<aq>                NORMAL
   21      H/+<aq>                 NORMAL
   22      O4S/-2<aq>              NORMAL
   23      /-<aq>                  NORMAL
   24      FeH3O3                  NORMAL
   25      FeH2O5S                 NORMAL
   26      FeH14O11S               NORMAL
   27      Fe0.947O                NORMAL
   28      Fe2O3                   NORMAL
   29      Fe3O4                   NORMAL
   30      FeO4S                   NORMAL
   31      Fe2O12S3                NORMAL
   32      FeS                     NORMAL
   33      FeS2                    NORMAL
   34      H2<g>                   NORMAL
   35      H2O<g>                  NORMAL
   36      H2S<g>                  NORMAL
   37      O2<g>                   NORMAL
   38      O2S<g>                  NORMAL
   39      O3S<g>                  NORMAL
   40      S2<g>                   NORMAL
   41      H2O                     NORMAL
   42      S                       NORMAL

 COPLOT OPTION ? cl ab 35 41 !
 COPLOT OPTION ? range pH 0 14 Eh -2 2 !
 COPLOT OPTION ? co zero mark !

Pourbaix diagram for iron in contact with aqueous solutions at 573 K

Pourbaix diagram for iron in contact with aqueous solutions at 573 K containing sulphur species at a concentration of 0.01 molar. This diagram shows the coexistence fro condensed phases and aqueous species of iron at a concentration of 10-5 molar. The dashed lines delineate over-constratined regions in which the partial pressures of O2 and H2 (species 37 and 34 respectively) exceed 1 atm and the molality of OH- (species 18) exceeds one.


Predominance area diagrams comprise a set of intersecting straight lines. Writers of articles on aqueous systems often report equations for these lines. It would be technically feasible to provide an automatic facility for generating the equations in COPLOT itself but unfortunately there are some complexities that arise, for example whenthe type of one component is polynuclear, and the other pressures have got in the way. The following suggestions are amde that will assist uers to provide their own equations.

Consider a relatively difficult case. The equation required for the coexistence line between HS-<ag> and SO42-<ag> is:

HS/- <aq> = SO4/-2<aq> - 4 H2O + 9 H/+<aq> + 8 /-<aq>

The slope of the line representing the equilibrium would be 9/8. In pH-Eh space it would be multiplied by the factor Eh to pE as given earlier.

In order to write the equation, begin by putting an amount of two coexisting species bearing one mole of the type 1 component on either side of the equals sign. The cumbersome form of this sentence is needed to take into account polynuclear species. In, for example, the reaction involving the equilibrium between trivalent chromium and dichromate ions, which carries two chromium atoms, the equation would be as follows.

Cr/+3<aq> = 0.5 Cr2O7/-2<aq> - 3.5 H2O<aq> + 7 H/+<aq> + 3 /-<aq>

After the species have been entered, balance the difference between them using the components one by one in the sequence required to minimise the difficulty. In this case the only component carrying oxygen in H2O and this should be used first. After the oxygen has been balanced the hydrogen can be balanced using H/+<aq>, leaving the charge to be balanced last by means of the electron. If the reverse order had been chosen the balancing would have been more difficult.

With a bit of ingenuity THEMOTAB can be used to balance equations and of course to generate the equilibrium constants. Create macro using an editor. Type the following four lines, with appropriate changes to match your needs in the first three, as follows.

tabulate file 'myeqtns.txt' ! set format 'T beta' !
use mydata def !
set temperature 298.15 303.15 308.15 !
define equation "= H2O<aq> + H/+<aq> + /-<aq>" ! go

Copy the fourth line as many times as necessary and edit in the species names on either side of the equals sign, Make sure that the first species is not polynuclear or, if it is, multiply it by the inverse of the number of atoms of the type 1 component it contains. Run the macro from the THERMOTAB OPTION prompt. If you have made no mistakes and if all the data are available, THERMOTAB will automatically balance the equations and give a list of equilibrium constants for each. Unfortunately THERMOTAB will insist on moving the compounds to the side of the equation on which their stoichiometry is positive. Note that the procedure may not work smoothly uncless all the species are in one database.

When the macro is finished leave MTDATA and edit the files having the name you have specified. You will still be faced with the task of augmenting the equations by preceding the items in the chemical equation by log10p or log10a as appropriate and converting H/+<aq> to pH (with a change of sign) and /-<aq> to Eh usign the expression given earlier. No terms need appear in the final equation for aqueous water or condensed species that are functioning as the carriers for type 1 components of larger amount as their activity is always unity within or at the boundary of areas ion which they are dominant.

When more than one type 1 component is present, the only equations of interest are those relating to the component of lowest amount. For example if iron and sulphur are both type 1 components an iron is present in the smaller amount, a typical equation might be

FeS = 1/2 Fe3O4 + HS/-<aq> - 4/3 H2O<aq> + 5/3 H/+<aq> + 2/3 /-<aq>

The equation would apply only in the domain where HS/- is the dominant species carrying sulphur. Note the point that the activity of HS/-<aq> has not been set, only the amount of sulphur relative to 1 kg of water. In this case the values of activitiy and the amount are numerically equal.

Sometimes a complication occurs when, after the first pass of COPLOT, a domain belongs to a species with a different stoichimetry from the type 1 component. The problem applies only to domains corresponding to aqueous or gaseous species and not to domains corresponding to stoichiometric compounds, for example Fe3O4. Consider, for example, a case where the type 1 component in the first pass was H2 and the amounts were set so that the pressure of H2 was 1 atm in its area of predominance. In a zone where hydrogen was predominantly combined as HCl, the partial pressure of HCl would be taken to be 2 atm and coexistence lines between species or compounds in this area would be influenced accordingly.

The equations generated by the above procedure will be correct but the partial pressures to be used to calculate the equilibrium lines will be different fro the H2<g> and the HCl<g>.

Updated 5 July 2010