Stoichiometric saturations

The final solid solution-aqueous solution compositions of Table I will fall into one of three catagories (1) they will either be at equilibrium, (2) at stoichiometric saturation, or (3) correspond to some non-equilibrium state. 

Stoichiometric saturation defines equilibrium between an aqueous solution and homogeneous multi-component solid of fixed composition (10). At stoichiometric saturation the composition of the solid remains fixed even though the mineral is part of a continuous compositional series. Since, in this case, the composition of the solid is invariant, the solid may be treated as a one-component phase and Equation 6 is the only equilibrium criteria applicable. Equations 1 and 2 no longer apply at stoichiometric saturation because, owing to kinetic restrictions, the solid and saturated solution compositions are not free to change in establishing an equivalence of individual component chemical potentials between solid and aqueous solution. The equilibrium constant, K(x), is defined identically for both equilibrium and stoichiometric saturation. 

If the solid is neither at equilibrium nor stoichiometric saturation, the Equations 1, 2, or 6 are not applicable. 

In testing for equilibrium in the KCl-KBr-I O system (8), the analysis that follows initially assumes that all solids are at stoichiometric saturation with the aqueous solution. 

This permits provisional calculation of the compositional dependence of the equilibrium constant and determination of provisional values of the solid phase activity coefficients (discussed below). The equilibrium constant and activity coefficients are termed provisional because it is not possible to determine if stoichiometric saturation has been established without independent knowledge of the compositional dependence of the equilibrium constant, such as would be provided from independent thermodynamic measurements. Using the provisional activity coefficient data we may compare the observed solid solution-aqueous solution compositions with those calculated at equilibrium. Agreement between the calculated and observed values confirms, within the experimental data uncertainties, the establishment of equilibrium. The true solid solution thermodynamic properties are then defined to be equal to the provisional values. 

If there is no agreement in calculated and observed solid-solution properties we can only conclude that equilibrium was not established. The validity of the provisional activity coefficients depends on the validity of the original assumption that stoichiometric saturation was established. If independent data for the standard free energy of formation of the solid... 

By examining the compositional dependence of the equilibrium constant, the thermodynamic properties of the solid solution can be determined if the final solution is either at equilibrium or stoichiometric saturation. That is, the provisional activities and activity coefficients will be valid if either equilibrium or stoichiometric saturation is attained in the solubility data. 

These activities can be verified if It can he shown that the solubility data of (8) are at stoichiometric saturation, but as mentioned above, this requires independent thermodynamic definition of K(x). 

Finally, it is not appropriate to derive thermodynamic properties of solid solutions from experimental distribution coefficients unless it can be shown independently that equilibrium has been established. One possible exception applies to trace substitution where the assumptions of stoichiometric saturation and unit activity for the predominant component allow close approximation of equilibrium behavior for the trace components (9). The method of Thorstenson and Plummer (10) based on the compositional dependence of the equilibrium constant, as used in this study, is well suited to testing equilibrium for all solid solution compositions. However, because equilibrium has not been found, the thermodynamic properties of the KCl-KBr solid solutions remain provisional until the observed compositional dependence of the equilibrium constant can be verified. One means of verification is the demonstration that recrystallization in the KCl-KBr-H20 system occurs at stoichiometric saturation. 

Most thermodynamic data for solid solutions derived from relatively low-temperature solubility (equilibration) studies have depended on the assumption that equilibrium was experimentally established. Thorstenson and Plummer (10) pointed out that if the experimental data are at equilibrium they are also at stoichiometric saturation. Therefore, through an application of the Gibbs-Duhem equation to the compositional dependence of the equilibrium constant, it is possible to determine independently if equilibrium has been established. No other compositional property of experimental solid solution-aqueous solution equilibria provides an independent test for equilibrium. If equilibrium is demonstrated, the thermodynamic properties of the solid solution are also... 

Thorstenson and Plummer (1977), in an elegant theoretical discussion (see section on The Fundamental Problems), discussed the equilibrium criteria applicable to a system composed of a two-component solid that is a member of a binary solid solution and an aqueous phase, depending on whether the solid reacts with fixed or variable composition. Because of kinetic restrictions, a solid may react with a fixed composition, even though it is a member of a continuous solid solution. Thorstenson and Plummer refer to equilibrium between such a solid and an aqueous phase as stoichiometric saturation. Because the solid reacts with fixed composition (reacts congruently), the chemical potentials of individual components cannot be equated between phases the solid reacts thermodynamically as a one-component phase. The variance of the system is reduced from two to one and, according to Thorstenson and Plummer, the only equilibrium constraint is IAP g. calcite = Keq(x>- where Keq(x) is the equilibrium constant for the solid, a function of... 

Note that the value of KdSiSs depends on the mole fraction x, and therefore will vary with the composition of the mixed solid. Unlike Kdis for a pure solid phase, Kd must be measured as a function of mixed solid composition in order to apply Eq. 3.29 to all possible states of stoichiometric saturation. 

Stoessell R. K. and Carpenter A. B. (1986) Stoichiometric saturation tests of NaCli Br and KCli Br. Geochim. Cosmochim. Acta 50, 1465-1474. 

The effect of substitutional impurities on the stability and aqueous solubility of a variety of solids is investigated. Stoichiometric saturation, primary saturation and thermodynamic equilibrium solubilities are compared to pure phase solubilities. Contour plots of pure phase saturation indices (SI) are drawn at minimum stoichiometric saturation, as a function of the amount of substitution and of the excess-free-energy of the substitution. SI plots drawn for the major component of a binary solid-solution generally show little deviation from pure phase solubility except at trace component fractions greater than 1%. In contrast, trace component SI plots reveal that aqueous solutions at minimum stoichiometric saturation can achieve considerable supersaturation with respect to the pure trace-component end-member solid, in cases where the major component is more soluble than the trace. 

Field or laboratory observations of miscibility gaps, spinodal gaps, critical mixing points or distribution coefficients can be used to estimate solid-solution excess-free-energies, when experimental measurements of thermodynamic equilibrium or stoichiometric saturation states are not available. As an example, a database of excess-free-energy parameters is presented for the calcite, aragonite, barite, anhydrite, melanterite and epsomite mineral groups, based on their reported compositions in natural environments. 

Several thermodynamic states are of interest in the study of SSAS systems. The following sections discuss the concepts of thermodynamic equilibrium, primary saturation and stoichiometric saturation states. 

Figure 1. Lippmann diagram (with stoichiometric and pure-phase saturation curves) for the Ag(Cl,Br) - H2O system at 30° C. Calculated ao and ai values are 0.30 and -0.18 respectively. pK gci = 9.55 (16J. pK gBr = 12.05 (12). T1 and T2 give the aqueous and solid phase compositions, respectively, of a system at thermodynamic equilibrium with respect to an AgCl.sBr 5 solid. PI and P2 describe the state of a system at primary saturation with respect to the same solid. MSI gives the composition of an aqueous phase at congruent stoichiometric saturation with respect to that solid.

Stoichiometric saturation was formally defined by Thorstenson and Plummer (1). These authors argued that solid-solution compositions typically remain invariant during solid aqueous-phase reactions in low-temperature geological environments, thereby preventing attainment of thermodynamic equilibrium. Thorstenson and Plummer defined stoichiometric saturation as the pseudoequilibrium state which may occur between an aqueous-phase and a multi-component solid-solution, "in situations where the composition of the solid phase remains invariant, owing to kinetic restrictions, even though the solid phase may be a part of a continuous compositional scries". 

The stoichiometric saturation concept assumes that a solid-solution can under certain circumstances behave as if it were a pure one-component phase. In such a situation, the dissolution of a solid-solution Bi xCxA can be expressed as ... 

Applying the law of mass action then gives the defining condition for stoichiometric saturation states ... 

According to Thorstenson and Plummer s (1) definition of stoichiometric saturation, an aqueous-solution at thermodynamic equilibrium with respect to a solid Bi.xCxA will always be at stoichiometric saturation with respect to that same solid. The converse statement, however, is not necessarily true stoichiometric saturation does not necessarily imply thermodynamic equilibrium. 

Stoichiometric saturation states can be represented on Lippmann phase diagrams (figure 1) by relating the total solubility product variable Ellgg (defined specifically at stoichiometric saturation with respect to a solid Ex. CxA) to the Kgg constant (equation 12) and to the aqueous activity fractions and c,aq-... 

In contrast to thermodynamic equilibrium, for which a single ( B,aq eq) point satisfies equations 1 and 2, stoichiometric saturation with respect to a given solid composition is represented by a series of ( B,aq points, all defined by relation... 

As shown in figure 1, stoichiometric saturation states never plot below the solutus curve. This is consistent with the fact that stoichiometric saturation can never be reached before primary saturation in a solid-solution dissolution experiment. The unique point at which a stoichiometric saturation curve (for a given solid Bj.xCxA) joins the Lippmann solutus represents the composition of an aqueous solution at thermodynamic equilibrium with respect to a solid Bx xCxA. 

In predicting solid-solution solubilities, one of two possible hypotheses must be chosen. In the first, the solid-solution is treated as a one-component or pure-phase solid, given that the equilibration time is sufficiently short, the solid to aqueous-solution ratio is sufficiently high and the solid is relatively insoluble. These requirements are needed to ensure that no significant recrystallisation of the initial solid or precipitation of a secondary solid-phase occurs. For such situations, the stoichiometric saturation concept may apply. 

There are currently insufficient data to determine the exact conditions for which each of these assumptions may apply, especially in field situations. In many instances, neither one of these assumptions will explain the observed solubility of a solid-solution, which may lie between the "maximum" stoichiometric saturation solubility and the "minimum" primary saturation solubility. Nonetheless, these solubility limits can often be estimated. 

Assuming that the dissolution to stoichiometric saturation takes place in initially pure water and that the aqueous activity ratio of the major and minor ions is equal to their concentration ratio, the relation B,aq/ c,aq = (l-x)/x will apply. Using this relation, applicable only at "minimum stoichiometric saturation" (Glynn and Reardon, Am. J. Sci.. in press), the following equations may be derived from equations 18, 19 and 20 ... 

Figure 2. Major and trace component saturation index values (in solid lines) for (Ca,Cd)C03 (insets A, B) and (Ca,Ni)C05 (insets C, D) solids at congruent stoichiometric saturation. Miscibility gap lines (short-dashed) and spinodal gap lines Oong-dashed) are also shown.

Figures 2A and 2B show the case of a solid-solution series, (Ca,Cd)COs, with a much less soluble trace end-member. If the mole-fraction of trace component is sufficiently high ( cdCO > lO- -S), the aqueous phase at stoichiometric saturation will be supersaturated with respect to the trace end-member (except at unrealistic negative ao values not shown on the plot). The lower solubility of the trace component will generally cause negative SI values for the major component, except at high ao values (higher than 7.5 in the (Ca,Cd)CO case) for which the solid-solutions will generally be metastable or unstable. Calcite SI values drawn in figure 2A show that the mole-fraction of trace component must be sufficiently high ( cdcos > 10-2-5) for this effect to be measurable in the field (typical uncertainty 0.01) or in the laboratory.

The composition of a SSAS system at primary saturation or at stoichiometric saturation will be generally independent of the initial solid to aqueous-solution ratio, but will depend on the initial aqueous-solution composition existing prior to the dissolution of the solid. In contrast, the final thermodynamic equilibrium state of a SSAS system attained after a dissolution or recrystallisation process will generally depend not only on the initial composition of the system but also on the initial solid to aqueous-solution ratio (Glynn et al, submitted to Gcochim, Cosmochim. Acta). 

Stoichiometric saturation measurements in carefully controlled laboratory experiments offer perhaps the most promising technique for the estimation of thermodynamic mixing parameters (3 Glynn and Reardon, Am. J. ScL, in press). Unfortunately, the results obtained can usually not be verified by a second independent and accurate method, such as reaction calorimetry or measurement of thermodynamic equilibrium solubilities (4). The conditions necessary in obtaining good stoichiometric saturation data (as opposed to thermodynamic equilibrium data) were discussed earlier. 

Lippmann phase diagrams can be used to describe and compare thermodynamic equilibrium (equations 3, 4), primary saturation (equations 9, 10), stoichiometric saturation (equation 13) and pure end-member saturation states (equations 14, 15) in binary SSAS systems. 

Techniques are presented for the estimation of excess-free-energies. These techniques should only be used, as an alternative to an ideal mixing model, in systems for which no laboratory stoichiometric saturation or thermodynamic equilibrium data is available. 

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