Lippmann diagram

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.

Primary saturation is the first state reached during the congruent dissolution of a solid-solution, for which the aqueous-solution is saturated with respect to a secondary solid-phase (JJ., J 4, Glynn and Reardon, Am. J. ScL, in press). This secondary solid will usually have a composition different from that of the dissolving solid. At primary saturation, the aqueous phase is at thermodynamic equilibrium with respect to this secondary solid but remains undersaturated with respect to the primary dissolving solid. The series of possible primary-saturation states for a given SSAS system is represented by the solutus curve on a Lippmann diagram. 

In the specific case of a "strictly congruent" dissolution process occurring in an aqueous phase with a [B+]/[C+] activity ratio equal to the B+/C+ ratio in the solid, primary-saturation can be approximately found by drawing a straight vertical line on the Lippmann diagram from the solid-phase composition to the solutus (see figure 1). For an exact calculation, the following relations may be used to determine the primary saturation state ... 

Saturation curves for the pure BA and CA end-member solids can also be drawn on Lippmann diagrams (2,5) ... 

These equations define the families of ( ba ba) and ( cA> ncA) conditions for which a solution containing A-, B+ and C ions will be saturated with respect to pure BA and pure CA solids. Thermodynamic equilibrium with respect to a mechanical mixture of the two pure BA and CA solids, in contrast to a solid-solution of BA and CA, will be represented on a Lippmann diagram by a single point, namely the intersection of the pure BA and pure CA saturation curves. The coordinates of this intersection are ... 

Many researchers have employed log([M" J/[H i") versus log[H4Si04 j and similar diagrams to explain and interpret natural water systems, where M denotes a cation and n its charge (cf. Helge-sonetal. 1969 Lippmann 1979 Faust andAly 1981 Bowers et al. 1984 Drever 1988 Nesbitt and Wilson 1992 Anderson and Crerar 1993 Nordstrom and Munoz 1994 Cramer and Smellie 1994). Of necessity, simplified clay compositions have been assumed in order to show them on such diagrams. Assumptions and limitations comparable to those that were inherent in the construction and use of Figs. 9.8 and 9.9 apply to all such diagrams. 

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-... 

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. 

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