Solid-solution aqueous-solution equilibria; thermodynamic theory and representation
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Solid activity coefficients of CaCO3 and MnCO3 in terms of solid components can be estimated by the Redlich and Kister equations.
“The solid activity coefficients of CaCO3 () and MnCO3 () in terms of solid components (1−x, x) can be estimated by the Redlich and Kister equations [50, 54, 60], which are expressed as:1617 where 1−x and x are the molar ratios ( and ) of CaCO3 and MnCO3 in the (Ca1-xMnx)CO3 solid solutions, respectively.”
From Dissolution and solubility of calcite-rhodochrosite solid solutions [(Ca1-xMnx)CO3] at 25 °C (2021) · cites this paper as [50]
When stoichiometric saturation state was reached during dissolution, the excess free energy of mixing for (BxC1-x)A solid solutions can be estimated with Eq. (18).
“When the stoichiometric saturation state was reached during dissolution, the excess free energy of mixing for the (BxC1-x)A solid solutions (GE) can be estimated with the following:18 where KSS is the stoichiometric saturation constant and KCA and KBA are the solubility products of CA and BA, respectively [34, 50].”
From Dissolution and solubility of calcite-rhodochrosite solid solutions [(Ca1-xMnx)CO3] at 25 °C (2021) · cites this paper as [50]
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“The series of minimum stoichiometric points for a series of solid-phase compositions ranging from x = 0 to x = 1 defines the minimum stoichiometric saturation curve (Glynn and Reardon 1990), also called the equal-G curve (Königsberger and Gamsjäger 1992).”
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“dynamic principles governing solid-solution– aqueous-solution (SS AS) systems on which this assertion is made are well established (Glynn and Reardon, 1990; Tesoriero and Pankow, 1996) and have recently been reviewed by Prieto (2009).”
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“A Lippmann phase diagram can be used to visualize SS-AS equilibrium states (Lippmann, 1977, 1980; Glynn and Reardon, 1990; Putnis and others, 1995; Glynn, 2000; Prieto, 2009) and the thermodynamic framework is given below.”
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“Lippmann diagram Glynn and Reardon, 1990 , in which SP is represented on the ordinate and the composition of the solid and the aqueous phase are represented in a double scale on the abscissa.”
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“In constructing the Lippmann diagram, the total solubility product (ΣΠ) for (PbxCa1‒x)(PO4)3/5OH1/5 can be expressed as [47]:”
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“According to the three models, the Lippmann's total solubility product (ΣΠ) and Ksp values of each zeolite were calculated ([55,56], see details in Text A1) and plotted in Fig.”
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“(Glynn and Reardon, 1990; Lippmann, 1980; Prieto, 2009) defined as”
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“The values of interaction parameters in these equations for (pseudo)binary systems can be predicted theoretically, as done above, or simply adjusted in graphical fitting of the solidus and solutus curves against the empirical 65 points on the Lippmann diagram plots (Glynn and Reardon, 1990).”
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“However, following Lippmann theory [28] the solution composition is supersaturated with respect to an intermediate composition Ca0.”
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“From Glynn and Reardon (1990),36 the standard Gibbs free energy associated with the congruent dissolution reaction of a real solid solution can be expressed in terms of the standard Gibbs free energy associated with the dissolution of an ideal solid solution, ΔRG°,id with the same composition and…”
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“Then thermodynamicmodelswere proposed (Lippmann, 1977; Glynn and Reardon, 1990) based on mixing properties of solid solutions, but their utility is limited to conditions near equilibrium.”
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- Authors
- Glynn, P. D., & Reardon, E. J.
- ORCID
- Glynn, P. D.
- Venue
- American Journal of Science
- Publisher
- American Journal of Science (AJS)
- Published
- 1990-02-01
- Volume
- 290
- Issue
- 2
- Pages
- 164-201
- ISSN
- 0002-9599 (ISSN-L)
- OpenAlex
- W1981362259
- Cited by
- 219
- References
- 0
- Citations by year
- 2026: 3 · 2025: 6 · 2024: 5 · 2023: 3 · 2022: 7 · 2021: 5 · 2020: 6 · 2019: 3 · 2018: 9 · 2017: 12 · 2016: 7 · 2015: 6 · 2014: 8 · 2013: 7 · 2012: 18
- FWCI
- 12.55
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- American Journal of Science (publishedVersion)
- Topics
- Physical Sciences › Chemical Engineering › Filtration and Separation › Chemical and Physical Properties in Aqueous Solutions
- Physical Sciences › Engineering › Biomedical Engineering › Phase Equilibria and Thermodynamics
- Physical Sciences › Materials Science › Materials Chemistry › Crystallization and Solubility Studies
- Keywords
- aqueous solution equilibria, thermodynamic theory, phase equilibria, chemical thermodynamics
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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