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Warren PB. Partial osmotic pressures of ions in electrolyte solutions and the Gibbs-Guggenheim uncertainty principle. Phys Rev E 2023; 107:034606. [PMID: 37073044 DOI: 10.1103/physreve.107.034606] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/05/2022] [Accepted: 03/15/2023] [Indexed: 04/20/2023]
Abstract
The concept of the partial osmotic pressure of ions in an electrolyte solution is critically examined. In principle these can be defined by introducing a solvent-permeable wall and measuring the force per unit area which can certainly be attributed to individual ions. Here I demonstrate that although the total wall force balances the bulk osmotic pressure as required by mechanical equilibrium, the individual partial osmotic pressures are extrathermodynamic quantities dependent on the electrical structure at the wall, and as such they resemble attempts to define individual ion activity coefficients. The limiting case where the wall is a barrier to only one species of ion is also considered, and with ions on both sides the classic Gibbs-Donnan membrane equilibrium is recovered, thus providing a unifying treatment. The analysis can be extended to illustrate how the electrical state of the bulk is affected by the nature of the walls and the container handling history, thus supporting the "Gibbs-Guggenheim uncertainty principle," namely the notion that the electrical state is unmeasurable and usually accidentally determined. Since this uncertainty is conferred also onto individual ion activities, it has implications for the current (2002) IUPAC definition of pH.
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Affiliation(s)
- Patrick B Warren
- The Hartree Centre, STFC Daresbury Laboratory, Warrington WA4 4AD, United Kingdom
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Bonadiman C, Brombin V, Andreozzi GB, Benna P, Coltorti M, Curetti N, Faccini B, Merli M, Pelorosso B, Stagno V, Tesauro M, Pavese A. Phlogopite-pargasite coexistence in an oxygen reduced spinel-peridotite ambient. Sci Rep 2021; 11:11829. [PMID: 34088914 PMCID: PMC8178368 DOI: 10.1038/s41598-021-90844-w] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2020] [Accepted: 05/04/2021] [Indexed: 02/04/2023] Open
Abstract
The occurrence of phlogopite and amphibole in mantle ultramafic rocks is widely accepted as the modal effect of metasomatism in the upper mantle. However, their simultaneous formation during metasomatic events and the related sub-solidus equilibrium with the peridotite has not been extensively studied. In this work, we discuss the geochemical conditions at which the pargasite-phlogopite assemblage becomes stable, through the investigation of two mantle xenoliths from Mount Leura (Victoria State, Australia) that bear phlogopite and the phlogopite + amphibole (pargasite) pair disseminated in a harzburgite matrix. Combining a mineralogical study and thermodynamic modelling, we predict that the P-T locus of the equilibrium reaction pargasite + forsterite = Na-phlogopite + 2 diopside + spinel, over the range 1.3-3.0 GPa/540-1500 K, yields a negative Clapeyron slope of -0.003 GPa K-1 (on average). The intersection of the P-T locus of supposed equilibrium with the new mantle geotherm calculated in this work allowed us to state that the Mount Leura xenoliths achieved equilibrium at 2.3 GPa /1190 K, that represents a plausible depth of ~ 70 km. Metasomatic K-Na-OH rich fluids stabilize hydrous phases. This has been modelled by the following equilibrium equation: 2 (K,Na)-phlogopite + forsterite = 7/2 enstatite + spinel + fluid (components: Na2O,K2O,H2O). Using quantum-mechanics, semi-empirical potentials, lattice dynamics and observed thermo-elastic data, we concluded that K-Na-OH rich fluids are not effective metasomatic agents to convey alkali species across the upper mantle, as the fluids are highly reactive with the ultramafic system and favour the rapid formation of phlogopite and amphibole. In addition, oxygen fugacity estimates of the Mount Leura mantle xenoliths [Δ(FMQ) = -1.97 ± 0.35; -1.83 ± 0.36] indicate a more reducing mantle environment than what is expected from the occurrence of phlogopite and amphibole in spinel-bearing peridotites. This is accounted for by our model of full molecular dissociation of the fluid and incorporation of the O-H-K-Na species into (OH)-K-Na-bearing mineral phases (phlogopite and amphibole), that leads to a peridotite metasomatized ambient characterized by reduced oxygen fugacity.
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Affiliation(s)
- Costanza Bonadiman
- grid.8484.00000 0004 1757 2064Dipartimento di Fisica e Scienze della Terra, Università degli Studi di Ferrara, Via Saragat 1, 44122 Ferrara, Italy ,Istituto di Geologia Ambientale e Geoingegneria del Consiglio Nazionale delle Ricerche (IGAG-CNR), Via Salaria km 29, 300, 00015 Montelibretti, Italy ,Istituto di Geoscienze e Georisorse del Consiglio Nazionale delle Ricerche (CNR-IGG-CNR), Via G. Moruzzi 1, 56124 Pisa, Italy
| | - Valentina Brombin
- grid.8484.00000 0004 1757 2064Dipartimento di Fisica e Scienze della Terra, Università degli Studi di Ferrara, Via Saragat 1, 44122 Ferrara, Italy ,Istituto di Geologia Ambientale e Geoingegneria del Consiglio Nazionale delle Ricerche (IGAG-CNR), Via Salaria km 29, 300, 00015 Montelibretti, Italy
| | - Giovanni B. Andreozzi
- grid.7841.aDipartimento di Scienze della Terra, Sapienza Università di Roma, Piazzale Aldo Moro 5, 00185 Rome, Italy
| | - Piera Benna
- grid.7605.40000 0001 2336 6580Dipartimento di Scienze della Terra, Università degli Studi di Torino, Via Valperga Caluso 35, 10100 Turin, Italy
| | - Massimo Coltorti
- grid.8484.00000 0004 1757 2064Dipartimento di Fisica e Scienze della Terra, Università degli Studi di Ferrara, Via Saragat 1, 44122 Ferrara, Italy
| | - Nadia Curetti
- grid.7605.40000 0001 2336 6580Dipartimento di Scienze della Terra, Università degli Studi di Torino, Via Valperga Caluso 35, 10100 Turin, Italy
| | - Barbara Faccini
- grid.8484.00000 0004 1757 2064Dipartimento di Fisica e Scienze della Terra, Università degli Studi di Ferrara, Via Saragat 1, 44122 Ferrara, Italy
| | - Marcello Merli
- grid.10776.370000 0004 1762 5517Dipartimento di Scienze della Terra e del Mare (DiSTeM), Università di Palermo, Via Archirafi 36, 90123 Palermo, Italy
| | - Beatrice Pelorosso
- grid.8484.00000 0004 1757 2064Dipartimento di Fisica e Scienze della Terra, Università degli Studi di Ferrara, Via Saragat 1, 44122 Ferrara, Italy
| | - Vincenzo Stagno
- grid.7841.aDipartimento di Scienze della Terra, Sapienza Università di Roma, Piazzale Aldo Moro 5, 00185 Rome, Italy
| | - Magdala Tesauro
- grid.5133.40000 0001 1941 4308Dipartimento di Matematica e Geoscienze, Università di Trieste, Via Weiss 2, 34128 Trieste, Italy ,grid.5477.10000000120346234Department of Earth Sciences, Utrecht University, Princetonlaan 8a, Utrecht, 3584 CB The Netherlands
| | - Alessandro Pavese
- grid.7605.40000 0001 2336 6580Dipartimento di Scienze della Terra, Università degli Studi di Torino, Via Valperga Caluso 35, 10100 Turin, Italy
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Kutzner S, Schaffer M, Licha T, Worch E, Börnick H. Sorption of cationic organic substances onto synthetic oxides: Evaluation of sorbent parameters as possible predictors. THE SCIENCE OF THE TOTAL ENVIRONMENT 2018; 643:632-639. [PMID: 29958165 DOI: 10.1016/j.scitotenv.2018.05.393] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/10/2018] [Revised: 05/30/2018] [Accepted: 05/31/2018] [Indexed: 06/08/2023]
Abstract
Knowledge on the sorption behavior of cationic organic substances in aquatic systems is vital for their risk assessment due to the increasing detection of such chemicals in the hydrosphere. Their sorption behavior is strongly influenced by sorption processes onto mineral surfaces (e.g., oxides, clays). To contribute to the development of prediction tools, the impact of sorbent characteristics on the sorption strength was studied in a highly-idealized model system. In addition to the properties of the solid phase, the concentration of other ions in direct competition for sorption sites and the molecular structure of the sorbate were changed to separate ion exchange and non-ion exchange processes. The study includes in total 120 systematic column experiments using five extensively characterized synthetic oxides (three silica gels, two aluminum oxides), three probe molecules (two structurally related cationic substances, one neutral compound), and four distinctively different NaCl concentrations. The results show that the concentration of OH groups on the sorbent surface is a meaningful descriptor for the observed variations in sorption capacity onto different oxides. Compound-specific linear correlations were obtained, enabling the prediction of sorption coefficients. In addition, a more complex sorption behavior of organic cations compared to uncharged molecules were observed as demonstrated by the sorption results at different electrolyte concentrations. Thus, the study provides an important step towards a better principal mechanistic understanding of organic cation sorption. However, further work using other sorbents including natural ones and other probe molecules is needed to verify the identified relationships within the scope of developing reliable prediction models for cation sorption.
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Affiliation(s)
- Susann Kutzner
- Institute of Water Chemistry, Technische Universität Dresden, 01062 Dresden, Germany.
| | - Mario Schaffer
- Geoscience Centre, Department of Applied Geology, Hydrochemistry Group, University of Göttingen, Goldschmidtstr. 3, 37077 Göttingen, Germany; Lower Saxony Water Management, Coastal Defence and Nature Conservation Agency (NLWKN), Hannover-Hildesheim branch, An der Scharlake 39, 31135 Hildesheim, Germany
| | - Tobias Licha
- Geoscience Centre, Department of Applied Geology, Hydrochemistry Group, University of Göttingen, Goldschmidtstr. 3, 37077 Göttingen, Germany
| | - Eckhard Worch
- Institute of Water Chemistry, Technische Universität Dresden, 01062 Dresden, Germany
| | - Hilmar Börnick
- Institute of Water Chemistry, Technische Universität Dresden, 01062 Dresden, Germany
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