Spin-Exchange Term in the Solvent Equation of State Near the Critical Point for Electron-Transfer Reactions

• Published in: Journal of solid state chemistry Vol. 151; no. 1; pp. 102 - 110
• Main Author: Acrivos, J.V.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.04.2000
• Subjects: electron spin exchange reactions; equations of state for supercritical metallic; polar and non-polar solvents; semi-metallic; equations of state for supercritical metallic; polar and non-polar solvents; semi-metallic; electron spin exchange reactions
• ISSN: 0022-4596; 1095-726X
• DOI: 10.1006/jssc.1999.8629

Phenomenological equations of state (EOS) for fluids near their critical point have been obtained using literature compression factor data, Zc=PcVc/(nRTc)=0.40 to 0.10 in (Pc, Vc, and Tc are the pressure, volume per nmole, and the absolute temperature of the fluid at the critical point). The objective is to explain the deviations from the van der Waals value, Zc(vdW)=3/8 (−70% for molten Se and alkali metals up to 6% for molten Pb, Hg, and In) by including in the commonly used phenomenological thermodynamic relations a term which explicitly describes the Heisenberg spin-exchange interactions, in order to understand electron-transfer reactions in solvents near their critical point. Literature data near the critical point indicate that the 199,201Hg(Zc≅0.4) Knight shift pluments to zero while the alkali metals and Se (Zc=0.2 to 0.1) are paramagnetic fluids, and that the enhanced rates for free radical electron-exchange reactions in CO2, n-C2H6, and CHF3 with intermediate values of Zc, are correlated to Zc. The difference in the solvent behavior for electron-exchange reactions near its critical point is ascribed to spin-exchange interactions. The analysis shows that the solvated electron osmotic pressure in metal–ammonia solutions goes through a maximum where enhanced rates of electron exchange also attain a maximum versus the solvent density ρr=Vc/V≅0.5. The results can be applied to choose the best solvents, near their critical point, for the syntheses of new materials and heavy metal oxide extraction.