On the linear orthobaric-density representation of near-critical solvation quantities: What can we conclude about the accuracy of this paradigm?

Abstract

In this work, we have derived rigorous expressions for the thermodynamic description of the solvation behavior of a model solute in highly-compressible environments of a real solvent, in order to address the question posed in the title of this manuscript. Toward that end, we first provide the essential statistical thermodynamic foundations to support a fundamentally-based approach for the determination of the Krichevskii parameter of a solute in any solvent, based solely on the knowledge of the corresponding Henry's law constant. Second, we analyze the actual orthobaric-density behavior of lnQ(T,Pσ) and TσlnQ(T,Pσ), when Q=KD∞ and Q=(Hi,jIS/fjo), for an infinitely dilute ideal gas solute in an aqueous solution, a system for which we have complete knowledge of its microscopic and thermodynamic behaviors. Third, we invoke these results to test the assumptions behind the modeling of the orthobaric-density dependence of the Henry's law constant, infinite dilution vapor-liquid distribution, and Ostwald coefficients of real solutes. Fourth, we discuss the implications underlying the interpretation of the regressed orthobaric-density slopes, the accuracy of the resulting effective Krichevskii parameters, and the extension of the current analysis to the orthobaric-density behavior for the corresponding Ostwald coefficient, TσlnLi,j∞(T,Pσ). Finally, we show how the fundamentally-based orthobaric-density linear expressions of lnQ(T,Pσ) for the three Q−quantities converge to the corresponding, empirically-found, TσlnQ(T,Pσ) asymptotic linear representations for near-critical infinitely dilute solutions.