Thermodynamics of Nonelectrolyte Solubility

EMMERICH WILHELM Institute of Physical Chemistry, University of Wien, Währinger Straße 42, Wien (Vienna) A-1090, Austria

Magic means rather different things to different people. Brigadier Donald Ffellowes in "The Kings of the Sea", by S.E. Lanier, The Magazine of Fantasy & Science Fiction, November 1968.

1.1 Introduction

The liquid state is one of the three principal states of matter. The majority of chemical synthesis reactions are carried out in the liquid state, and separation processes usually involve liquid/fluid states, i.e. solutions. Thus, not surprisingly, for a century and a half experimental investigations of physical properties of solutions and of phase equilibria involving solutions (vapour–liquid equilibrium: VLE; liquid–liquid equilibrium: LLE; solid–liquid equilibrium: SLE; solid–vapour equilibrium: SVE) have held a prominent position in physical chemistry. The scientific insights gained in these studies can hardly be overrated, and have been of immense value for the development of the highly formalized, general discipline of mixture thermodynamics, for instance by providing idealized solution models, such as the one based on the Lewis–Randall (LR) rule, or the one based on Henry's law (HL). In addition to its profound theoretical interest, this topic includes many important practical, industrial applications in chemical process design, in the environmental sciences, in geochemistry, in biomedical technology and so forth. Water is the most abundant liquid on the earth, and because it sustains life as we know it, it is also the most important liquid solvent. The preponderance of scientific papers dealing with aqueous solutions is thus not surprising. We note that the study of the solubility in water of the rare gases and of simple hydrocarbons have provided fundamental information on hydrophobic effects that are thought to be of pivotal importance for the formation and stability of higher order structures of biological substances, such as proteins, nucleic acids, and cell membranes.

Evidently, this short review cannot possibly be comprehensive, and I shall focus on just a few topics which reflect my current research interests and idiosyncrasies. For instance, VLE with supercritical solutes, that is the solubility of gases in liquids, will be discussed in some detail, and so will the van't Hoff type analysis of high-precision solubility data. SLE and SVE will not be considered at all. Almost inevitably, pride of place will be given to the Henry fugacity, or Henry's law constant, which is one of most misunderstood thermodynamic quantities. The goal is to clarify some points often overlooked, and to dispel misconceptions frequently encountered in the literature.

1.2 Thermodynamics

In this section I will present a brief overview of classical thermodynamics applicable to nonelectrolyte solutions in general, and to solutions of gases in liquids in particular.' When discussing solutions, one is either interested in single-phase properties, such as partial molar volumes, or in quantities which characterize the equilibrium solubility itself, for instance the amount of substance i, the solute, dissolved in a given amount of solvent j in the presence of both coexisting phases. The equations governing VLE and LLE will be considered first. For details see refs. 1 and 2.

A general criterion for phase equilibrium at temperature T and pressure P is the equality of the chemical potential μπ[i] of each constituent component i in all coexisting phases π, or equivalently, the equality of the fugacity fπi of each component in all coexisting phases. Thus, for the specific case of VLE (π = V or L),

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

where N is the number of components present, each with mole fraction XVi in the vapour phase and XLi in the liquid phase. Similarly, for LLE (π = L' or L")

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

From now on, however, I shall confine attention to binary systems, where i = 1 or 2.

Two entirely equivalent formal procedures are commonly used to establish the link with experimental reality:

(I) When using the fugacity coefficient of component i in solution in phase π, which quantity is defined by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

and adopting the convenient notation XVi = yi,...