Activity and Equilibrium in Nonelectrolyte Solutions

This generally nntrue statement can be rehabilitated by multiplying the mole fractions by rational activity coefficients,/, to reconvert them to activities  

We now imagine a solvent in which all the solutes form ideal solutions, and applying Raoult s law (Eq. 1.5) to each p mK (Eq. 1.4 rewritten for this reaction, with F = 1), we obtain  

Since the p° s, the vapor pressures of the several pure substances, depend only on temperature, /(/ideal) is a true constant, just as good as K. This is probably the most convenient candidate for the thermodynamic constant, K, in all cases of interest to us except those involving ionic species. Unless a comment is made to the contrary, it may be assumed that K=K (ideal) in the following pages. 

Deviations of from K can be of three sorts. Deviations at low and moderate concentrations from the zero-concentration limiting value are most important where ionic solutes are dissolved in nonionic solvents. Where all the solutes are molecular, even at extreme dilution, departures from Raoult s law on the part of each solute can arise in two distinct ways, with opposite effects. Deviations that are due to specific chemical or quasi-chemical attractive interactions between unlike molecules and that lead to enhanced mutual solubilities, lower partial vapor pressures, and activity coefficients less than unity are called negative deviations. Those that arise from mere differences between the molecules of the two kinds, such as differences of size or shape or of the intensity of intermolecular forces (reflected in differences in the solubility parameter, defined later), and that lead to diminished solubility, higher partial vapor pressures, and activity coefficients greater than unity are called positive deviations (see Fig. 1.2). 

The effect of mere difference between molecules, such as different size, shape, or polarizability, as it affects intermolecular forces was considered by Hildebrand and Scott (1962). They were led to the concepts of cohesive energy density (which is defined as the molar energy of evaporation divided by the molar volume, and which has the dimensions of pressure) and its square root, the solubility parameter, defined by  

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