A thermodynamic treatment of dilute solutions of gases in liquids

Abstract

A rigorous, compact, somewhat unconventional, thermodynamic analysis is presented for the treatment of very precise data on the solubilities of gases in liquids. Relationships among the chemical potentials, fugacities, fugacity coefficients, activity coefficients, molar volumes, and mole fractions, and the standard states involved, are carefully delineated. Both the symmetrical and asymmetrical choices for the activity coefficients are discussed, together with the connections between them. The symmetrical activity coefficient at infinite dilution, γ ^°₂ (T,p), is shown to be a very useful parameter for generalizing the ideal solubility concept of Hildebrand and Scott, and to be the factor which links corresponding concepts in the symmetrical and asymmetrical standard states. Arguments are presented for adopting

$$\mathop {\lim }\limits_{{\text{as }}x_2 \to 0} {\text{ [}}f_2^{\text{L}} (T,p,x_2 )/x_2 {\text{] = }}k_2 (T,p)$$

where k₂ is the Henry constant as the statement of Henry's law. The measured ratio,f ^V₂ /x ₂, is given the name Henry function and denoted by F _H2 . The Krichevsky-Kasarnovsky equation can be generalized to

$$F_{{\text{H2}}} (T,p,x_2 ) = k_2 (T.p_{\sigma 1} )[\gamma '_2 (T,p,x_2 )]{\text{ exp }}\mathop \smallint \nolimits_{p_{\sigma 1} }^p [\nu _2^{ - {\text{o}}} (T,p')/RT]{\text{d}}p'$$

which is the basis for the determination of very precise values for k₂(T,p_σ1). Several hypothetical functional representations for the activity coefficient are used in conjunction with the ideas above, to explore the implications of the very non-ideal character of dilute aqueous solutions of gases. Exact expressions are derived for the differences in partial molar Gibbs free energy, enthalpy, entropy, and heat capacity at constant pressure, of the solute gas between the hypothetical liquid standard state and the ideal gas state. Corrections for the temperature variation of p_σ1 are included.