Theory of partial molar properties. Defining isochoric thermal capacity and isentropic compression at constant temperature and pressure, and introducing partial molar properties at constant temperature and molar volume, at constant molar entropy and pressure, and at constant molar entropy and molar volume

Abstract

The concept and properties of partial molar quantities are presented and discussed in a generalized fashion within a thermodynamic framework.

X being any thermodynamic extensive property of a homogeneous phase of fixed composition, it is proposed to consider X_B(y, z) as a generalized partial molar property of substance B with respect to constant (y, z) whenever X_B(y, z)=(∂X/∂n_B)_y,z,n′ where n′ indicates that all n are held constant apart from n_B, complies with the condition [graphic omitted]. This is shown to be true whenever the independent variables y and z, one thermal and the other mechanical, are intensive properties of the system.

Concerning common partial molar properties, those defined at constant temperature and pressure, particular attention is paid to the partial molar isochoric thermal capacity C_V,B(T, p) and to the partial molar isentropic compression K_S,B(T, p). Contrary to generally accepted views, their relations with C_p,B(T, p) and with K_T,B(T, p), respectively, which are rederived directly from the equations relating the parent extensive properties, are far from being similar to the relations involving the corresponding molar properties. To express this behaviour, C_V,B(T, p) and K_S,B(T, p) are designated as non-Lewisian properties. A summary of thermodynamic relations among the usual X_B(T, p) properties (those of the Lewisian type) is presented, and it is suggested that non-partial molar quantities be defined in order to fill the place of non-Lewisian partial molar properties in the thermodynamic formalism for Lewisian ones.

Generalized partial molar properties at constant temperature and molar volume X_B(T, V_m), at constant molar entropy and pressure X_B(S_m, p), and at constant molar entropy and molar volume X_B(S_m, V_m) are introduced and briefly discussed. Their general relations to X_B(T, p) are given and non-Lewisian properties are identified for each kind of partial molar properties. The origin of the non-Lewisian behaviour is ascribed to purely mathematical reasons. The concept of a ‘partial fractional property’ is introduced to allow intensive properties of the system which are not independent variables to be treated in a similar fashion to the extensive ones.

Finally, some observations concerning the thermodynamic meaning of a partial molar property are made.