Partial and Apparent Molar Properties

Abstract

To this point we have developed a method of dealing with processes involving for the most part material (phases) of fixed composition. To progress further, we need to develop ways of dealing with the properties of dissolved substances, and with phases of variable composition. In other words, we need to deal with solutions. We have seen that the properties of homogeneous substances (usually, but not necessarily pure) are either total or molar properties (neglecting, as usual, specific properties). But obviously substances change drastically when they dissolve. How can we obtain properties for the dissolved substance alone, as opposed to the solution of which it is a part? Properties of dissolved substances are called apparent molar and partial molar properties, and these are the tools we need to discuss the thermodynamics of solutions in the following chapters. Partial molar properties are defined by partial derivatives (equations 2.22,9.7), which does not provide a very easy route to understanding them. There is however a highly intuitive way of thinking about partial molar properties. We will use volume as an example because it is readily visualized, but all relations derived can be used equally well for any other state variable. It will be useful to begin by realizing that we can also use derivatives to define molar properties of pure phases; this mathematical treatment is discussed in Chapter 2. Consider first the volume of a crystalline phase such as NaCl. The volume occupied by the salt, V, varies directly with the quantity of salt, so that a plot of volume versus number of moles of salt is a straight line (Figure 9.1).