Excess Gibbs Function - Experimental Methods

Having established the definitions and conventions for the activity function and for the excess Gibbs function in Chapter 16, we are in a position to understand the experimental methods that have been used to determine numeric values of these quantities. 

In this chapter, we shall consider the methods by which values of partial molar quantities and excess molar quantities can be obtained from experimental data. Most of the methods are applicable to any thermodynamic property J, but special emphasis will be placed on the partial molar volume and the partial molar enthalpy, which are needed to determine the pressure and temperature coefficients of the chemical potential, and on the excess molar volume and the excess molar enthalpy, which are needed to determine the pressure and temperature coefficients of the excess Gibbs function. Furthermore, the volume is tangible and easy to visualize hence, it serves well in an initial exposition of partial molar quantities and excess molar quantities. 

This chapter deals with experimental methods for determining the thermodynamic excess functions of binary liquid mixtures of non-electrolytes. Most of it is concerned with techniques suitable for measurements in the temperature range 250 to 400 K and the pressure range 0 to 100 kPa. Techniques suitable for lower temperatures will be briefly reviewed. Techniques for measuring the molar excess Gibbs function G, the molar excess enthalpy and the molar excess volume will be discussed. The molar excess entropy can only be determined indirectly from either measurements of (7 and at a specific temperature = (If — C /T], or from the temperature dependence of G m [ S m = The molar excess functions have been defined by... 

Activity coefficients and thence excess Gibbs functions can be calculated from the results of measurements at given temperature of the pressure and the compositions of the liquid (or solid) mixture and of the coexisting gas phase. Excess enthalpies can be measured calorimetrically and excess volumes dilatometrically. The experimental methods used to measure excess functions and the results obtained will be reviewed in a subsequent volume. 

The experimental studies of three-component systems based on phase equilibria follow the same principles and methods discussed for two-component systems. The integral form of the equations remains the same. The added complexity is the additional composition variable the excess chemical potentials become functions of two composition variables, rather than one. Because of the similarity, only those topics that are pertinent to ternary systems are discussed in this section of the chapter. We introduce pseudobinary systems, discuss methods of determining the excess chemical potentials of two of the components from the experimental determination of the excess chemical potential of the third component, apply the set of Gibbs-Duhem equations to only one type of phase equilibria in order to illustrate additional problems that occur in the use of these equations, and finally discuss one additional type of phase equilibria. 

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