The Measurement of Thermodynamic Excess Functions of Binary Liquid Mixtures

BY K. N. MARSH

1 Introduction

This chapter deals with experimental methods for determining the thermo-dynamic 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 GEm the molar excess enthalpy HEm and the molar excess volume VEm will be discussed. The molar excess entropy SEm can only be determined indirectly from either measurements of GEm and HEm at a specific temperature [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], or from the temperature dependence of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. The molar excess functions have been defined by McGlashan in the Introduction to Volume 1 of this series.

Experimental excess functions of liquid mixtures are useful in that they provide data to test theories of liquid mixtures and provide a guide for the formulation of new theories. The data are also useful in the chemical and petroleum industries. This chapter does not contain a summary of experimental data since Chapter 9 of this volume consists of a bibliography of excess function and related measurements on binary mixtures of non-electrolytes.

To date there has been no comprehensive review written on experimental techniques. Williamson's survey 2 in 1967 is now out of date as a number of new techniques have since been published. Moreover, his survey did not include a detailed analysis of the accuracy of the various techniques.

The excess Gibbs function, unlike the excess enthalpy and excess volumes, cannot be measured directly. The methods from which GE can be derived include: the simultaneous measurement of the total vapour pressure p, mole fraction y in the vapour phase and mole fraction x in the liquid phase at a fixed temperature, or any two of these three, in either a recirculating still or a static vapour-pressure apparatus; gas–liquid chromatography; isopiestic measurements; light-scattering measurements; and freezing-temperature determinations combined with excess enthalpies measured over a temperature range. In 1967 Hala et al. gave a detailed review of techniques suitable for vapour–liquid equilibrium measurement but their review was confined mainly to recirculating stills. In recent years the dynamic method has been superseded by the static method for measuring isothermal vapour–liquid equilibria data. The dynamic method is still commonly used to obtain isobaric data. This review will include only a limited discussion on recirculating stills and the reader is referred to ref. for further information on this method. Recent significant developments in techniques for the determination of GEm include two stepwise dilution static vapour-pressure systems, a compression apparatus for the measurement of the dew pressure of a vapour mixture of known composition, a precision freezing-temperature apparatus, and the extension of gas–liquid chromatography to finite concentrations.

Methods for measuring the excess enthalpy HE were last reviewed by McGlashan in 1961. Since that review the most widely used calorimeters have been modifications of that described by Larkin and McGlashan. Recently a number of stepwise dilution calorimeters, based on the original design of Savini et al., have been described. With this technique only two runs are required to cover the whole composition range, as each run can give values of HEm for more than half the volume fraction range. These calorimeters have a higher precision than previous calorimeters and they have the added advantage that a large number of results can be obtained quickly. Flow calorimetric techniques have been developed in recent years to give a precision equal to that of the Larkin and McGlashan type calorimeter. The main disadvantage of a majority of flow calorimeters is that large quantities of pure liquids are required, some requiring up to 300 cm3 of each component for a few measurements. The method has however served to confirm results obtained by other methods.

Until recently, excess volumes VE have been determined by precision density measurements on mixtures of known composition. If one or both components are volatile, then the method can give values of VE which are quite wrong. Great care must be taken both in the measurements and in applying the corrections due to vaporization during any transfer process. All serious measurements of VE should be made from direct measurements but this is difficult at low temperatures. One method is to use a dilatometer in which known amounts of each component are initially separated, usually by mercury, and then mixed. The volume change is observed in a fine precision-bore capillary. A recent development, based on the method used by Geffcken et al., for aqueous solutions, is the stepwise dilution dilatometer. With this dilatometer one component. is added stepwise to the other component and the volume change is measured directly. Two runs are required to cover the composition range. Benson and co-workers have confirmed the results obtained by dilution dilatometry on cyclohexane + benzene with a magnetic float method and with a mechanical oscillator densimeter.

2 Excess Gibbs Function — Data Reduction

The molar excess Gibbs function GEm(T,p[??],x) of a liquid mixture of A + B containing mole fraction x of B in the liquid phase at temperature T and pressure p]??] is defined by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

where µEA and µEB are the excess chemical potentials of component A and B respectively. Provided p]??] is less than atmospheric pressure, where the gas-phase behaviour can be represented by pVm = RT(1+Bp), the excess chemical potentials are given with amply sufficient accuracy by the relations:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)