Activity coefficient relationships thermodynamic consistency tests

Some years ago a research chemist tried to develop a thermodynamic consistency test for hydrogen and helium systems where one component is above its critical temperature, and where a vapor pressure and therefore, the activity coefficient, cannot be obtained. His relationship required the use of a generalized chart to get a property—of course it was before the days of computers. When attempts were made to use the generalized chart, it was found that near the critical region an accurate property value could not be read, certainly not accurate enough to test consistency without adding as much error as would be measured in the consistency test. Unless one takes the time to sufficiently test, one does not see the problems that may be encountered. 

Many additional consistency tests can be derived from phase equiUbrium constraints. From thermodynamics, the activity coefficient is known to be the fundamental basis of many properties and parameters of engineering interest. Therefore, data for such quantities as Henry s constant, octanol—water partition coefficient, aqueous solubiUty, and solubiUty of water in chemicals are related to solution activity coefficients and other properties through fundamental equiUbrium relationships (10,23,24). Accurate, consistent data should be expected to satisfy these and other thermodynamic requirements. Furthermore, equiUbrium models may permit a missing property value to be calculated from those values that are known (2). 

Each of the above three methods employs a different data base. Most of the property values required for the evaluation of in Equations 7-9 have been experimentally determined for III—V systems and these three relationships can be used as a test for thermodynamic consistency. The first method, Equation 7, is most reliable at or near the binary compound melting temperature. As the temperature is lowered below the melting one, uncertainties in the extrapolated stoichiometric liquid heat capacity and component activity coefficients become important. The second method, Equation 8, is limited to the temperature range in which an experimental determination of AG. is feasible (e.g., high temperature galvanic cell). Method II is also valuable for "pinning down" the low temperature values of 0yp. Method III is the preferred procedure when estimating solution model parameters from liquidus data. Since the activity coefficients of the stochiometric liquid... 

This relationship may be used to test the thermodynamic consistency of activity coefficient data (5, 9, 18), for which purpose we may put it in the form... 

In this section, we explore the relationship between the activity coefficients of the different species in a mixture. Using the Gibbs-Duhem equation, we will show that the activity coefficients are not independent. Their interrelationship will motivate development of a new type of thermodynamic property—excess Gibbs energy. Finally, we will illustrate an application of these principles by coming up with a way to test the quality of experimental data and see whether they are thermodynamically consistent. 

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