More on Chemical Potentials

Chemical potentials are central for an understanding of material/phase equilibrium and phase stability. FST can be used to study metastable phase and phase instabilities. However, the vast majority of the studies using the FST of solutions involve a single stable phase with multiple components. Here, we are concerned with the relationships among the chemical potentials, and their derivatives, and the local solution distributions. Thermodynamically, from Equations 1.2 and 1.3, we have  

In practice, the relative chemical potential of a species in solution obtained from experiment can be expressed in many closely related forms. The primary differences relate to the choice of the reference (or standard) states, together with the concentration scale adopted for quantifying changes in composition. The most common choice was proposed by Lewis and Randall (LR) and adopts the pure liquids at the same T and p for the reference states and mole fractions for the composition variables (O Connell and Haile 2005). Consequently, the chemical potentials are expressed in the form 

There are, however, no perfectly ideal solutions—although many systems may approach this behavior. Ideal behavior is observed in the limit of a pure component, where the activity coefficient approaches unity and its composition derivative is then zero. Nevertheless, ideal solutions provide very useful reference points for real solution behavior (see Section 1.3.7). 

Unfortunately, the LR scale is not always the most convenient for practical use. In many cases, one would like to be able to use molalities or molarities as concentration variables, and to use different reference states. This does not change the form of Eqnation 1.19 nor the valne of the chemical potential, but it does alter the activities and the activity coefficients. It might seem strange that one can have a variety of activity coefficients. However, we shall see that it is only derivatives of the activities, which enter into fluctnation theory. Hence, the exact choice of reference state is often irrelevant. 

The fugacity was defined by G. N. Lewis as a substitute for the chemical potential to more directly relate a component s mixture properties to measurable properties and to avoid the divergence of the chemical potential at the limit of infinite dilution (Lewis 1900a, 1900b, 1901). The definition is an isothermal differential. 

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