Reference States for the Liquid Phase

In this section, we explore how we can calculate fugacity in the liquid phase. In doing so, we will develop an appropriate reference state for the liquid phase, the ideal solution, and then correct for real behavior through the activity coefficient. We will then learn a type of empirical model that correlates experimental data efficiently. The methodology developed in this section can also be applied to solids. Finally, an alternative approach to calculating fugacity in the liquid using PvT equations of state is discussed. This approach is similar to that used for the vapor phase in Section 7.3. 

In the liquid phase, just as in the vapor phase, we need to choose a suitable reference state with a corresponding reference chemical potential and reference fugacity to complete the definition provided by Equation (7.3). We then adjust for the difference between the reference phase and the real system. However, while there is an obvious reference case for gases—the ideal gas—there is no single suitable choice for the liquid phase. There are two common choices for the reference state (1) the Lewis/Randall rule and (2) Henry s law. The choice of reference state often depends on the system. Both these reference states are limiting cases that result from a natural idealization for condensed phases the ideal solution. 

We wish to define a reference state for the liquid phase to which we can compare the fugacity of a real liquid. Hence, we need something analogous to what an ideal gas provided us for real gases. For liquids, however, we cannot extrapolate to a state where there are no intermolecular interactions as we did at zero pressure for gases. Indeed, it is the very presence of intermolecular forces that makes condensed phases possible without these forces, only the entropically favored gas phase would exist. Accordingly we will choose an ideal solution as our reference state. 

An ideal solution can be defined in several ways. On a macroscopic level, a solution is ideal when aU the mixing rules are the same as for an ideal gas. Analogous to the discussion previously, an ideal solution is characterized by the following mixing rules  

In analogy to Equation (7.25) for an ideal gas, the following relation must hold for an ideal solution  

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The ideal gas provides the reference state for the vapor phase. To set up our discussion of reference states for the liquid phase, we will review the property changes of mixing for an ideal gas as discussed in Section 6.3. Recall that a property change of mixing is defined as the difference between the total solution property and the sum of the pure species properties apportioned by the amount each species present in the mixture ... 

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