Symmetry in Routes to Conceptuals

We will need values of conceptuals for two classes of problems (a) calculation of thermodynamic properties for one-phase systems and (b) calculation of multiphase and chemical reaction equilibria. For both kinds of problems, we use the same basic strategy (i) Compare raw or modeled experimental data with computed properties of an ideal substance to obtain measures for deviations from the ideality, then (ii) exploit the deviation measures to obtain expressions for the required conceptuals in terms of measurables. Calculations of one-phase properties are typically based on differences, while phase and reaction equilibrium calculations typically use ratios. In 6.2.1 and 

2 we focus on difference measures, while in 6.2.3 and 6.2.4 we consider ratio measures. 

The ideal substance may be real or hypothetical, so long as its state (T, P, x ) is well-defined. To make the difference measure /j useful, the ideal property value / must be readily obtained, either from experiment, theory, or correlation. Note that in this most general form, the ideal state (T , P , x ) need not be the same as the state of the real substance (T, P, x ). 

Since the properties/and/ are state functions and the definition (6.2.1) is a linear combination of state functions, the difference/ is also a state function. This means/ forms exact differentials, so (6.2.1) can be written as 

In other words, the concept of an ideal substance can be interpreted mathematically as the lower limit of an integration. If the ideal substance is chosen to be the ideal gas at the same state as the real substance (T = T, P = P, x = x ), then the differences/ are the residual properties of Chapter 4. Alternatively, if the ideal substance is taken to be the Lewis-Randall ideal solution at (T, P, x ), then the differences/ j are the excess properties of Chapter 5. These two possibilities are compared in Table 6.1. 

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