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The solution to phase equilibrium problems can be achieved in the manner of Chapter 15 (Eqn 15.20), where Eqns. 19.1 and 19.2 describe the enhanced equation of state. Eqns. 19.75–19.77 completely characterize the temperature, density, and composition dependence of the chemical contribution to Helmholtz energy. The Zchem contribution is implied, but requires differentiation as in RT·Zchem = –V∂(A – Aig)/∂V. Similarly, the fugacity coefficient is implicitly determined through differentiation.…

The thermodynamics and phase behavior are sufficiently described by Eqns. 19.75 and 19.77, but you may be curious about the true mole fractions of the species. Furthermore, it is interesting to see how this “fraction of acceptor sites not bonded” is closely related to the fraction monomer, xM. This turns out to be a bit subtle, and it should…

The general approach is exactly what you would expect: Write all the reaction and phase equilibrium constraints and then solve the nonlinear system of equations. Making this approach into a practical alternative to, say, the Peng-Robinson model requires several clever observations, approximations, and rearrangements, however. Wertheim’s theory is based on the contribution to the Helmholtz…

The assumptions of ideal chemical theory are known to be oversimplifications for many systems and physical interactions must be included. For a liquid phase, the activity coefficients of the true species can be reintroduced. Then Utilizing this result with Eqns. 19.20 and 19.22, the following equations are obtained: Since most activity coefficient models require two parameters per pair…

The simplest method of modeling complex behavior is to neglect the nonidealities by modeling a vapor phase as an ideal gas mixture including the complexes (true fugacity coefficients equal to 1), and to model a liquid phase as an ideal solution containing complexes (true activity coefficients equal to 1). This approach is called Ideal Chemical…

The balance equations to be solved take the same form for both vapors and liquids. The liquid equations will be shown, and the reader should recognize the vapor equations by analogy. First, the true mole fractions must sum to unity: In a binary system, a balance equation can be written for either component to match…

Mole Balance One may wonder how quantification of the phenomena can be approached in a generalized fashion, but the criteria are presented clearly by Prigogine and Defay (1954) whose proof we reproduce here with modified notation. The first balances that must be satisfied are the material balances. For a binary solution created from nA moles of A, and nB moles…

Evidence of complexation is often subtle and could be overlooked or ignored in many situations, but its effects are irrefutable in other situations, so a question arises about ignoring facts because they are inconvenient. For example, dimerization of carboxylic acids is observable in the saturated vapor compressibility factor of small acids, but less so for…