Category: 3. Chemical Contribution

P19.1. a. A gas-phase A+B system solvates A + B  AB with Ka = 0.5 at 298.15 K. Calculate the compressibility factor, apparent fugacity coefficients, and the true vapor phase mole fractions in a mixture at 298.15 K and 2 bar when the apparent concentration is yA = 0.45 using ideal chemical theory. b. A liquid-phase A+B system solvates A + B  AB with Ka = 0.7 at 298.15 K. Calculate the true…

A simple way of remembering the qualitative conclusions of this analysis can be derived by considering the behavior of the fugacity coefficient. One can easily demonstrate that the fugacity coefficient of the monomeric species is insensitive to the extent of association if it is expressed on the basis of the true number of moles in…

To this point in the discussion, we have assumed that the constants needed for a fluid are available. However, association models add complexity in the sense that two association parameters must be characterized in addition to the usual size (b), energy (a or ε), and shape (k, m, q, or c). One simple approach is to assign standardized values…

Shortly after Wertheim’s work appeared, Chapman et al. formulated an equation of state that incorporated the bonding contribution and complexation as well as the disperse repulsive and attractive terms. Their perspective was to treat any solution in the conventional way as a fluid of independent spheres, then to add the bonding contribution required to assemble…

Now that we have an accounting for the thermodynamics of bond formation, it is natural to wonder what happens to the thermodynamics as the bond energy approaches infinity. This would be a natural limit for covalent bond formation. Having a theoretical basis for nonspherical molecules would be a big step forward, considering that all theories…

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…