Partial Molar Equation-of-State Parameters

Partial Molar Equation-of-State Parameters The parameters in equations of state as applied to mixtures are related to composition by mixing rules. Eor the second virial coefficient 

The partial molar second virial coefficient is by definition 

Because B is independent of F, this is in accord with Eq. (4-171). Th e two equations lead through derivation to useful expressions for Bi, as shown in detail by Van Ness and Abbott [Classical Thermodynamics of Nonelectroly te Solutions With Applications to Phase 

Equilibria, pp. 137-140, McGraw-Hill, New York (1982)]. The simplest result is 

An analogous expression follows from Eq. (4-114) for parameter a in the generic cubic equation of state given by Eqs. (4-100), (4-103), and (4-104)  

---

In Eqs. (1.3-30) and (1.3-31), all unsubscripted quantities refer to die mixture. (Quantities b/and 9, m partial molar equation-of-state parameters, defined by... 

For simplicity, the Peng-Robinson equation of state should suffice in providing reasonable estimates of the partial molar volumes of the benzophenone triplet, isopropanol and transition state, as well as the isothermal compressibility. Since no tetter information was available, the binary interaction parameters for all pairs were set to zero. The predicted values of RT 31nkbm/9P are shown in Figure 9. 

Molar area, adsorbed phase Parameter, cubic equations of state Partial parameter, cubic equations of state Second virial coefficient, density expansion... 

Partial parameter, cubic equation of state 2d virial coefficient, density expansion Partial molar second virial coefficient Reduced second virial coefficient... 

It should be evident from the examples in Chapters 10, 11, and 12 that the evaluation of species fugacities or partial molar Gibbs energies (or chemical potentials) is central to any phase equilibrium calculation. Two different fugacity descriptions have been used, equations of. state and activity coefficient models. Both have adjustable parameters. If the values of these adjustable parameters are known or can be estimated, the phase equilibrium state may be predicted. Equally important, however, is the observation that measured phase equilibria can be used to obtain these parameters. For example, in Sec. 10.2 we demonstrated how activity coefficients could be computed directly from P-T-x-y data and how activity coefficient models could be fit to such data. Similarly, in Sec. 10.3 we pointed out how fitting equation-of-state predictions to experimental high-pressure phase equilibrium data could be used to obtain a best-fit value of the binary interaction parameter.. /"... 

Now, commencing with the partition function for the mixture and the definitions of parameters p and T in terms of the properties of equations of state for single liquids and additional parameters Xjj and j/ 2> the equations for S , (P, and the corresponding partial molar [Pg.75]

The difficulties encountered in the Chao-Seader correlation can, at least in part, be overcome by the somewhat different formulation recently developed by Chueh (C2, C3). In Chueh s equations, the partial molar volumes in the liquid phase are functions of composition and temperature, as indicated in Section IV further, the unsymmetric convention is used for the normalization of activity coefficients, thereby avoiding all arbitrary extrapolations to find the properties of hypothetical states finally, a flexible two-parameter model is used for describing the effect of composition and temperature on liquid-phase activity coefficients. The flexibility of the model necessarily requires some binary data over a range of composition and temperature to obtain the desired accuracy, especially in the critical region, more binary data are required for Chueh s method than for that of Chao and Seader (Cl). Fortunately, reliable data for high-pressure equilibria are now available for a variety of binary mixtures of nonpolar fluids, mostly hydrocarbons. Chueh s method, therefore, is primarily applicable to equilibrium problems encountered in the petroleum, natural-gas, and related industries. 

All volumes are given in cm3 mol-1. The structural parameters necessary for the calculation of the van der Waals volume for the transition state (TS) were taken from ab initio calculations159,160. The partial molar volume for the TS was calculated from the equation ... 

---