Wohl expansion

The liquid-phase activity coefficients for the Wohl expansion can be obtained from Eq. 9.5-8 by taking the appropriate derivatives ... 

The excess Gibbs energy models for binary mixtures discussed in Sec. 9.5 can be extended to multicomponent mixtures. For example, the Wohl expansion of Eq. 9.5-8 can be extended to ternary mixtures ... 

One should keep in mind that this ability to predict multicomponent behavior from data on binary mixtures is,not an exact result, but rather arises from the assumptions made or the models used. This is most clearly seen in going from Eq. A9.2-1 to Eq. A9.2-2. Had the term oti23ZiZ2Z3 been retained in the Wohl expansion, Eq. A9.2-2 would contain this a 123 term,. which could be obtained only from experimental data for the ternary mixture. Thus, if this more complete expansion were used, binary data and some ternary data would be needed to determine the activity coefficient model parameters for the ternary mixture. 

The experimental data for the partial solubility of perfluoro-n-heptane in various solvents has been plotted as a function of both mole fraction and volume ftaction in Fig. 11.2-3. It is of interest to notice that these solubility data are almost symmeuic functions of the volume fraction and nonsymmetric functions of the mole fraction. Such behavior has also been found with other thermodynamic mixture properties these observations suggest the use of volume fractions, rather than mole fractions or mass fractions, as the appropriate concentration variables for describing nonideal mixture behavior. Indeed, this is the reason that volume fractions have been used in both the regular solution model and the Wohl expansion of Eq. 94-8 for liquid mixtures. 

Because of its flexibility, simplicity, and ability to fit many systems well, the van Laar equation is widely used in practice. It can be derived from the general energy expansion of Wohl, which considers effective volume fractions and molecular interactions. The so-called Carlson and Colburn natural logarithm version of the van Laar equation is given in Table 5.3. However, a common logarithm form is more common. The Margules and Scatchard-Hamer equations in Table 5.3 can also be derived from the Wohl expansion by a set of different assumptions. 

The expansion of Eq. 9.5-6 is certainly not unique other types of expansions for the excess Gibbs energy could also be used. Another expansion is that of Wohl. ... 

During the current period of review, the study of the chemistry of thiazoles has attracted the same steady attention as in previous years. A comprehensive and unifying survey of the subject as a whole is still lacking. A summary of the synthesis of 2-thiazolines and thiazolidines by the ring-expansion of aziridines forms a useful introduction to Wohl and Headley s study of the stereochemistry of this reaction. 

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