Infinite-dilution //-values

The symmetrical nature of these relations is evident. The infinite-dilution values of the activity coefficients are In yF = Iri JT = B. 

Outlined below are the steps required for of a X T.E calciilation of vapor-phase composition and pressure, given the liquid-phase composition and temperature. A choice must be made of an equation of state. Only the Soave/Redlich/Kwong and Peng/Robinson equations, as represented by Eqs. (4-230) and (4-231), are considered here. These two equations usually give comparable results. A choice must also be made of a two-parameter correlating expression to represent the liquid-phase composition dependence of for each pq binaiy. The Wilson, NRTL (with a fixed), and UNIQUAC equations are of general applicabihty for binary systems, the Margules and van Laar equations may also be used. The equation selected depends on evidence of its suitability to the particular system treated. Reasonable estimates of the parameters in the equation must also be known at the temperature of interest. These parameters are directly related to infinite-dilution values of the activity coefficients for each pq binaiy. 

Since the infinite dilution values D°g and Dba. re generally unequal, even a thermodynamically ideal solution hke Ya = Ys = 1 will exhibit concentration dependence of the diffusivity. In addition, nonideal solutions require a thermodynamic correction factor to retain the true driving force for molecular diffusion, or the gradient of the chemical potential rather than the composition gradient. That correction factor is ... 

The solvent and the key component that show most similar liquid-phase behavior tend to exhibit little molecular interactions. These components form an ideal or nearly ideal liquid solution. The ac tivity coefficient of this key approaches unity, or may even show negative deviations from Raoult s law if solvating or complexing interactions occur. On the other hand, the dissimilar key and the solvent demonstrate unfavorable molecular interactions, and the activity coefficient of this key increases. The positive deviations from Raoult s law are further enhanced by the diluting effect of the high-solvent concentration, and the value of the activity coefficient of this key may approach the infinite dilution value, often aveiy large number. 

The effect of solvent concentration on the activity coefficients of the key components is shown in Fig. 13-72 for the system methanol-acetone with either water or methylisopropylketone (MIPK) as solvent. For an initial-feed mixture of 50 mol % methanol and 50 mol % acetone (no solvent present), the ratio of activity coefficients of methanol and acetone is close to unity. With water as the solvent, the activity coefficient of the similar key (methanol) rises slightly as the solvent concentration increases, while the coefficient of acetone approaches the relatively large infinite-dilution value. With methylisopropylketone as the solvent, acetone is the similar key and its activity coefficient drops toward unity as the solvent concentration increases, while the activity coefficient of the methanol increases. 

GLC is a well-established and accurate method used to obtain and the partial molar excess enthalpies at infinite dilution values AHf" , which is determined from the Gibbs-Helmholtz equation ... 

For simplicity, let represent the infinite-dilution value of the fugacity coefficient of species 1 in solution. 

One can readily show that application of Eq. (11.11) regenerates the original equation for M. The infinite dilution values are given by ... 

In summary, it is the lower dielectric constants of the typical nonaqueous solvent that cause a far greater decrease in equivalent conductivity with an increase of concentration than that which takes place in typical aqueous solutions over a similar concentration range. Even if the infinite-dilution value A makes a nonaqueous electrochemical system look hopeful, the practically important values of the specific conductivity (i.e., the ones at real concentrations) are nearly always much less than those in the corresponding aqueous solution. That is another unfortunate aspect of nonaqueous solutions, to be added to the difficulty of keeping them free of water in ambient air. 

It is assumed that all the solute molecules in the sample contribute addi-tively and independently to the measured value of the solution property. This assumption can only be true in extremely dilute solution where the polymer molecules are not affected by each other s existence. Such solutions would have properties very close to those of pure solvent. It is intuitively evident that the conflicting requirements of independence of solute contributions and a magnitude of such contributions sufficient to outweigh experimental uncertainty can only be achieved by making measurements at low, but finite, concentrations and extrapolating these to infinite dilution values. 

Because the parameters of 2-parameter correlations of G data are directly related to infinite-dilution values of the activity coefficients, our primary interest in Eq. (14.59) is its application to binary systems at infinite dilution of one of tlie constituent species. For this purpose, we divide Eq. (14.59) by the product xixi- For Cp independent of T (and thus with... 

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