Partial molal volumes evaluation

The preceding derivations are given in more detail by Marek and Standart (5) and are applied by Marek (4) to several binary systems. The terms and 02 are evaluated from partial molal volume data or approximated from generalized correlations. According to Marek and Standart, the products and T2y2 must satisfy all criteria of thermodynamic consistency, as should yi and y2 for nonassociating systems. 

Eckert, C. A., D. H. Ziger, K. P. Johnston, and T. K. Ellison. 1983. The use of partial molal volume data to evaluate equations of state for supercritical fluid mixtures. J. Fluid Phase Equilib. 14 167. 

Density measurements, like solubilities, have also frequently been obtained for purposes other than calculating thermodynamic properties, and consequently many of these are not useful for evaluating partial molal volumes. There are, however, some excellent recent measurements in this area which have been used to evaluate partial molal volumes. Since Millero has thoroughly examined all volume data for electrolytes in both aqueous and non-aqueous solutions in a recent review, only some of the more interesting results, from a structural point of view, will be included here. 

Evaluation of partial molal volumes of electrolytes, and in particular the standard partial molal volume, Fg, is similar to the determination of partial molal heat capacities. As in the case of heat capacities, the apparent molal quantity is of interest. Corresponding to eqns. 2.3.52, 2.3.54 and 2.3.55 we have... 

Although density measurements of varying degrees of accuracy have been reported for ethanolic solutions, standard state partial molal volumes in ethanol have been evaluated for only a few electrolytes. Vosburgh, Connell and Butler reported for LiCl in water and a series of alcohols, including ethanol. They observed that the salt had a much smaller value of F in the alcohols than in water, and that for all the systems studied it was smallest in ethanol. Sobkowski and Mine have reported for HCl in water and the three lower alcohols and also observe F to be smaller in the alcohols than in water, but it is smallest in methanol rather than ethanol. Lee and Hyne have reported F° at 50.25°C for the tetraalkylammonium chlorides in ethanol-water mixtures up to 0.4 mol fraction of ethanol. With the tetramethyl and tetraethyl salts, the volumes are all very positive in water but decrease rapidly with an increase in alcohol content and appear to be at a minimum around 0.3 to 0.4 mol fraction of ethanol. The higher tetraalkyl salts are not entirely consistent with this pattern. 

The division of partial molal volumes into their absolute ionic components presents the same problems as the division of other thermodynamic properties in that non-thermodynamic arguments must be invoked. Millero has reviewed the the various methods of making this division for aqueous solutions and has summarised the corresponding values. Most of the methods yield values falling in the range of 0 to —5cm mol. From a critical evaluation of the data, Millero suggests that a of close to — S.Ocm mol" at 25°C is the best value. 

The apparent molar volume is given as a function of one of the composition variables. The methods of evaluating the partial derivatives in Equations (6.55) and (6.56) are identical to those discussed in Section 6.3. The final expressions for the partial molar volumes of the two components in terms of the molality are... 

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