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Diffusivities in the ethanol-water system : the applicability of the diaphragm cell method to the case of systems where volume changes occur on mixing Dullien, Francis Andrew Leslie

Abstract

Smith and Storrow [J. Appl. Chem. (London) 2: 225, (1952)] and Hammond and Stokes [Trans. Faraday Soc. 40: 890, (1953)], using their individual modifications of the diaphragm-cell method for measuring liquid diffusivities, reported diffusion coefficients on the ethanol-water system that disagreed by as much as 100 per cent. It was apparently in view of this disagreement that Johnson and Babb gave a very reserved summary opinion on the diaphragm-cell method in a comprehensive review article [Chem. Rev. 56: 387, (1956)]. In the present work a diaphragm cell was designed which, unlike prior designs, is suitable for use with practically all organic liquids. A compact machine, accommodating and stirring a battery of six such cells, was designed and used. The precision of the cell constant determinations, using aqueous KC1 solutions, was ± 0.1%, a scatter completely accounted for by the errors arising from a standard gravimetric analysis of the solutions which, in this case, was improved in accuracy by one order of magnitude over hitherto reported analyses. Using this apparatus, the diffusivity results obtained by Hammond and Stokes were confirmed within the accuracy of the ethanol-water measurements (± 2%). Critical experiments on an apparatus similar to that used by Smith and Storrow revealed that there was a possibility of distillation through a wetted ground glass joint from the one solution into the other. The apparent higher diffusivities obtained by these authors were attributed to this phenomenon. Detailed derivation of the general equation of diffusion, using the methods of the thermodynamics of irreversible processes, and discussion of the question of the various frames of references and the various diffusivities defined by some authors is given. Using the general equation of diffusion in a binary system new formulae which apply regardless of volume changes on mixing were derived for use with the diaphragm cell method. It was shown that, in the case where the density of the solution is linear in the volume concentration, the general equation of diffusion reduces to Fick's first law and the various formulae based upon the general equation reduce to the corresponding simple formulae. The trial-and-error procedure used with electrolytes by R. H. Stokes was generalized and used to compute the true differential diffusivities from the measured integral values and it was shown that, contrary to the contention of Stokes, this type of procedure is applicable in the case of systems where the limiting values of the diffusivity are not known and the diffusivity changes strongly with concentration. Also, an alternate procedure, based on the differentiation of the integral diffusivities, is suggested. It was noted that the minimum of the diffusivity-concentration curve and that of the relative volume decrease-concentration curve, and the maximum of the viscosity-concentration curve are at a composition corresponding to one molecule of ethanol and three molecules of water. This coincidence may be evidence for the existence of a molecular complex. It was found that the activity-based diffusivity is practically constant over some 70% of the composition range.

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