Fundamental questions about entropy II. The combinatorial entropy of mixing in liquids
P. Huyskens, G. G. Siegel · Bulletin des Sociétés Chimiques Belges · 1988
Abstract In liquid mixtures a molecule A is separated on the average from the nearest molecule of the same kind by XA−1/2 −1 molecules of a different kind, according to the relation of Einstein and Smoluchowski. In this direction (between a molecule and its nearest neighbour of the same kind) which continuously changes but which has a physical meaning, there exist thus XA−1/2 standardized possibilities of exchange with the other molecules. This is a characteristic of the stationary wave function of each A molecule in the liquid and intervenes in the counting of the standardized possibilities . In this direction the number of places available for one A can thus be calibrated by molecules of a different kind. In the other directions the places in the standardized domain A> have to be calibrated by the volume of A itself. This leads to a value of XA−1/2 ϕA−1/2 for Acomb>, the standardized number of places available for one A in the mixture. The combinatorial entropy of mixing derived from this value is intermediate between the Flory‐Huggins expression and the classical one. Experimental evidence for the correctness of this new equation can be found in the predicted solubilities of solid n‐alkanes in liquid n‐alkanes.