The Entropy of Solution of Molecules of Different Size

The entropy of mixing two liquids whose molecules differ in size is expressed in terms which avoid the assumption of a lattice as an artificial frame of reference, and which is not limited to linear polymers. The equation obtained is ΔSR=N1lnV−N1b1−N2b2N1(v1−b1)+N2lnV−N1b1−N2b2N2(v2−b2),where N1 and N2 denote number of moles, V the volume of the solution, v1 and v2 the molal volumes of the pure components and b1 and b2 the sum of the actual geometrical volumes of 6×1023 molecules. With certain simplifying assumptions, equivalent to those used by authors who have analyzed the problem for linear polymers in a lattice frame of reference, the above equation reduces to the form obtained by the latter method. Various methods of obtaining experimental values for b are outlined.