On the Evaluation of the Second Virial Coefficient and Activity in Dilute Solution by Vapor Pressure Osmometry

Abstract

Summary The possibility of evaluating the second virial coefficient for dilute solution by use of vapor pressure osmometry was studied on the basis of the steady state theory established in the previous paper (K. Kamide et al.: The Chemistry of High Polymers, Japan 24, 751 (1967)). Except for the case where heat transfer other than condensation could be completely ignored, the apparent second virial coefficint A “2, vobtained from concentration dependency of steady state values of temperature difference does not generally agree with the second virial coefficient A2, o derived from the osmometry, but there holds a relation between A” 2, vand A2, o, as shown below:_??_where_??_V0: molar volume of solvent, M1: molecular weight of solute, ΔH: heat of condensation of solvent vapor, R: gas constant, T0: temperature of solvent drop, k1and k2: coefficients of heat transfer at the interfaces between vapor-solution and between solution-ther-mistor, respectively, k3: coefficient of material transfer between vapor-solution, A1: surface area of solution drop, A2: surface area of thermistor in contact with solution. When the molecular weight of solute is up to 104, the third term on the right-hand-side of the above formula is larger than or equal to A2, o. If the apparent second virial coefficient A “2, v is evaluated by ignoring concentration changes caused by condensation of solvent and by approximating steady state concentration with initial one, the result does not agree with true A” 2, v so far as the molecular weight of solute is smaller than 104. In practice, heat transfer other than condensation is by no means ignorable, and the maximal measurable molecular weight through the vapor pressure osmometry is about 104. Accordingly, it is actually impossible to appreciate A2, o exactly by use of the latter method. On the other hand, solvent activity in solution can be determined exactly through the vapor pressure osmometry.The theoretical prediction given in the above was ascertained by the experimental results for benzene solution of m-terphenyl and by the values for other solutions of low molecular weight compounds found in the literature.