Analytical expressions of the second and third virial coefficients obtained by vapor pressure osmometry were derived rigorously on the basis of the theory of KAMIDE and SANADA, previously developed. The apparent second virial coefficient A2,v′ in the following relation: is given by with where T and T0 represent temperature of a solution drop and a solvent drop, respectively, suffix s means that the measurements are made in the steady state, Ks a calibration parameter, ca initial concentration, M1 the molecular weight of solute, A2,0 and A3,0 the osmotic second and third virial coefficients, V0 the molar volume of solvent, R gas constant, ΔH the heat of condensation of solvent, k(t) a correction parameter due to a dilution effect, t time of measurement. Unexpectedly, A2,v′ differs significantly from A2,0, even if dilution effect can be neglected (i.e., k(t) = 0) for solute having M1 < 2ċ103, unless Ks/Ke = 1/{1 + (2 RT0/ΔH)1/2}. The numerical calculations and analysis of the experimental data show that the second term in the right‐hand side of the second equation approaches zero when M1 becomes larger than (105/2)1/2V01/2. However, the third term due to a dilution effect can not be ignored if M1 < 104.
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Kamide et al. (1970) studied this question.