Predictions from Binary Constants of Vapor-Liquid Equilibria in Multicomponent Systems

Yamada I., Yoshida T., Haruyama S.

doi:10.1252/kakoronbunshu1953.25.158

Assuming triangular configurations of molecules in a liquid phase and the zeroth approximation for the calculation of the same configurations, the authors have obtained vapor-liquid equilibrium relations in multicomponent systems. The final result obtained with respect to γ_i is as follows: RTlnγ_i={2x_i(1-x_i)Σ_jx_jω_ijj+(1-2x_i)Σ_jx_j²ω_ijj+2(1-2x_i)Σ_jkx_jx_kω_ijk-2Σ_jkx_j²x_kω_jjk-4Σ_jklx_jx_kx_lω_jkl} (i≠j, k, l j≠k, l k≠l) (10) where ω_iij and ω_ijj are binary constants which are determined by components i and j, and ω_ijk is a ternary constant determined by components i, j and k. Then, Eq. (10) becomes similar to Margules' formula of type 3-suffix, which can be transformed into A_j-i=ω_iij/2.303RT and (A_j-i+A_i-k+A_k-j-C_ijk)=2ω_ijk/2.303RT. As the experimental determination of a ternary constant ω_ijk is very much complicated, the authors propose to introduce the following relation into binary constants, as a matter of convenience. ω_ijk=1/4(ω_iij+ω_ijj+ω_jjk+ω_jkk+ω_kki+ω_kii) (14) Consequently, from Eqs. (10) and (14), vapor-liquid equilibrium relations in multicomponent systems can be expressed by binary relations. As shown in Tables 7 and 8, in Methylethylketone-n-Heptane-Toluene and n-Heptane-cyclohexane toluene systems, the values of y and T, as calculated for x_i and ω_iij to be obtained for each binary system, approximately “agree with” the experimental results. At an azeotropic point, the following relation can be given, -ω_iijΔS_j^-1≤T_i⁰-T_j⁰≤ω_ijjΔS_i^-1 (20) Hence, in the case of multiazeotropes, the same relation as expressed by Eq. (20) should be established for all the combinations comprising n components. Therefore, the conditions of the azeotropic formation in multicomponent systems can be expressed by the binary constants.

Predictions from Binary Constants of Vapor-Liquid Equilibria in Multicomponent Systems

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