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.

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Boiler water and industrial water which are treated by ion exchange resin, contain sulfate and chloride as strong acidic salt and bicarbonate as weak acidic salt. Previously, we reported on Na⁺-H⁺ exchange equilibrium in the mixed solution of strong acidic salt and weak acidic salt.
The present work was carried out to study the rate of exchange reaction in the mixed solution of NaCl-CH₃COONa, and NaCl-HCOONa. The relation between H, height of exchange zone, and H. T. U. is given by Eq. (4). H was obtained by means of measuring the break-through curves of the solution. The values of H. T. U. decreased with β, equivalent fraction of strong acidic salt, and increased with Re. Correlating H. T. U. with Re and Sc as shown in Fig. 6, H. T. U. is expressed by Eq. (6). Fig. 7 shows the comparison between the values of the break-through capacity of resin bed obtained from experiments and the values calculated by means of Eqs. (6) and (7).

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This paper deals with an investigation into the plate efficiency of a sieve plate tower for stripping chlorine from return brine in soda-chlorine mercury cell process.
Experiments were made, varying the liquid flow rates from 1, 400 to 27, 000kg/m·hr and gas rates from 0.73 to 2.80cm/sec, in the G/L range of 0.000170.0025mol/mol.
To find out (L. T. U.)_ox, the following equation was derived on an assumption that the liquid and the gas come into contact with each other in a cross flow and that the liquid has constant composition in the direction perpendicular to the plate.
x_n-1-x_n/x_n-1-x_n+1^*=1-exp.{-lφ/(L. T. U.)_ox} (12)
As (L. T. U.)_ox' is independent of the gas rates when the latter is in the neighborhood of 2.8cm/sec, as shown in Fig. 3, it can be concluded that l_A shows the effective travelling length of the liquid and that (L. T. U.)_ox' is equal to (L. T. U.)_ox at this gas rate. The values of (L. T. U.)_ox are plotted against L' in Fig. 6 and the following correlation is obtained from the line drawn in this figure.
(L. T. U.)_ox=0.34·L'^0.6 (21)
As the gas rate is lower than 2.8cm/sec, (L. T. U.)_ox' is higher than (L. T. U.)_ox calculated by using Eq. (21). This deviation is due to the more ineffective travelling length of liquid at lower gas rates and is compensated by F which is defined by means of Eq. (17).
F=l_E/l_A (17)
F=(L. T. U.)_ox/(L. T. U.)_ox' (18)
F obtained by using Eq. (20) which has been derived from Eqs. (15), (16) and (17) is represented by the following empirical equations.
F=(0.0011×L')^-P (19)
P=0.11(u/u_c-u)^-1.29 (20)
From these results the author derived the optimum velues of φ and l_A at constant G/L which are explained by Eqs. (30) and (31), respectively.
P>0.4: ∂E_ML/∂φ>0
P<0.4: ∂E_ML/∂φ<0 (30)
For Maximum E_ML: d ln F/d ln l_A=-1 (31)
Eq. (30) shows that it is recommended to make φ as small as possible in case P<0.4 (corresponding to u>0.75cm/sec). Eq. (31) shows the maximum point of l_A-E_ML diagram shown in Fig. 8. l_Max can be derived by graphical method as shown in Fig. 9.

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The mixing mechanisms of solid particles by paddle-type impellers were studied for two pairs of dry powders, having the same particle size distribution, viz., sand-sodium chloride (3242 mesh) and sodium carbonate-polyvinyl chloride (100200 mesh). The degree of mixing was defined anew by Eq. (8) and the relations between the degree of mixing and the operating variables, such as impeller size, rotational speed etc. were determined as given by Eqs. (20) and (21).
By analogy with the process of diffusion, the apparent diffusivities from the concentration distribution of the two kinds of particles were evaluated. The relations between the apparent diffusivities and the operating variables were obtained by means of Eq. (22). Furthermore, the theoretical degree of mixing was given in terms of apparent diffusivities as in Eq. (18).
Introducing the obtained values of apparent diffusivities into Eq. (18) and comparing the theoretical degree of mixing with observed one, the authors found good agreement between both the values and concluded that in the case of mixing solid particles by paddle-type impellers, the diffusive mixing was quite conspicuous.

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