Determination of Activity Coefficients from Measured LLE Data for an Essentially Immiscible Mixture From the data in Volume III of the International Critical Tables (McGraw-Hill, New York, 1929) we see that the equilibrium state in the carbon tetrachloride–water system at 25°C is two phases: one an

Question

Determination of Activity Coefficients from Measured LLE Data for an Essentially Immiscible Mixture

From the data in Volume III of the International Critical Tables (McGraw-Hill, New York, 1929) we see that the equilibrium state in the carbon tetrachloride–water system at 25°C is two phases: one an aqueous phase containing 0.083 wt%carbon tetrachloride, and the other an organic phase containing 0.011 wt % water. Estimate the activity coefficient of [latex]CCl _{4}[/latex] in the aqueous phase and [latex]H _{2} O[/latex] in the organic phase.

Accepted Answer

Since the aqueous phase, which we designate as phase I, is 99.917 wt % water, it seems reasonable to assume that the activity coefficient of water in the aqueous phase is unity. Similarly, the activity coefficient of carbon tetrachloride in the organic phase will be taken to be unity. Therefore, from Eq. 11.2-2, we have

[latex]x_{ i }^{ I } \gamma_{ i }^{ I }\left(T, P, x^{ I } ight)=x_{ i }^{ II } \gamma_{ i }^{ II }\left(T, P, \underline{x}^{ II } ight)[/latex] (11.2-2)

[latex]\gamma_{ CCl _{4}}^{ I }=\frac{x_{ CCl _{4}}^{ I }}{x_{ CCl _{4}}^{ I }} \cong \frac{1}{x_{ CCl _{4}}^{ I }}[/latex]

[latex]\gamma_{ H _{2} O }^{ II }=\frac{x_{ H _{2} O }^{ I }}{x_{ H _{2} O }^{ II }} \cong \frac{1}{x_{ H _{2} O }^{ II }}[/latex]

where we have used the superscripts I and II to denote the aqueous and organic phases, respectively.

The first calculation to be done is the conversion of the weight fraction data to mole fractions. Since the organic phase is almost pure carbon tetrachloride and the aqueous phase is essentially pure water, either the equations in this illustration or Eq. 11.2-18 can be used to compute the activity coefficients of carbon tetrachloride inwater andwater in carbon tetrachloride. The results are given in the table.

[latex]1=x_{1}^{ II } \gamma_{1}^{ II } \quad ext { or } \quad x_{1}^{ II }=\frac{1}{\gamma_{1}^{ II }}[/latex] (11.2-18)

	[latex]x_{ CCl _{4}}[/latex]	[latex]x _{ H _{2} O }[/latex]	[latex]\gamma_{ CCl _{4}}[/latex]	[latex]\gamma_{ H _{2} O }[/latex]
Aqueous phase	[latex]0.9708 imes 10^{-4}[/latex]	0.9999	[latex]1.029 imes 10^{4}[/latex]	1 (assumed)
Organic phase	0.9991	[latex]0.9403 imes 10^{-3}[/latex]	1 (assumed)	[latex]1.063 imes 10^{3}[/latex]

Comment

The values of the activity coefficients here are very large, especially compared with those we found previously from vapor-liquid equilibrium data. Such values for the activity coefficient of the dilute species in a mixture with species of very different chemical nature, such as carbon tetrachloride and water, is quite common. Note that because of the concentrations involved, the activity coefficients found are essentially the values at infinite dilution.

Question 11.2.3: Determination of Activity Coefficients from Measured LLE Dat...

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