Chapter 13, Problem 13.37P

VLE data for methyl tert-butyl ether(1)/dichloromethane(2) at 308.15 K are as follows:

Extracted from F. A. Mato, C. Bcrru. and A. Pcncloux, J. Cheni. Eng. Data. Vol. 36, pp. 259-262. 1991.

The data are well correlated by the three-parameter Margules equation [an extension of Eq. (13.39)]:

$\frac{G^E}{RT}=\left(A_{21}{x}_1+A_{12}{x}_2-C{x}_1{x}_2\right)x_1{x}_2$

Implied by this equation are the expressions:

$In{\gamma }_1=x_2^2\left[A_{12}+2\left(A_{21}-A_{12}-C\right)x_1+3C{x}_1^2\right]$

$In{\gamma }_2=x_1^2\left[A_{12}+2\left(A_{12}-A_{21}-C\right)x_2+3C{x}_2^2\right]$

1. Basing calculations on Eq. (13.24), find the values of parameters Aj₂, A₂|. and C that provide the best fit of G^E/RT to the data.
2. Prepare a plot of In ${\gamma }_1$ In ${\gamma }_2$ , and $\begin{array}{l}\\ G^E/\left(x_1{x}_{2}RT\right)\end{array}$ vs. $x_1$ showing both the correlation and experimental values.
3. Prepare a Pxy diagram [see Fig. 13.8(a)] that compares the experimental data with the correlation determined in (a).
4. Prepare a consistency-test diagram like Fig. 13.9.
5. Using Barker’s method, find the values of parameters A₁₂. A₂₁, and C that provide the best fit of the P-x₁data. Prepare a diagram showing the residuals $\delta P$ and $\delta y_1$ plotted vs. x₁

Figure 13.8: The diethyl ketone(l)/n-hexane(2) system at 65°C. (a) Pxy data and their correlations.