Lewis, Gilliland, Chertow, and Hoffman [J. Am. Chem. Soc., 72, 1153-1157 (1950)] measured adsorption equilibria for pure propane, pure propylene, and binary mixtures thereof, on activated carbon and silica gel. Adsorbate capacity was high on carbon, but selectivity was poor. Selectivity was high on silica gel, but capacity was low. For silica gel $\left(751 \mathrm{~m}^{2} / \mathrm{g}\right)$, the following pure component data were obtained at $25^{\circ} \mathrm{C}$ :
$$
\begin{array}{rcrc}
\text { P, torr } & q, \mathrm{mmol} / \mathrm{g} & \text { P, torr } & q, \mathrm{mmol} / \mathrm{g} \\
\hline 11.1 & 0.0564 & 34.2 & 0.3738 \\
25.0 & 0.1252 & 71.4 & 0.7227 \\
43.5 & 0.1980 & 91.6 & 0.7472 \\
71.4 & 0.2986 & 194.3 & 1.129 \\
100.0 & 0.3850 & 198.3 & 1.168 \\
158.9 & 0.5441 & 271.5 & 1.401 \\
227.5 & 0.7020 & 353.2 & 1.562 \\
304.2 & 0.843 & 550.7 & 1.918 \\
387.0 & 1.010 & 555.2 & 1.928 \\
468.0 & 1.138 & 760.6 & 2.184 \\
569.0 & 1.288 & & \\
677.8 & 1.434 & & \\
775.0 & 1.562 & &
\end{array}
$$
The following mixture data were measured at $25^{\circ} \mathrm{C}$, over a pressure range of 752-773 torr:
$$
\begin{array}{cccc}
\begin{array}{c}
\text { Total } \\
\text { Pressure, } \\
\text { torr }
\end{array} & \begin{array}{c}
\text { Millimoles } \\
\text { of Mixture } \\
\text { Adsorbed/g }
\end{array} & \begin{array}{c}
y_{\mathrm{C}_{3}}, \text { Mole } \\
\text { Fraction in } \\
\text { Gas Phase }
\end{array} & \begin{array}{c}
x_{\mathrm{C}_{3}}, \text { Mole } \\
\text { Fraction in } \\
\text { Adsorbate }
\end{array} \\
\hline 769.2 & 2.197 & 0.2445 & 0.1078 \\
760.9 & 2.013 & 0.299 & 0.2576 \\
767.8 & 2.052 & 0.4040 & 0.2956 \\
761.0 & 2.041 & 0.530 & 0.2816 \\
753.6 & 1.963 & 0.5333 & 0.3655 \\
766.3 & 1.967 & 0.5356 & 0.3120 \\
754.0 & 1.974 & 0.6140 & 0.3591 \\
753.6 & 1.851 & 0.6220 & 0.5550 \\
754.0 & 1.701 & 0.6252 & 0.7007 \\
760.0 & 1.686 & 0.7480 & 0.723 \\
- & 2.180 & 0.671 & 0.096 \\
760.0 & 1.993 & 0.8964 & 0.253 \\
760.0 & 1.426 & 0.921 & 0.401
\end{array}
$$
(a) Fit the pure component data to Freundlich and Langmuir isotherms. Which gives the best fit? Which component is most strongly adsorbed?
(b) Use the results of the Langmuir fits in part (a) to predict binarymixture adsorption using the extended Langmuir equation, (15-32). Are the predictions adequate?
(c) Ignoring the pure-component data, fit the binary-mixture data to the extended Langmuir equation, (15-32). Is the fit better than that obtained in part (b)?
(d) Ignoring the pure-component data, fit the binary mixture data to the extended Langmuir-Freundlich equation, (15-33). Is the fit adequate? Is the fit better than that in part (c)?
(e) For the binary-mixture data, compute the relative selectivity,
$$
\alpha_{C_{3}, C_{3}^{-}}=y_{C_{3}}\left(1-x_{C_{3}}\right) /\left[x_{C_{3}}\left(1-y_{C_{3}}\right)\right]
$$
for each condition. Does $\alpha$ vary widely or is the assumption of constant $\alpha$ reasonable?