$(20\%)$ Table below presents the experimental VLE data for the isopropanol $(1)/$ benzene $(2)$ system at $45C.($a$)$ Plot the dew$-$and bubble point curves versus mole fraction of isopropanol. Calculate and plot versus $x_1$ on the same diagram the vapor$-$phase partial pressures $P_1$ and $P_2.$ Compare these curves with the bubble point and partial$-$pressure curves given by Raoult's law. $($b$)$ Derive values of $ln{}_1$ and $ln{}_2$ from the data and plot them against $x_1.$ Plot on the same graph the $\frac{G^E}{x_1}{x}_{2}RT$ curve, and show for comparison the $\frac{G^E}{x_1}{x}_{2}RT$ curve one would obtain from the two$-$parameter Margules equation if the constants were determined from experimental activity coefficients at infinite dilution.

$\backslash$table$[[x_1,y_1,\frac{P}{k}Pa,x_1,y_1,\frac{P}{k}Pa$