QUESTION $4$

The binary VLE system $CC{l}_4(1)+$ EtOH $(2)[$carbon tetrachloride $-$ ethanol$]$ forms an azeotrope at $P=101\mathrm{.}3$

kPa,$T=64\mathrm{.}95C,x_1=0\mathrm{.}613.$ At this temperature the vapour pressure of the two components are $P_1^{\text{s}\text{a}\text{t}}=70\mathrm{.}78$

kPa and $P_2^{\text{s}\text{a}\text{t}}=59\mathrm{.}84$kPa.

Assuming that the system obeys the Van Laar equations, calculate the pressure at which a CC$14-$EtOH liquid

mixture containing a $CC{l}_4$ mole fraction of $x_1=0\mathrm{.}5$ would boil at $64\mathrm{.}95C.$

State any assumptions needed to solve the problem with the given data.

The Van Laar equations are:

$ln{}_1=\frac{A}{[1+\frac{A{x}_1}{B{x}_2}{]}^2}$

$ln{}_2=\frac{B}{[1+\frac{B{x}_2}{A{x}_1}{]}^2}$

$A=ln{}_1[1+\frac{x_{2}ln{}_2}{x_{1}ln{}_1}{]}^2$

$B=ln{}_2[1+\frac{x_{1}ln{}_1}{x_{2}ln{}_2}{]}^2$