$13\mathrm{.}47.$ For one of the binary systems listed in Table $13\mathrm{.}10,$ based on Eq$.(13\mathrm{.}19)$ and the Wilson equation, make the following calculations:

$($a$)$ BUBL P: $t=60C,x_1=0\mathrm{.}3.$

$($b$)$ DEWP:$t=60C,y_1=0\mathrm{.}3.$

$($c$)P,T-$ flash: $t=60C,P=\frac{1}{2}(P_{\text{b}\text{u}\text{b}\text{b}\text{l}\text{e}}+P_{\text{d}\text{e}\text{w}}),z_1=0\mathrm{.}3.$

$($d$)$ If an azeotrope exists at $t=60C,$ find $P^{az}$ and $x_1^{az}=y_1^{az}.$

Table $13\mathrm{.}10$: Parameter Values for the Wilson and NRTL Equations

Parameters $a_{12},a_{21},b_{12},$ and $b_{21}$ have units of cal. $*mo{l}^{-1},$ and $V_1$ and $V_2$ have units of $c{m}^3*mo{l}^{-1}.$

$\backslash$table$[[,V_1,$Wilson Equation,NRTL Equation$],[$System$,V_2,a_{12},a_{21},b_{12},b_{21},$