$13\mathrm{.}20.$ For the acetone$(1)/$methanol$(2)$ system, a vapor mixture for which $z_1=0\mathrm{.}25$ and $z_2=0\mathrm{.}75$ is cooled to temperature $T$ in the two$-$

phase region and flows into a separation chamber at a pressure of $1$ bar. If the composition of the liquid product is to be $x_1=$

$0\mathrm{.}175,$ what is the required value of $T,$ and what is the value of $y_1?$ For liquid mixtures of this system, to a good approximation,

$ln{}_1=0\mathrm{.}64x_2^2$ and $ln{}_2=0\mathrm{.}64x_1^2.$