For the system that consists of species $1$ and $2,$ provide a reasonable correlation for the activit coefficients:

$ln{}_1=(0\mathrm{.}273+0\mathrm{.}096x_1)x_2^2$

$ln{}_2=(0\mathrm{.}273-0\mathrm{.}096x_2)x_1^2$

In addition, the vapor pressures at temperature $T$ :

$P_1^{\text{s}\text{a}\text{t}}=101\mathrm{.}05$kPa and $P_2^{\text{s}\text{a}\text{t}}=38\mathrm{.}83$kPa

The overall mole fraction of species $1$ in the system is $z_l=0\mathrm{.}44.$ Assuming the validity of Modified Raoult's Law, calculate:

$($a$)$ Over what range of pressures can the system exist in two phases under current conditions $(T,z_1)?$

$($b$)$ Does the system form an azeotrope at given conditions?