For the system ethyl ethanoate$(1)/$ n$-$heptane$(2)$ at $343\mathrm{.}15K,$

$P_1^{\text{s}\text{a}\text{t}}=79\mathrm{.}8$kPa,$P_2^{\text{s}\text{a}\text{t}}=40\mathrm{.}5$kPa,$\frac{G_E}{R}T=0\mathrm{.}95x_1{x}_2$

At this temperature,

a$)$ Estimate the bubble pressure and value of $y_1$ when $x_1=0\mathrm{.}5$

b$)$ Estimate the dew pressure and value of $x_1$ when $y_1=0\mathrm{.}5$

c$)$ What is the azeotrope composition and pressure?

State and justify any assumption you make on the behavior of the vapor and liquid phases.