$(1)$ For the system ethyl acetate $(1)/$n$-$heptane $(2)$ at $343\mathrm{.}15K,ln{}_1=0\mathrm{.}95(x_1{)}^2$ and $ln{}_2=0\mathrm{.}95(x_1{)}^2$;$P_1^{\text{s}\text{a}\text{t}}=79\mathrm{.}80$kPa; and $P_2^{\text{s}\text{a}\text{t}}=40\mathrm{.}50$kPa.

$($a$)$ Determine the bubble point $P$ for $T=343\mathrm{.}15K,x_1=0\mathrm{.}05.$

$($b$)$ Determine the dew point $P$ for $T=343\mathrm{.}15K,y_1=0\mathrm{.}05.$

$($c$)$ What are the azeotrope composition and pressure at $T=343\mathrm{.}15K?$