For the system methanol $(1)/$methyl acetate $(2),$ the following equations provide a

reasonable correlation for activity coefficients:

$ln{}_1=1\mathrm{.}1x_2^2,ln{}_2=1\mathrm{.}1x_1^2$

If $P_1^{\text{s}\text{a}\text{t}}=44\mathrm{.}5$kPa and $P_2^{\text{s}\text{a}\text{t}}=65\mathrm{.}6$kPa at $35C,$ determine:

$($a$)$ The bubble point pressure and vapor composition for $x_1=0\mathrm{.}25$

$($b$)$ The dew point pressure and liquid composition for $y_1=0\mathrm{.}20$

$($c$)$ The dew point temperature and liquid composition for $y_1=0\mathrm{.}20$ and $100$kPa