For the system methanol (1)-methyl acetate (2), the activity coefficients for components 1 and 2 are represented by

\[ \ln \gamma_{1}=A x_{2}^{2} \quad \text { and } \quad \ln \gamma_{2}=A x_{1}^{2} \]

where

\[ A=2.771-0.00523 T \]

The vapour pressures of the components are given by the Antoine equations

\[ \ln P_{1}^{\text {Sat }}=16.5915-\frac{3,643.31}{T-33.424} \quad \text { and } \quad \ln P_{2}^{\text {Sat }}=14.2532-\frac{2,665.54}{T-53.424} \]

where \(P\) is in \(\mathrm{KPa}\) and \(T\) in \(\mathrm{K}\). Calculate

(a) \(P\) and \(y_{i}\) at \(T=318.15 \mathrm{~K}\) and \(x_{1}=0.25\)

(b) \(P\) and \(x_{i}\) at \(T=318.15 \mathrm{~K}\) and \(y_{1}=0.60\)

(c) \(T\) and \(y_{i}\) at \(P=101.33 \mathrm{KPa}\) and \(x_{1}=0.85\)

(d) \(T\) and \(x_{i}\) at \(P=101.33 \mathrm{KPa}\) and \(x_{1}=0.40\)