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

\[ \begin{aligned} \ln \gamma_{1} & =A x_{2}^{2} \quad \text { and } \quad \ln \gamma_{2}=A x_{1}^{2} \\ A & =2.771-0.00523 T \end{aligned} \]

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

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

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

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