The vapour pressure of acetone, acetonitrile and nitromethane can be represented by Antoine equations as

\[ \begin{aligned} & \ln P_{1}^{\text {Sat }}=14.3916-\frac{2795.82}{T+230.0} \\ & \ln P_{2}^{\text {Sat }}=14.2724-\frac{2945.47}{T+224.0} \end{aligned} \]

and

\[ \ln P_{3}^{\text {Sat }}=14.2043-\frac{2972.64}{T+209.0} \]

where \(P_{1}^{\text {Sat }}, P_{2}^{\text {Sat }}\) and \(P_{3}^{\text {Sat }}\) are in \(\mathrm{kPa}\) and \(T\) is in \({ }^{\circ} \mathrm{C}\).

Assuming that the system follows Raoult's law, calculate:

(a) \(P\) and \(y_{1}\) at \(T=75^{\circ} \mathrm{C}, x_{1}=0.30, x_{2}=0.40\)

(b) \(P\) and \(x_{1}\) at \(T=80^{\circ} \mathrm{C}, y_{1}=0.45, y_{2}=0.35\).