$3\mathrm{.}11.$ At $80C,$ vapor pressure of pure A and pure $B$ is $100$mmHg and $600mmHg,$ respectively.

a$)$ Draw a diagram "pressure$-$ liquid composition" $(P-x)$ of the ideal solution of A$-$B$.$

b$)$ A solution containing $40\%$molB into is put into a closed vessel and there is $\frac{1}{3}$ total mole of solution evaporated. Determine the composition of liquid and vapor phase at the equilibrium.