The vapour pressure of the mixture of benzene $($b$)$ and toluene $($t$)$ at $100CK$ are $150$kPa and $75$ kPa, respectively. Experiments performed in the lab generated binary liquid$-$vapour equilibria phase data of the mixture at $750$torr, the data is presented below.

$x_{\text{t}\text{o}\text{l}\text{u}\text{e}\text{n}\text{e}},y_{\text{t}\text{o}\text{l}\text{u}\text{e}\text{n}\text{e}}$

a$)$ Using the data determine the equilibrium $($xb$,xt,yb,yt$ between liquid and vapour phases of a solution at $100C.$

b$)$ Use the information to calculate the activities and activity coefficients of both components in this solution on the Raoult's law basis.