A reactor contains toluene $(1)$ at $50C$ and is connected to a nitrogen$(2)$ cylinder to purge vapor

from the reaction vessel. Consider that the pressure in the reactor is $0\mathrm{.}50\mathrm{.}5$MPa. Assuming that

the solubility of nitrogen in the toluene is small enough for the liquid phase to be considered

pure toluene, calculate the mole fraction of the toluene in the vapor phase.

Data: $V_1^L=109\mathrm{.}6c{m}^3*mo{l}^{-1}$;$P_1^{\text{s}\text{a}\text{t}}=0\mathrm{.}0132$MPa;$B_{11}=-1880c{m}^3*mo{l}^{-1}$;$B_{22}=-1\mathrm{.}6c{m}^3*mo{l}^{-1}$

and $B_{12}=-150c{m}^3*mo{l}^{-1}.$