$(PO2,CO2,C4)$

In a gas$-$liquid separator, the gas and liquid phases are in equilibrium. The gas mixture which consists of $20$ mol$\%$ n$-$heptane $(n-C_7{H}_{16}),35$mol$\%n-$pentane $)$ and the balance toluene $(C_7{H}_8),$ is in equilibrium with the liquid mixture at $100C$ and system pressure of $1$atm. Using the Antoine equation constant and Raoult's law relationship, determine the partial pressure of each components and the composition of the liquid mixture $(x).$ If the volume of the gas mixture is $10L_{?},$ determine the total mole of the gas mixture when it behaves as an ideal gas.

Raoult's law: $p_A=y_{A}p=x_A{p}_A^{**}(T)$

$(14$ marks$)$