In a batch distillation column, a mixture containing $60\%$ benzene and $40\%$ toluene is being separated. The column operates at vapor$-$liquid equilibrium, where the liquid phase is predominant. The relative volatility of benzene to toluene is $2\mathrm{.}6.$ a$)$ Determine the change in the amount of liquid in the tank over time. b$)$ If the product rate is constant at $0\mathrm{.}05$ mol$/$s$,$ calculate the time required for the benzene composition in the tank to reach $95\%.$