A distillation column with two equilibrium stages and a partial reboiler $($three equilibrium contacts$)$ is separating methanol and water. The column has a total condenser. Feed, a $45$ mol$\%$ methanol mixture, enters the column on the second stage below the condenser. Feed rate is $150$ mol$/$h$.$ The feed is a subcooled liquid. To heat $2$ moles of feed to the saturated liquid temperature, $1$ mole of vapor must condense at the feed stage. A distillate concentration of $80$ mol$\%$ methanol is desired. Reflux is a saturated liquid, and CMO can be assumed. An external reflux ratio of L$/$D $=2\mathrm{.}0$ is used. Find the resulting bottoms concentration xB$.$ Data are in Table $2-7.$ Explain step by step, the trial and error method