A column with a packing material of $0\mathrm{.}4$ m diameter is used to clean a soluble gas $($with molecular weight, MB$=22)$ from an air$-$air mixture. Pure water enters from the top of the column with a mass flow rate of $450$ kg$/$hr$.$ The incoming gas stream contains $5\%$ soluble gas and $95\%$ air. $95\%$ of the soluble gas is removed. The operating line and the equilibrium curve are assumed to be straight lines. The equation for the equilibrium curve is y $=1\mathrm{.}2$x$,$ where x and y are the mole fractions in the liquid and gas phases, respectively. The feed rate of the incoming gas mixture is $350$ kg$/$hr$.$ Calculate: $($a$)$ The concentration of the soluble gas in the exiting liquid when the column operates at minimum flow rate. $($b$)$ The concentration of the soluble gas at a point in the column where y$=0\mathrm{.}02$