EXAMPLE $2\mathrm{.}7($Non$-$equimolar counterdiffusion in distillation of a binary mixture$)$ An aqueous solution of methanol is being separated by distillation in a column. Methanol $(A),$ which is the more volatile component, moves from the liquid phase to the vapour phase while water $(B),$ the less volatile component, gets transported in the opposite direction. At a section of the column, the vapour phase contains $0\mathrm{.}76$ mole fraction methanol and the liquid has $0\mathrm{.}6$ mole fraction of it$.$ The temperature is $71\mathrm{.}2C$ and the total pressure is essentially atmospheric. The diffusional resistance offered is equivalent to that of a 'stagnant' vapour film of $1mm$ thickness. If the latent heat of vaporization of methanol is $274\mathrm{.}6$kca$\frac{l}{k}g$ and that of water is $557\mathrm{.}7$kca$\frac{l}{k}g$ at the given temperature, calculate the flux of methanol and that of water vapour. Given: if the mole fraction of methanol in the solution is $0\mathrm{.}6,$ its mole fraction in the equilibrium vapour would be $0\mathrm{.}825.$ The vapour$-$phase mutual diffusivity, $D_{AB}=1\mathrm{.}816{10}^{-5}\frac{m^2}{s}.$