Q$3)$

An absorption column, operating at $4\mathrm{.}5$ bar and $30C,$ is applied to separate $S{O}_2($A$)$ from air $($B$)$ using water as an absorbent$.$ At a particular point in the column, the bulk concentrations of $A$ in the gas and liquid phases are $y_{AG}=0\mathrm{.}02$ and $x_{AL}=0\mathrm{.}0014,$ respectively.

The individual gas$-$phase and liquid$-$phase mass transfer coefficients are $k_y=15$kmo$\frac{l}{hr}(m^2)(y)$ and $k_x=80$kmo$\frac{l}{hr}(m^2)(x),$ respectively.

The equilibrium solubilities of $S{O}_2$ in water are given in Table Q$3.$

$\backslash$table$[[p_{sO\text{:}},mmHg,0\mathrm{.}6,1\mathrm{.}7,4\mathrm{.}7,8\mathrm{.}1,11\mathrm{.}8,19\mathrm{.}7,36,52,79],[gS{O}_2$ per $100g{H}_{2}O,0\mathrm{.}02,0\mathrm{.}05,0\mathrm{.}1,0\mathrm{.}15,0\mathrm{.}2,0\mathrm{.}3,0\mathrm{.}5,0\mathrm{.}7,1\mathrm{.}0]]$

Given: Molecular weight of $S{O}_2$ and $H_{2}O$ are $64$ and $18\frac{g}{g}$mol, respectively; Calculate:

i$-$ The interfacial concentrations $(x_A$ and $y_{Ai})$ at the particular location.

ii$-$ The overall mass transfer coefficients $K_y$ and $K_x$ and the rate of absorption $N_A.$