EXAMPLE $4\mathrm{.}5($Graphical determination of interfacial concentrations$)$ The equilibrium solubility of $S{O}_2$ in water at $30C$ is given by Sherwood $[$Ind$.$ Eng. Chem., $17(1925)745]$

$\backslash$table$[[p_{S{O}_2},mmHg,0\mathrm{.}6,1\mathrm{.}7,4\mathrm{.}7,8\mathrm{.}1,11\mathrm{.}8,19\mathrm{.}7,36,52,79],[gS{O}_2$ per $100g{H}_{2}O,0\mathrm{.}02,0\mathrm{.}05,0\mathrm{.}10,0\mathrm{.}15,2\mathrm{.}0,0\mathrm{.}3,0\mathrm{.}5,0\mathrm{.}7,1\mathrm{.}0]]$

At a point in an absorption column operating at a total pressure of $4\mathrm{.}5$ bar, the bulk concentrations in the gas and the liquid$-$phases are $x=0\mathrm{.}0014$ and $y=0\mathrm{.}02.$ The individual gas$-$phase and liquid$-$phase mass transfer coefficients are $k_x=80$kmo$\frac{l}{h}(m^2)(x)$ and $k_y=15$kmo$\frac{l}{h}(m^2)(y).$

Calculate $($a$)$ the interfacial concentrations at the particular location, $($b$)$ the overall mass transfer coefficients and the rate of absorption$,($c$)$ the mass transfer coefficients $k_x^{\text{'}}$ and $k_y^{\text{'}},$ and $($d$)$ the individual and overall driving forces at the location in terms of $x$ and $C.$

What fraction of the total resistance is offered by the gas$-$film? What should have been the value of the coefficient $k_y,$ if the gas$-$phase offered $60\%$ of the total resistance to mass transfer $($for the given liquid$-$phase coefficient$)?$