$C_{Ai}=(1\mathrm{.}03)(0\mathrm{.}1136)=0\mathrm{.}117$kmo$\frac{l}{m^2}$

$C_{Ab}=0($because of the small contact time, the depth of penetration of the solute in the jet will be small and the bulk liquid free from $H_{2}S)$

The given rate of absorption of $H_{2}S=4\mathrm{.}42{10}^{-4}\frac{g}{s}=(\frac{4\mathrm{.}42}{34}){10}^{-4}{10}^{-3},$ i$.$e$.1\mathrm{.}3{10}^{-8}$kmo$\frac{l}{s}.$

Using Eqs. $($i$)$ and $($ii$)$ and the given rate of absorption $[$note that $r=(\frac{Q}{}v{)}^{\frac{1}{2}}],$

$1\mathrm{.}3{10}^{-8}=2l\sqrt[\phantom{2}]{\frac{Q}{v}}*2\sqrt[\phantom{2}]{\frac{D_{AB}v}{l}}(0\mathrm{.}117-0)=4\sqrt[\phantom{2}]{D_{AB}(1\mathrm{.}32{10}^{-5})(0\mathrm{.}05)}(0\mathrm{.}117)$

$=>,D_{AB}=$

$[$Diffusivity of $H_{2}S$ in water at $25C$ reported in the literature $=1\mathrm{.}21{10}^{-9}\frac{m^2}{s}]$

EXAMPLE $3\mathrm{.}6($Gas absorption from bubbles$)$ A mixture of $50\%C{O}_2$ and $50\%N_2$ is bubbling through water in a laboratory column at $30C$ and $1$atm. The depth of water in the column is $30cm.$ A single$-$nozzle gas distributor is used. The gas flow rate is $15c{m}^3$ per minute and the bubbles are of $1cm$ diameter on the average. The bubble rise velocity is $20c\frac{m}{s}.$ Calculate the rate of absorption of carbon dioxide. The diffusivity of $C{O}_2$ in water is $2\mathrm{.}19{10}^{-5}c\frac{m^2}{s}.$ Henry's law can be used to calculate the solubility of $C{O}_2$ in water at the given temperature, $p=1860x^{**}(p=$ partial pressure of $C{O}_2,$ in atm; $x^{**}$ is its mole fraction in water at equilibrium$).$

Hints: Contact time of a liquid element with a gas bubble, $t_c=\frac{d_b}{v_b}=\frac{1cm}{20c\frac{m}{s}}=0\mathrm{.}05s$ Mass transfer coefficient, $k_L=2(\frac{D_{AB}}{}{t}_c{)}^{\frac{1}{2}}=0\mathrm{.}0236c\frac{m}{s}.$ Residence time of a single bubble in the liquid $=($liquid depth