The absorption of hydrogen sulfide in monoethanolamine $($MEA$)$ is coupled with an extremely

fast reaction. It is desired to reduce the content of $H_{2}S$ from $1\%$ to $1ppm$ by absorption in a

water solution of MEA, $250mol{m}^{-3}.$ The reaction is irreversible and its stoichiometry is:

$H_{2}S+HOC{H}_{2}C{H}_{2}N{H}_{2}H{S}^{-}+HOC{H}_{2}C{H}_{2}N{H}_3^{+}.$

The absorption is carried out in a filler tower, in which ideal plug flow is considered to prevail

in both the gas and liquid phases. The phases flow counter$-$currently and the gas enters from

the bottom. What height should the reactor be to obtain the desired conversion?

The following data are available:

$G=30molm{m}^{-2}{s}^{-1}$;

$\frac{G}{L}=0\mathrm{.}1$;

$k_{La}(H_2(S))=0\mathrm{.}03s^{-1}$;

$k_{g}a=6{10}^{-4}mol{m}^{-3}{s}^{-1}P{a}^{-1}$;

$(D_{H2s}{)}_L=1\mathrm{.}5{10}^{-9}{m}^2{s}^{-1}$;

$(D_{\text{M}\text{E}\text{A}}{)}_L=1{10}^{-9}{m}^2{s}^{-1}$;

$He=11\mathrm{.}5m^{3}Pamo{l}^{-1}$;

$P=2$MPa;

$C_T=55kmol{m}^{-3}$