$(40$ pts$)$

Q$2)1000$kmo$\frac{l}{h}$ of hydrocarbon gas at $70F$ with the following tabulated data is to be absorbed by $500$kmo$\frac{l}{h}$ solvent of $n-C_{10}{H}_{22}$ at $90F$ absorber operating at $4$atm

$\backslash$table$[[$Component$,$Composition, mol$\%,$K value$],[C{H}_4,25,38],[C_2{H}_6,15,7\mathrm{.}6],[C_3{H}_8,25,2\mathrm{.}25],[n-C_4{H}_{10},20,0\mathrm{.}64],[n-C_5{H}_{12},15,0\mathrm{.}195]]$

If $99\mathrm{.}99+\%$ absorption of $n-C_5{H}_{12}$ is required. Assume flooding $80\%$ flooding. Assume gas is ideal and density liquid is $700k\frac{g}{m^3}.$ The viscosity of $n-C_{10}{H}_{22}$ is $7cp.$ Calculate

a$)$ Number of required theoretical stages

b$)\%$ absorption for all components

c$)$ The required column diameter if $0\mathrm{.}05m$ metal Pall rings packing bed is used

d$)$ The pressure drop through the column in $P\frac{a}{m}$ of packing height