Consider a packed column for the adsorption of A from a gas containing inert material (in addition to A) by
a liquid containing B (nonvolatile) under continuous, steady-state conditions. Adsorption is accompanied by
the instantaneous reaction A(g) + bB(l) ? products. Assume the overall process is liquid-film controlled.
(a) Show by means of a material balance on B, that under certain conditions (state the assumptions made),
the height of packing required is given by
$L = \frac{L}{a_i'} \int_{C_{B,out}}^{C_{B,in}} \frac{dC_B}{(-r_B)} = \frac{L}{ba_i'} \int_{C_{B,out}}^{C_{B,in}} \frac{dC_B}{(-r_B)}$
(b) Show that if the enhancement factor, E is relatively large, the equation in part (a) becomes
$h = \frac{L}{k_{BI}a_i'} \ln{\left(\frac{C_{B,in}}{C_{B,out}}\right)}$
(c) Calculate the height h for the following:
$C_{B,in} = 1500 \text{ mol } m^{-3}$; $y_{A,in} = 0.08$; $y_{A,out} << y_{A,in}$; b = 2; G = 150 mol m$^{-2}$s$^{-1}$; $k_{BI} = 5 \times 10^{-5} \text{ m s}^{-1}$;
L = 2L$_{min}$; and a'$_i$ = 100 m$^2$ m$^{-3}$ (packing).
