$1.$ A gaseous effluent stream containing $1\mathrm{.}6\%(\frac{v}{v})$ ammonia is to be scrubbed from air using water in a counter$-$current packed tower at atmospheric pressure. The outlet gas concentration must be reduced to $0\mathrm{.}08\%(\frac{v}{v}).$ The water entering the top of the tower contains $0\mathrm{.}25kg{m}^{-3}$ ammonia and the molar liquid to gas ratio is $3\mathrm{.}2.$ The molecular weight of ammonia is $17kgkmo{l}^{-1}.$ For this system with $25mm$ packing, the height of a transfer unit, $H_{Oy},$ is $0\mathrm{.}32m.$ The equilibrium relationship for the system at the temperature of operation is given by Henry's law: $p=1\mathrm{.}08x,$ where $p$ is the partial pressure of ammonia in atmospheres and $x$ is the mole fraction in water. a$.$ Calculate the mole fraction of ammonia in the water leaving the tower. Assume that the density of the liquid is the same as that of water.

b$.$ Calculate the number of transfer units needed to carry out the separation and the height of packing required.