$2\mathrm{.}2.$ A gas stream containing a mixture of $N{H}_3$ and air at a flow rate of $57\mathrm{.}8$kgmo$\frac{l}{h}$ comprises $4\mathrm{.}0$mol$\%N{H}_3$ in the total gas. The $N{H}_3$ content is decreased to $0\mathrm{.}5$mol$\%$ in a packed absorption tower at $293K$ and $1\mathrm{.}013105Pa.$ A stream of pure water is introduced to the column at a flow rate of $68\mathrm{.}8$kgmo$\frac{l}{h}.$ The tower's diameter is $0\mathrm{.}747$ metres. The film mass transfer coefficients are provided as: $k_{y}a=0\mathrm{.}0739$kgmo$\frac{l}{s}{m}^3*mol$ frac $k_x^{\text{'}}a=0\mathrm{.}169$kgmo$\frac{l}{s}.m^3$mol frac.

Using the design method for dilute gas mixtures, determine the following:

$2\mathrm{.}2\mathrm{.}1.$ Calculate the tower height using k$\text{'}$y a$.$

$20$