A bubble $-$ cap absorption column is to be used to absorb ammonia, $N{H}_3$ by using water.

E A gaseous mixture containing $15$mol$\%N{H}_3$ and $85$mol$\%$ air enters the bottom of the absorption tower. $57$mol of gaseous $N{H}_3$ enters the tower per hour, while $3\mathrm{.}7kg$ of pure water enters the top of the tower per hour. The column operates at the atmospheric pressure and at a constant temperature of $30C.$

E It is desired to absorb $N{H}_3$ such as only $2\mathrm{.}5\%N{H}_3$ leaves the tower with air. Determine the number of theoretical plates required for the above process.