A mixture of ammonia and air is scrubbed in a plate column with fresh water. If the ammonia concentration is reduced from $5$ per cent to $0\mathrm{.}01$ per cent, and the water and air rates are $0\mathrm{.}65$ and $0\mathrm{.}40k\frac{g}{m^2}s,$ respectively, how many theoretical plates are required? The equilibrium relationship may be written as $Y=x,$ where $x$ is the mole ratio in the liquid phase.