A gas stream from a process plant has it's concentration of ammonia reduced from $5\%$ to $0\mathrm{.}6\%$ by scrubbing with a solvent in a counter current packed tower. The equilibrium relationship for this system at its operating temperature and atmospheric pressure is $Ye=5x,$ where $x$ and $Y$ are the mole ratios of the ammonia in the liquid solvent and the gas respectively. Solvent with $0\mathrm{.}1\%$ ammonia is supplied to the tower from a recovery process at $250$ moles per hour. If the flow of gas from the plant is $30$mole$\frac{s}{h}r.$ Find the minimum solvent rate required for this operation and the number of stages required for the mass transfer.

If a packed column were to be used for the operation above, estimate the height of the column if the Overall mass transfer coefficient Kga is $10$ mole$/$ m$.$atm.h$.$