A plate column separation unit produces $95$ mol $\%$ nitrogen product in the overhead and a $98$mol$\%$ oxygen product in the

bottom from a saturated liquid feed with a molar composition of $50\%$ oxygen and $50\%$ nitrogen. It utilizes a normal single column with both a total condenser and a reboiler. How many additional theoretical plates would have to be added to the rectifying section of the column if the desired composition of the liquid overhead product is $99\mathrm{.}5$mol$\%$ nitrogen rather than the $95$ mol $\%$ originally requested? The $\frac{L}{V}$ ratio is $0\mathrm{.}7347$ and corresponding equilibrium constant for oxygen at this temperature $K_2=0\mathrm{.}3925.$