A liquid mixture at its boiling point is made of $n-$ heptane $(10\%$mol$)$ and $n-$ octane $(90\%$mol$).$ It enters to a top of stripping tower at $1$atm wherein liquid bottoms must contain $98\%$ mol $n-$ octane. For every $3$ mol of feed, $2$ mol of vapor is withdrawn as a product. Determine the composition of the vapor $(\%$ mol $n-$ octane$)$ as well as the number of theoretical plates. Use the equilibrium data below $($mole fractions of $n-$ heptane$)$: $(15$ PTS$)$

$\backslash$table$[[x,0\mathrm{.}284,0\mathrm{.}097,0\mathrm{.}067,0\mathrm{.}039,0\mathrm{.}012],[y,0\mathrm{.}459,0\mathrm{.}184,0\mathrm{.}131,0\mathrm{.}078,0\mathrm{.}025]]$