A mixture $($total flow rate $=100$ kmol$/$hr$)$ with $28$ mol$\%$ n$-$hexane, $42$ mol$\%$ n

heptane, and $30$ mol$\%$ of n$-$octane is to be distillated to produce a distillate product with $1$ mol$\%$ of n$-$heptane and a bottoms product with $0\mathrm{.}5$ mol$\%$ n$-$hexane. The column operates at $1\mathrm{.}2$ atm with $60\%$ of feed being in vapor state. At $1\mathrm{.}2$ atm, the relative volatilities of hexane and heptane with respect to octane are

approximated to be $4\mathrm{.}836$ and $2\mathrm{.}188,$ respectively. Calculate the number of equilibrium stages required to achieve this product specification at total reflux