A mixture of benzene and toluene containing $40$ mole per cent benzene is to be separated to give a product containing $90$ mole per cent benzene at the top, and a bottom product containing not more than $10$ mole per cent benzene. The feed enters the column at its boiling point, and the vapour leaving the column which is condensed but not cooled, provides reflux and product. It is proposed to operate the unit with a reflux ratio of $3$kmo$\frac{l}{k}$mol product. Using sorel$-$Lewis method, It is required to find the number of theoretical plates needed and the position of entry for the feed.

Mole fraction of benzene in liquid Mole fraction

$0\mathrm{.}1,0\mathrm{.}2,0\mathrm{.}3,0\mathrm{.}4,0\mathrm{.}5,0\mathrm{.}6,0\mathrm{.}7,0\mathrm{.}8,0\mathrm{.}9$ of benzene in vapour

$0\mathrm{.}22$

$0\mathrm{.}38$

$0\mathrm{.}51$

$0\mathrm{.}63$

$0\mathrm{.}7$

$0\mathrm{.}78$

$0\mathrm{.}85$

$0\mathrm{.}91$

$0\mathrm{.}96$