$f(x)f(x)$

Ex$830,000$ kg$/$h of a mixture of $40$ percent benzene and $60$ percent toluene into an A continuous fractionating column is to be designed to separate overhead product containing $97$ percent benzene and a bottom product containing $98$ percent toluene. These percentages are by weight. A reflux ratio of $3\mathrm{.}5$mol to $1$mol of product is to be used. The molal latent heats of benzene and toluene are $7,360$ and $7,960$ cal $\frac{?}{g}$ mol, respectively. Benzene and toluene form a nearly ideal system with a relative volatility of about $2\mathrm{.}5.$ The feed has a boiling point of $95C$ at a pressure of $1$atm.

a$)$ Calculate the moles of overhead product and bottom product per hour.

b$)$ Determine the number of ideal plates and the position of the feed plate $($i$)$ if the feed is liquid and at its boiling point; $($ii$)$ if the feed is liquid and at $20C($specific heat $0\mathrm{.}44c\frac{a}{g}.C)$; $($iii$)$ if the feed is a mixture of two$-$thirds vapor and one$-$third liquid.