A continuous fractionating column is to be designed to separate $30000k\frac{g}{h}$ of a

mixture of $40\%$ benzene and $60\%$ toluene by weight into an overhead product containing $94\mathrm{.}5\%$ benzene and a bottom product containing $96\%$ toluene. 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 $7360$ and $7960$ kca$\frac{l}{k}$gmol, respectively. Benzene and toluene form an ideal system with an average relative volatility of about $2\mathrm{.}5.$ If the feed is a mixture of two$-$thirds vapor and one$-$third liquid,

a$)$ calculate the moles of overhead product and bottoms product per hour,

b$)$ determine the number of ideal plates and the position of the feed plate,

c$)$ If the cooling water enters the condenser at $25C$ and leaves at $40C,$ how much cooling water is required in $\frac{m^3}{h},$ assuming that the condensate leaves the condenser as a saturated liquid?

Please, Can you answer the question according to the Mass Transfer, Geankapolis book? Can you write every step and detail? Don't use any AI system.