Pr$.2(40$ pts$)$ A feed mixture of $50$ mole$-\%$ n$-$hexane and $50$ mole$-\%$ n$-$heptane is subjected to distillation in a plate column at a rate of $150$kmo$\frac{l}{h}$ and at a total pressure of $1$atm. The feed is saturated liquid. The compositions of overhead and bottom products are $xD=0\mathrm{.}98$ and $xB=0\mathrm{.}02,$ respectively. A total condenser and a partial reboiler are used. Cooling water enters the total condenser at $25C$ and leaves at $40C.$ Overall efficiency of the column is $E_0=55\%.$ For $R_D=2,$ find the followings;

i$)$ Number of ideal plates,

ii$)$ Number of actual plates,

iii$)$ Feed plate location,

iv$)$ Flow rate of cooling water required in the total condenser.

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