A mixture of $45\%n-$pentane $(1)$ and $55\%n-$heptane $(2)$ is to be separated $($vapor$-$liquid equilibrium $($VLE$)$ diagram cf$.$ Figure $2)$ in a plate column. The feed stream of $F=200mo\frac{l}{s}$ is used as saturated vapor $)=(0.$ At the top a purity of the product $x_{1,0}=0\mathrm{.}95$ is obtained. The concentration of the $n-$pentane in the bottom product is $x_{1,8}=0\mathrm{.}1.$

a$)$ Set up the material and mass balances and calculate the top and bottom flows.

b$)$ Determine the minimum number of theoretical plates.

c$)$ What is the minimum reflux ratio? How many theoretical stages are required if the separation is carried out with a minimum reflux ratio?

d$)$ Determine the number of theoretical stages in the case that the real reflux ratio applied equals two times the value of the minimum reflux ratio.

e$)$ Determine the practical number of plates with an everall column efficiency of $0\mathrm{.}6.$

f$)$ Determine the position of the foed plate.