Please solve with detailed steps.

A $540$ kg solution containing $50$ wt$\%$ heptane and $50$ wt$\%$ octane is distilled in a batch still pot until only

$2\mathrm{.}50$ mol remain in the pot.

$($a$)$ Assuming a relative volatility of $2\mathrm{.}2,$ what will be the pot composition after distillation?

$($b$)$ What is the composition of the first vapor leaving the pot?

$($c$)$ If the relative volatility is $1\mathrm{.}1,$ what will what will be the pot composition after distillation?

$($d$)$ For relative volatility of $2\mathrm{.}2,$ how many moles of the feed remain in the pot for xe equal to three times the final composition found in part $($a$)?$

$($e$)$ For relative volatility of $2\mathrm{.}2,$ what is the average distillate composition when one third of the feed has boiled off?