Using A distillation column is designed to continuously separate $1000molh{r}^{-1}$ of Methanol and Water feed. The feed contains $40$mol$\%$ methanol and is a saturated vapour. The distillate will contain $90$mol$\%$ methanol and the bottom product, $5$mol$\%$ methanol. Using the McCabe$-$Thiele method determine:

$($i$)$ the flow rate of distillate and bottoms product;

$($ii$)$ the minimum reflux ratio and the minimum reflux rate;

$(8)$

$($iii$)$ the actual number of plates required to achieve this separation.

Assume that the column operates with a reflux ratio that is three times $(3x$ the minimum; the overall tray efficiency is $57\%$ and the reboiler is a partial type. The equilibrium curve of the Methanol$-$water mixture at $1$atm. is provided in Appendix $2.$