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Problem $2$

$[25\%]$

A $100$mol of a binary mixture of methanol and water is loaded into a still pot to be distilled using a simple batch distillation at $1$atm. If the head temperature when the first distillate is collected is $70C,$ the still is run until the head temperature is $95C.$ Assuming the applicability of Raoult's and Dalton's laws.

a$)$ Plot the change of $T,x_w,x_D,$ and $x_{\text{D}\text{a}\text{v}\text{g}}$ with respect to time.

b$)$ What is the total amount of distillate collected?

c$)$ What is the composition of the distillate and waste product?

d$)$ What should be the distillate rate to complete the run in $5hrs?$