Binary Flash $[30$ points$]$

We have a feed that is a binary mixture of methanol and water $(52\%$ methanol$)$ that is sent a system of two flash drums hooked together as shown below. The vapor from the first drum is cooled, which partially condenses the vapor, and then fed to the second flash drum. Both drums operate at $1$ atm and are also adiabatic. The same $x-$y diagram $($below$)$ is applicable for both drums. The feed rate to the first drum is $1000$ kmo$\frac{l}{h}.$ We desire liquid product from first drum to be $20-$mol$\%$ methanol $).$ The second drum operates at a $\frac{V}{F}=0\mathrm{.}2.$ Use the methanol$-$water system at $1$atm given in the second page.

a$)$ Find the vapor mole fraction $y_1,$ fraction vaporized $(\frac{V}{F}{)}_1$ and vapor flow rate $V_1$ for the first drum

b$)$ Find the vapor mole fraction $y_2.$ liauid mole fraction $x_2$ and vapor flow rate $V_2$ for the second drum