Question $1$

A fractionation tower is being supplied with a new input stream of $100mo\frac{l}{m}in,$ consisting of

$50$mol$\%$ of component A and $50$mol$\%$ of component B$.$ The gas leaving the upper section of the

tower contains $97$mol$\%$ of component A and is completely condensed. This condensed gas

stream is then divided into two equal parts: The top product stream, which contains $89\%$ of the

component A initially fed to the tower. The reflux stream, which is recirculated back to the upper

section of the tower. The liquid exiting the lower section of the tower is directed to a partial

reboiler where $45\%$ of the liquid is vaporized. This vaporized stream, referred to as the

vaporization stream, is recycled back to the tower. The remaining liquid from the reboiler is the

bottom product stream. The relationship that describes the compositions of the streams leaving

the reboiler is as follows:

$y_{A,6}=2\mathrm{.}25y_{A,7}$

where $y_{A,6}$ represents the mole fraction of component $A$ in the vapor stream $(6),$ and $y_{A,7}$

represents the mole fraction of Component $A$ in the liquid stream $(7).$

a$)$ Label the flowchart of the separation process.

b$)$ Do degrees of freedom analysis for all systems.

c$)$ Calculate the molar amounts of the overhead and bottom products.

d$)$ Calculate the mole fraction of component $A$ in the bottom product.