A vapor mixture of ethanol $($E$)$ and butanol $($B$)$ contains $50$ mole $\%$ ethanol at $150C$ and $1\mathrm{.}0$atm. A stream of this mixture flowing at a rate of $160\mathrm{.}0\frac{L}{s}$ is cooled and compressed, causing some but not all of the vapor to condense $($Treat this process as a single$-$unit operation$).$ Liquid and vapor product streams emerge from the process in the equilibrium at $T(C)$ and $600mmHg.$ The vapor product contains $60\mathrm{.}0$mole$\%$ ethanol.

$($a$)$ Draw and label a flowchart. Perform a degree$-$of$-$freedom analysis $($Gibbs phase rule$).$

$($b$)$ Calculate the molar flow rate of feed. Just write the Raoult's Law $($for ethanol and butanol$)$ by using Antoine Equation and mole balances $($for ethanol and butanol$).$

$($c$)$ Complete the calculations manually and Excel$-$Solver program $($Show your Excel$-$Solver calculation$).$