$($Another old exam question $-$ do this one with your Partner$)$ Ethene $(C_2{H}_4)$ reacts with water to create ethanol in a gas phase reaction. The ethene stream contains $50\%($by mole$)$ Nitrogen as an inert. Water is fed in $20\%$ excess.

$($a$)$ Write a balanced reaction for the transformation above. Use only whole numbers for your stoichiometry.

$($b$)$ If you assume you have $2$ moles of ethene entering the reactor, determine the initial number of moles of each species in this process. Show your work in this section.

$($c$)$ Assuming the fractional conversion of ethane is $15\%,$ determine the partial pressure of each species $($in bar$)$ if the reaction is performed at $400K$ and $3$ bar. To "show your work" on this problem, write out a mole table here and provide the extent of reaction value you obtained. And, of course, provide the partial pressure for each species $($in bar$).$ Note: once you get your extent of reaction value, you can plug into your spreadsheet to calculate the partial pressure if you want.

$($d$)$ If the reaction reaches equilibrium at $400K$ and $3$ bar, determine the partial pressure $($in bar$)$ of each species. To "show your work" on this problem $($since you should be using the reaction spreadsheet$),$ provide the main equation you used to solve the problem, the $K$ value and the extent of reaction value. And, of course, list the partial pressures $($in bar$)$ of each species.

$($e$)$ Without doing a calculation, how would the equilibrium composition of ethene change $($at $400K)$ if you increase the system pressure? Would the equilibrium composition of ethene increase, decrease or stay the same? Explain how you arrived at your answer.