In Brazil sugarcane is fermented to create bioethanol $($C$2$H$5$OH$),$ which in turn is converted into ethylene $($C$2$H$4),$ one of the most widely$-$used chemical feedstocks in the world. The dehydration reaction that takes place at $300$C and $40$ bar with a catalyst is C$2$H$5$OH$->$C$2$H$4+$H$2$O$.$

The process is fed with a liquid mixture containing $88$ mol$\%$ ethanol and $12$ mol$\%$ water. The fractional conversion of ethanol is $95\%.$ There are two outlet streams: one is essentially pure ethylene gas; the other is a liquid mixture of ethanol and water. Calculate the mole fraction of ethanol in this liquid outlet stream. Hints: An ethylene material balance is not needed. You can assume a basis if you like.