nly attempt this problem if you missed points on the "Brazil bioethanol" written problem on Exam $1.$ You must type out your final numerical answer in the box below and also upload a pdf of your solution procedure. The solution must be $100\%$ correct to get credit.

$(10$ points$)$ In contrast with alcoholic beverages, high$-$purity ethanol $($C$2$H$5$OH$)$ for chemical use is not generally made by fermenting sugars. Instead it is made by reacting ethylene gas $($C$2$H$4)$ with steam. The hydration reaction that takes place at $300$C and $60$ bar with a catalyst is

C$2$H$4+$H$2$O$->$C$2$H$5$OH

The reactor is fed with a single stream with a gas mixture containing $60$ mol$\%$ ethylene and $40$ mol$\%$ steam. The fractional conversion of ethylene is $10\%.$ There is one outlet gas stream. Using the procedures taught in this class, calculate the mole fraction of ethanol in this outlet stream.