Consider the separation of a feed stream consisting of $0\mathrm{.}4$ mol$\%$ ammonia and $99\mathrm{.}6$ mol$\%$ water. At the prevailing pressure the equilibrium relationship may be approximated as y$=12$x$,$ where y and x are the mole fractions of ammonia in the vapour and liquid respectively.

a$)$ This feed stream is to be separated in an ideal single$-$stage flash separation, which operates at steady$-$state. The molar flow rate of the vapour leaving the flash separator is $35\%$ of the feed molar flow rate. Calculate the mole fractions of ammonia in the vapour and liquid leaving the flash separator.