Cyclohexane $($C$6$H$12)$ can be made by the reaction of benzene with hydrogen according to

the following reaction:

C$6$H$6+3$H$2->$ C$6$H$12$

$20\%$ excess hydrogen is used in the fresh feed, and that the composition of the recycle

stream is $22\mathrm{.}74$ mol $\%$ benzene and $78\mathrm{.}26$ mol $\%$ hydrogen. If the overall conversion of

benzene is $95\%$ and the single$-$pass conversion through the reactor is $20\%,$

a$.$ Determine the all unknowns

b$.$ Determine the ratio of the recycle stream to the fresh feed stream