Engineers Lucy and Urban operate a reactor where two unbalanced gas phase reactions occur:

$C{H}_3\frac{C}{O}OH+H_2{C}_2{H}_{5}OH+H_{2}O$ and $C_2{H}_{5}OH(C_2{H}_5{)}_{2}O+H_{2}O$

In the first reaction, acetic acid $(C{H}_3\frac{C}{O}OH)$ and hydrogen $(H_2)$ react to produce ethanol $(C_2{H}_{5}OH)$ and

water $(H_{2}O)$; and ethanol decomposes to diethyl ether $((C_2{H}_5{)}_{2}O)$ and water in the second reaction. A

stream of $53\mathrm{.}1mo\frac{l}{s}$ hydrogen and the balance acetic acid at $163C$ is fed to the reactor, which

operates at steady state. The stream exiting the reactor contains acetic acid, hydrogen, ethanol, water,

and diethyl ether at $306C.$ The component flow rate of acetic acid entering the reactor is $13\mathrm{.}6mo\frac{l}{s}.$

The fraction conversion of acetic acid is $71\mathrm{.}9\%,$ and the selectivity, which is the ratio of the amount of

ethanol to diethyl ether in the exiting stream, is $6\mathrm{.}77.$ Assume all components are in the gas phase and

no phase changes occur in the reactor.

Determine the unknown component molar flow rates in the reactor effluent.

$n_{2,H}^{}=n_{2,E}^{}=n_{2,W}^{}=mo{l}_{2,DE}^{}=mo{l}_{mo\frac{l}{s}}^{mo\frac{l}{s}}$