Carbon monoxide at $25C$ and steam at $150C$ are fed to a continuous water$-$gas shift reactor. The product gas which contains $40$mole$\%H_2,40$mole$\%C{O}_2,$ and the balance $H_{2}O(v).$ Its temperature is $500C$ and flow rate is $112mo\frac{l}{h}.$ Product gas enters a condenser and some part of $H_{2}O$ vapor is condensed. Condensed liquid water is pure water. Temperature of gas and liquid stream from condenser is $15C.$ Mole fraction of water vapor is $0\mathrm{.}017$ in the gas stream leaving the condenser. Pressure is $1$atm throughout the process.

$($a$)$ Calculate the percent excess steam fed to the reactor and the rate of condensation of water $(k\frac{g}{h}).$

$($b$)$ Calculate the rate $(kW)$ at which heat must be transferred from the over$-$all system.

The reaction is: $CO(g)+H_{2}O(v)C{O}_2(g)+H_2(g)$

Data : $,C_{p,H2O(l)}=75\mathrm{.}4{10}^{-3}k\frac{j}{m}ol.{?}^{0}C$

$\backslash$table$[[$Component$,hat(H{)}_f^0,k\frac{j}{m}ol$