$9\mathrm{.}18.$ Carbon monoxide at $25C$ and steam at $150C$ are fed to a continuous water$-$gas shift reactor. The product gas, which contains $40\mathrm{.}0$ mole $\%H_2,40\mathrm{.}0\%C{O}_2,$ and the balance $H_{2}O(v),$ emerges at $500C$ at a rate of $3\mathrm{.}50$ SCMH $($standard cubic meters per hour$)$ and goes to a condenser. The gas and liquid streams leaving the condenser are in equilibrium at $15C$ and $1$ atm $.$ The liquid may be taken to be pure water $($no dissolved gases$).$

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

$($b$)$ Calculate the rate $(kW)$ at which heat must be transferred from the condenser.

$($c$)$ Taking atomic species at $25C$ as references, prepare and fill in an inlet$-$outlet enthalpy table and calculate the required rate of heat transfer $(kW)$ to or from the reactor.

$($d$)$ It has been suggested that the carbon monoxide feed stream could pass through a heat exchanger prior to entering the reactor and the reactor product gas could pass through the same heat exchanger before entering the condenser. Sketch and label a flowchart of the heat exchanger and state economic benefits that might result from its use. $($Hint: Heating and cooling operations are both expensive.$)$