A bioreactor hosts a genetically improved cell strain of $B.$ lactofermentum to convert glucose to glutamic acid $(C_5{H}_{9}N{O}_4)$ for production of MSG

and other products. The cells metabolize glucose according to the following balanced reaction:

$C_6{H}_{12}{O}_6(s)+N{H}_3(g)+\frac{3}{2}{O}_2(g)longrightarrow{C}_5{H}_{9}N{O}_4(l)+3H_{2}O(l)+C{O}_2(g)$

The liquid$-$phase inlet stream contains water and glucose; the mass fraction of glucose is $0\mathrm{.}05.$ The liquid phase inlet flow rate is $200k\frac{g}{h}r.$ The

liquid flow rate of the unreacted glucose is $2\mathrm{.}5k\frac{g}{h}r.$ Ammonia and oxygen enters in a separate gas phase stream. Carbon dioxide as well as excess

ammonia and oxygen leave in a second gas phase product stream.

The system is operated continuously, and reaction products and excess reactants are removed such that no accumulation occurs. The inlet and

outlet streams are at $25C$; in addition, the reactor is operated at $25C.$

Calculate the fractional conversion of glucose.

a$.$ Using standard heats of combustion values, find $hat(H_R),$ the standard heat of reaction, in $k\frac{J}{m}ol.$ Is the reaction exothermic or endothermic?

b$.$ What rate of heat should be added or removed from the system to maintain the bioreactor at a steady temperature. Report your answer in

$k\frac{J}{h}r.$ State the direction of heat transfer.

c$.$ After leaving the device, the liquid product stream that contains water, glutamic acid, and excess glucose $($all at $25C)$ is sent to a chiller. The

purpose of the chiller is to cool the three compounds from $25C$ to $4C.$ The chiller operates as an open, steady$-$state system, with compounds

leaving the chiller at $4C.$ Work is added to the chiller at a rate of $50k\frac{J}{m}in.$

d$.$ Calculate the rate of energy required to cool all the liquid phase compounds. Assume the heat capacity of glutamic acid is $175\frac{J}{\text{m}\text{o}\text{l}*K},$ and the

heat capacity of glucose is $208\frac{J}{\text{m}\text{o}\text{l}*K}.$