Production of cell biomass in a bioreactor

Cell biomass, represented as $C_{4\mathrm{.}4}{H}_{7\mathrm{.}3}{N}_{0\mathrm{.}9}{O}_{1\mathrm{.}2},$ is grown in a bioreactor. The reaction in the

bioreactor can be represented by the following equation:

$C_6{H}_{12}{O}_6+1\mathrm{.}45O_2+0\mathrm{.}83N{H}_{3}0\mathrm{.}92C_{4\mathrm{.}4H_{7\mathrm{.}3}{N}_{0\mathrm{.}9}{O}_{1\mathrm{.}2}}+3\mathrm{.}88H_{2}O+1\mathrm{.}95C{O}_2$

The feed to the bioreactor is oxygen gas and an aqueous solution of ammonia and glucose. The

water $($not including the ammonia and glucose dissolved in it$)$ in the feed aqueous solution enters

the bioreactor at a flowrate of $2982mol{s}_{2}O/$day $($see Figure below$).$ The Ammonia in the feed

is completely consumed in the bioreactor. The glucose is $15\%$ in excess with respect to

ammonia. The oxygen gas is $25\%$ in excess with respect to ammonia.

The feed to the bioreactor has $40$ mols $N\frac{H_3}{?}$ day and the bioreactor is operated at steady$-$state.

a$.$ Draw and label a flowchart for the process. $($The one given below is not completely

labeled$).$ Note: Please redraw the flowchart by hand. Cutting$-$and$-$pasting the above

diagram will not be graded

b$.$ From the General Balance Equation, derive the Balance Equation applicable to the

problem

c$.$ Do a degree$-$of$-$freedom analysis using the Molecular Species Balance method to prove

that we can solve for the molar flow rates of all species leaving the bioreactor.

d$.$ Solve for the molar flow rates of all species leaving the bioreactor.