Directions: Complete the following problems using the GRADS method to organize your solutions and submit them either handwritten neatly and

scanned into Canvas or typed and uploaded to Canvas by $9$:$30$ AM on the due date.

Glucose is converted into glutamic acid in many mammalian cells through the following unbalanced reaction formula:

$C_6{H}_{12}{O}_6+N{H}_3+O_{2}longrightarrow{C}_5{H}_{9}N{O}_4+C{O}_2+H_{2}O$

Mammalian cells can be placed in a simple mixing bioreactor and the biochemical conditions optimized to convert glucose to glutamic acid. After

some experimentation, you find that the respiratory quotient for mammalian cells bound in this way is $0\mathrm{.}46,$ and that one day is roughly enough

time to collect a meaningful amount of glutamic acid. You provide an inlet flow rate of glucose of $1\mathrm{.}15{10}^{2}mo\frac{l}{d}ay.$ Ammonia is delivered at a

rate of $1\mathrm{.}52{10}^{2}mo\frac{l}{?}$ day and dissolved oxygen is provided by an air pump such that $1\mathrm{.}52{10}^{2}mo\frac{l}{?}$ day are dissolved in the bioreactor liquid and

accessible to the cells for uptake.

a$)$ Balance the reaction formula.

b$)$ Determine the limiting reactant, the reaction rate, $R,$ and the fractional conversions of glucose, ammonia, and oxygen.

c$)$ Calculate the molar and mass flow rates of all constituents leaving the bioreactor including the products and excess reactants.

d$)$ Verify that total mass is conserved and that total moles is not.

HINT: MATLAB may be helpful for solving a set of algebraic equations. If you choose to use MATLAB, be sure to document your process on paper

first and copy the properly documented code from your $.m$ file if you choose to go this route.