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

C₆H₁₂O₆ + NH₃ + O₂ C₅H₉NO₄ + CO₂ + H₂O

Additionally, mammalian cells can be placed in bioreactors and the biochemical conditions optimized to convert glucose to glutamic acid. Assume a simple bioreactor system that contains mammalian cells. The inlet flow rate of C₆H₁₂O₆ is 1.50 10² mol/day. NH₃ is delivered at a rate of 1.70 10² mol/day. O₂ is provided such that 1.60 10² mol/day are dissolved in liquid (i.e., accessible to the cells for uptake). Assume that the reaction goes to completion.

a) Balance the reaction, given that RQ = 0.43. Determine the limiting reagent, the reaction rate, R, and the fractional conversions of C₆H₁₂O₆, NH₃, and O₂.

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

c) Confirm that total mass is conserved and that total moles is not.

HINT 1: RQ = Respiratory Quotient HINT 2: MATLAB may be helpful for solving a set of algebraic equations.