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2. A chemical engineer is monitoring the concentration of chemicals as a function of time in a cylindrical batch reactor of radius R and height H, running at full capacity. The following reaction takes place in the batch reactor: A + 2B ↔ 3C The rates of the forward and reverse reactions follow mass action kinetics; assume rate constants as appropriate.
a) At t=0, the reactor contains zero moles of C and non-zero moles of A and B. If the reactor conditions (e.g. temperature) are always maintained such that the forward reaction is dominant (i.e. safe to assume reverse reaction can be neglected in this case), derive expressions for the concentration of A, B, and C as a function of time for the two cases
i. nA0 >> nB0
ii. nB0 >> nA0
b) If the reactor conditions allow for the reversible reaction to proceed, write out all the unsteady state materials balances for A, B and C in this batch reactor. (Simplify as much as you can but no need to solve)