4. Isothermal Reactor Design

The irreversible liquid phase acid catalyzed reaction

is carried out in a semibatch reactor containing H ₂ SO ₄ . A is fed at a constant rate of 10 mol/min. The volumetric flow rate of liquid entering the semibatch reactor is 5 dm³ /min. The initial volume of a 3 M solution of H ₂ SO ₄ catalyst in the reactor is 100 dm³ (no A is present initially). The specific reaction rate is 0.05 min^-1 . The reaction is first order in A and zero-order in catalyst concentration.

(a) Use POLYMATH or MATLAB to determine both the number of moles of A in the tank and the concentration of A and of H ₂ SO ₄ as a function of time.
(b) Obtain an analytical solution for the number of moles of A, N_A , and the concentration of A, C_A , as a function of time. What is the concentration of A after 30 min? How many moles of A will there be in a tank after long times (i.e., )? (Ans.: N_A = 200 mol) Explain why the number of moles remains virtually constant at long times.
(c) Rework part (a) assuming the reaction is first order in H ₂ SO ₄ with k = 0.02 dm ³ / molmin.

(Hint: Do not try to use conversion in solving this problem!)