The irreversible liquid phase acid catalyzed reaction A > C (catalyzed by H2SO4) is carried out in a semi-batch reactor containing H2SO4. The initial volume of a 3 M H2SO4 solution in the reactor is 100 L (no A is present initially). Species A is fed at a constant rate of 10 mol/min. The volumetric flow rate of liquid entering the semi-batch reactor is 5 L/min. The specific reaction rate is 0.05 min-1. The reaction is first order in A and zero-order in catalyst concentration.

(a) Obtain an analytical solution for moles of A (NA) and concentration of A (cA) as a function of time. You must solve this by hand; do not use computer software/resources for this problem. Leave the answer in symbolic form; don’t substitute parameter values. Show your work to obtain full credit.

(b) What is concentration of A after 30 min?

(c) How many moles of A will there be in a tank after long times (t -> infinity)? Explain why the number of moles remains virtually constant at long times.

(d) For t = 0 to 300 min, provide a computer generated plot of cA vs. t.