At 730K the isomerization of A to R (rearrangement of atoms in the molecule) proceeds on a slowly deactivating catalyst with a second-order rate

Since reactant and product molecules are similar in structure, deactivation is caused by both A and R. With diffusional effects absent, the rate of deactivation is found to be

We plan to operate a packed bed reactor containing W = 1 metric ton of catalyst for 12 days using a steady feed of pure A, FA₀, = 5 kmol/hr at 730 K and 3 atm (C_A0 = 0.05 mol/liter).
(a) First evaluate -da/dt, τ, and then the general expression for 1 - X_A.
(b) What is the conversion at the start of the run?
(c) What is the conversion at the end of the run?
(d) What is the average conversion over the 12-day run?

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-rak'Ca = 200 C2a, [mol A/hr .gm cat]