Chapter 8, Problem 8.4P

Consider the following system of gas-phase reactions:

$\begin{array}{l}\text{A}\to \text{X}{r}_{\text{X}}=k_1{C}_{\text{A}}^{1/2}{k}_1=0.004{(}^{{\text{mol/dm}}^{\text{3}}}\cdot {\min }^{-1}\\ \text{A}\to \text{B}{r}_{\text{B}}=k_2{C}_{\text{A}}^{}{k}_2=0.3{\min }^{-1}\\ \text{A}\to \text{Y}{r}_{\text{Y}}=k_3{C}_{\text{A}}^2{k}_3=0.25{\text{dm}}^{\text{3}}\text{/mol}\cdot \min \end{array}$

B is the desired product, and X and Y are foul pollutants that are expensive to get rid of. The specific reaction rates are at 27°C. The reaction system is to be operated at 27°C and 4 atm. Pure A enters the system at a volumetric flow rate of 10 dm³/min.

1. (a) Sketch the instantaneous selectivities (S_B/X, S_B/Y, and S_B/XY = r_B/(r_X + r_Y)) as a function of the concentration of C_A.
2. (b) Consider a series of reactors. What should be the volume of the first reactor?
3. (c) What are the effluent concentrations of A, B, X, and Y from the first reactor?
4. (d) What is the conversion of A in the first reactor?
5. (e) If 99% conversion of A is desired, what reaction scheme and reactor sizes should you use to maximize S_B/XY?
6. (f) Suppose that E₁ = 20,000 cal/mol, E₂ = 10,000 cal/mol, and E₃ = 30,000 cal/mol. What temperature would you recommend for a single CSTR with a space time of 10 min and an entering concentration of A of 0.1 mol/dm³?
7. (g) If you could vary the pressure between 1 and 100 atm, what pressure would you choose?