Chapter 12, Problem 12.24P

The elementary liquid-phase reactions

$\begin{array}{rr}\hfill (1)& \hfill \text{A}+2\text{B}\stackrel{}{\to }2\text{C}\\ \hfill (2)& \hfill \text{A}+\text{C}\stackrel{}{\to }2\text{D}\end{array}$

are carried out adiabatically in a 10 dm³ PFR. After streams A and B mix, species A enters the reactor at a concentration of C_A0 = 2 mol/dm² and species B at a concentration of 4 mol/dm³. The entering volumetric flow rate is 10 dm³/s.

Assuming you could vary the entering temperature between 300 K and 600 K, what entering temperature would you recommend to maximize the concentration of species C exiting the reactor? (±25°K). Assume all species have the same density.

Additional information

$\begin{array}{l}{C}_{{\text{P}}_{\text{A}}}=C_{{\text{P}}_{\text{B}}}=20\text{cal/mol/K,}{C}_{{\text{P}}_{\text{C}}}=60\text{cal/mol/K,}{C}_{{\text{P}}_{\text{D}}}=80\text{cal/mol/K}\hfill \\ \Delta H_{\text{Rx1A}}=20,000\text{cal/mol}\text{A,}\Delta H_{\text{Rx2A}}=-10,000\text{cal/mol}\text{A}\hfill \\ k_{\text{1A}}=0.001\frac{{\text{dm}}^6}{{\text{mol}}^2\cdot \text{s}}at300\text{K}withE=5000\text{cal/mol}\hfill \\ k_{\text{2A}}=0.001\frac{{\text{dm}}^3}{\text{mol}\cdot \text{s}}at300\text{K}withE=7500\text{cal/mol}\hfill \end{array}$