Chapter 5, Problem 5.6P

A reversible liquid-phase isomerization is carried out A ⇄ B is carried out isothermally in a 1000-gal CSTR. The reaction is second order in both the forward and reverse directions. The liquid enters at the top of the reactor and exits at the bottom. Experimental data taken in a batch reactor shows the CSTR conversion to be 40%. The reaction is reversible with K_C = 3.0 at 300 K, and $\Delta H_{\text{Rx}}^{\text{ο}}$ = −25,000 cal/mol.

Assuming that the batch data taken at 300 K are accurate and that E = 15,000 cal/mol, what CSTR temperature do you recommend to obtain maximum conversion? [Hint: Read Appendix C and assume ΔC_P = 0 in the appendix Equation (C-9)]:

$K_{\text{C}}(T)=K_{\text{C}}(T_0)\exp \left[\frac{\Delta H_{\text{Rx}}^{\text{ο}}}{R}\left(\frac{1}{T_0}-\frac{1}{T}\right)\right]$

Use Polymath to make a plot of X versus T. Does it go through a maximum? If so, explain why.