Chapter 4, Problem 4.3P

A liquid-phase chemical reaction A -* B takes place in a well-stirred tank. The concentration of A in the feed is f-AO (mol/m³), and that in the tank and outlet stream is C_A (mol/nr). Neither concentration varies with time. The volume of the tank contents is V(m³) and the volumetric flow rale of the inlet and outlet streams is V (m7s). The reaction rate (the rate at which A is consumed by reaction in the lank) is given by the expression

r(mol A consumed/s) = JtVC_A

where k is a constant.

1. Is this process continuous, batch, or semibatch? Is it transient or steady-state?
2. What would you expect the reactant concentration C_A to equal if k = 0 (no reaction)? What should it approach if k —» oo (inflnitely rapid reaction)?
3. Write a differential balance on A, stating which terms in the general balance equation (accumulation = input + generation — output — consumption) you discarded and why you discarded them. Use the balance to derive the following relation between the inlet and outlet reactant concentrations: