Consider the stirred-tank reactor shown in Fig. P5-5.

The reaction occurring is

A ? B

and it proceeds at a rate

r = kCo

where r = (moles A reacting)/(volume)(time)

k = reaction rate constant

Co (t) = concentration of A in reactor at any time t (mol A/volume)

V = volume of mixture in reactor

Further, let

F = constant feed rate, volume/time

Ci (t) = concentration of A in feed stream, moles/volume

Assuming constant density and constant volume V, derive the transfer function relating the concentration in the reactor to the feed-stream concentration. Prepare a block diagram for the reactor. Sketch the response of the reactor to a unit-step change in Ci.

C, F B Volume V Co. F