A continuous, stirred-tank reactor is initially full of water with the inlet and exit volumetric flow rates of water having the same numerical value. At a particular time, an operator shuts off the water flow and adds caustic solution at the same volumetric flow rate q, but with concentration cÌ…_i. If the liquid volume V is constant, the dynamic model for this process is

where c(t) is the exit concentration. Calculate c(t) and plot it as a function of time.

Data: V = 2 m³;    q = 0.4 m³/min;    cÌ…_i = 50 kg ˆ• m³

+ qc = q; c(0) = 0 dt