The reaction A → B takes place in two reactors in series.

The reactors are well mixed but are not at steady state. The unsteady-state mass balance for each tank reactor is shown below:

dCA_l/dt = 1/τ(CA₀ - CA_l) - kCA_l

dCB_l/dt = - 1/τ CB_l + kCA_l

dCA₂/dt = 1/τ(CA_l – CA₂) – kCA₂

dCB₂/dt = 1/τ(CB_l – CB₂) + kCA₂

Where CA₀ = concentration of A at the inlet of the first reactor, CA_l = concentration of A at the outlet of the first reactor (and inlet of the second), CA₂ = concentration of A at the outlet of the second reactor, CB₁ = concentration of B at the outlet of the first reactor (and inlet of the second), CB₂ = concentration of B in the second reactor, τ = residence time for each reactor, and k = the rate constant for reaction of A to produce B. If CA₀ is equal to 20, find the concentrations of A and B in both reactors during their first 10 minutes of operation. Use k = 0.12/min and τ = 5 min and τ = 5 min and assume that the initial conditions of all the dependent variables are zero.