Consider the chemical reaction: taking place in CSTRs (continuously stirred tank reactors) in series. The tanks' holding time, , is assumed constant equal to 1. The inlet to the first reactor is pure . The reaction rate constants are chosen as: , , , and . It is also assumed that the concentration of all species in all tanks is initially equal to zero. An analytical expression for the exit concentration of the three chemical species was found by Acrivos and Amundson in 1955 (see reference below a for detailed derivation using matrix mathematics).