An isothermal CSTR is used to carry out the following first order aqueous reaction A B with the rate expression r1 = -k1 CA, where r1 is the rate of reaction in moles of A reacting per unit time per unit volume of the reactor, k1 is the rate constant equal to 0.5 min-1 and CA is concentration of A in the reactor in moles/liter. Feed rate to the reactor is F= 20 liters/minute with concentration of A, CA0= 2 moles/liter. The volume of the reactor is constant V= 120 liters and the density of the feed and the reaction mixture is constant = 1 kg/liter.

Develop a dynamic model for variation of concentration CA in response to changes in feed composition CA0. Express the variables as deviation variables and obtain the transfer function CA (s)/ CA0 (s). Give your answers for the steady state gain (K), time constant () in minutes, and initial steady state composition of A (CAi-SS) in the reactor in moles/liter. The feed composition CA0 is changed by a step change from 2 moles/liter to 4 moles/liter, or a step change M of 2 moles/liter. Give your answers for the final steady state composition of A in the reactor in moles/liter (CAf-SS) and the time in minutes it takes for the normalized response CA (t)/(KM) to reach 0.95.