A liquid-phase chemical reaction with stoichiometry A ! B

QUESTION:

A liquid-phase chemical reaction with stoichiometry A ! B takes place in a semibatch reactor. The rate of consumption of A per unit volume of the reactor contents is given by the first-order rate expression (see 10.19) rAmol/Ls kCA Equipment Encyclopedia absorberstirred tanks www.wiley.com/college/felder 601 WEBC10 06/04/2015 22:57:1 Page 602 where CAmol A/L is the reactant concentration. The tank is initially empty. Beginning at a time t 0, a solution containing A at a concentration CA0mol A/L is fed to the tank at a constant rate V_L/s. (a) Write a differential balance on the total mass of the reactor contents. Assuming that the density of the contents always equals that of the feed stream, convert the balance into an equation for dV/dt, where V is the total volume of the contents, and provide an initial condition. Then write a differential mole balance on the reactant, A, letting NAt equal the total moles of A in the vessel, and provide an initial condition. Your equations should contain only the variables NA, V, and t and the constants V_ and CA0. (You should be able to eliminate CA as a variable.) (b) Without attempting to integrate the equations, derive a formula for the steady-state value of NA. (c) Integrate the two equations to derive expressions for Vt and NAt, and then derive an expression for CAt. Determine the asymptotic value of NA as t ! 1 and verify that the steady-state value obtained in Part (b) is correct. Briefly explain how it is possible for NA to reach a steady value when you keep adding A to the reactor and then give two reasons why this value would never be reached in a real reactor. (d) Determine the limiting value of CA as t ! 1 from your expressions for NAt and Vt. Then explain why your result makes sense in light of the results of Part (c).