A liquid-phase chemical reaction with stoichiometry A → B takes place in a semicontinuous reactor. The rate of consumption of A per unit volume of the reactor is given by the first-order rate expression rA(mol/liter·s) = kCA where CA(mol/liter) is the reactant concentration. The tank is initially empty. Beginning at a time t=0, a solution containing A at a concentration CA0(mol/liter) is fed to the tank at a steady rate Ф(liters/s). a. Write differential balances on the total volume of the tank contents, V, and on the moles of A in the tank, nA. Provide initial conditions for each equation. Your equations should contain only the variables nA, V, and t, and the constants Ф and CA0. Simplify the second equation to determine an expression for the steady-state value of nA. b. Integrate each equation to derive expressions for V(t) and nA(t). Use the latter solution to verify the expression for the steady-state value of nA derived in part a.