Irreversible first-order reaction in a continuous reactor, a well-stirred reactor of volume V is initially completely filled with a solution of solute A in a solvent S at concentration C_AO. At time t = 0, an identical solution of a in S is introduced at a constant mass flow rate w. A small constant stream of dissolved catalyst is introduced at the same time, causing A to disappear according to an irreversible first-order reaction with rate constant k^'''₁ sec the rate constant may be assumed independent of composition and time. Show that the concentration of A in the reactor (assumed isothermal) at any time is in which t₀ = [(w/pV) + k^'''₁].

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wto pV, wto -t/ta + /tot pV CA CAO