In an elementary chemical reaction, single molecules of two reactants A and B form a molecule of the product C: A + B → C. The law of mass action states that the rate of reaction is proportional to the product of the concentrations of A and B: d[C]/dt=k[A][B]. Thus, if the initial concentrations are [A] = a moles/L and [B] = b moles/L and we write x = [C], then we have dx/dt = k(a-x)(b-x). Assuming that a ≠ b, find x as a function of t. Use the fact that the initial concentration of C is 0.
