Many chemical reactions are the result of the interaction of two molecules that undergo a change to produce a new product. The rate of the reaction typically depends on the concentrations of the two kinds of molecules. If a is the amount of substance A and b is the amount of substance B at time t = 0, and if x is the amount of product at time t, then the rate of formation of x may be given by the differential equation

where k is a constant for the reaction. Integrate both sides of this equation to obtain a relation between x and t 

(a) If a = b, and

(b) If a ≠ b. Assume in each case that x = 0 when t = 0.

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or xp dt = k(a - - x)(b − x), 1 (a − x)(b - - dx ¹p (x - q)(x = k,