Half-life of a Reaction The half-life, t1/2, of a reaction is the amount of time it will take the concentration, [A], of a reactant to reduce to half its initial concentration, [Ao]. That is to say, @ t1/2, [A] = [Ao]/2 ...……(i) The half-life of the various orders of reaction can be calculated by substituting the above equation into the respective integrated rate laws. ( a) Half-life of a Zeroth-Order Reaction Recall that the zeroth-order integrated rate law is given by: [A] = [Ao] - kt …………(ii) [Ao] - [A] = kt @ t1/2, [A] = [Ao]/2 kt1/2 = [Ao] - ([Ao]/2) kt1/2 = (2[Ao] - [Ao])/2 kt1/2 = [Ao]/2 t1 /2 = [ Ao ]/2k …………(iii) Equation (iii) above, gives the half-life for a zeroth-order reaction, which can be obtained by finding the product of half the initial reactant concentration and the reciprocal of the reaction rate constant ([Ao]/2 × 1/k). (b) H alf-
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