Half-life, t_{1/2}, is the time for the amount of a reactant to reduce to half of its initial value. For the first order decomposition of hydrogen peroxide, the rate equation is given by eq13 of the previous article: .
Assuming that volume of the reacting mixture remains constant, the ratio of the amounts of peroxide, n, at t = t and t = 0 is the same as the ratio of the concentrations of peroxide, , at t = t and t = 0. Hence, hydrogen peroxide’s half-life is the time taken for its initial concentration to fall to half, i.e.:
Eq19 shows that the half-life of a species in a first order reaction does not depend on its concentration and only depends on the rate constant, k, of the reaction.
Experimental data for the decomposition of H_{2}O_{2} with an initial concentration of 8.96×10^{-2 }M is presented in the diagram above. The 1^{st} half-life of H_{2}O_{2} is about 480s. The 2^{nd} and 3^{rd} half-lives, which are the time taken for M to fall to M and M respectively, are also about 480s each. Hence, the experimental value of the successive half-lives of the first order decomposition of H_{2}O_{2} is a constant and is consistent with the theoretically derived eq19.
Using eq15 and eq17 from the previous article, the half-lives of a zero order reaction and a second order reaction for a chemical species A,are
and
respectively.
In summary,
Order |
Simple rate equation | Integral rate equation |
Half-life |
0 | |||
1 | |||
2 |
Next, we shall explore the various methods in monitoring the progress of a reaction and analysing the data obtained.