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The half-life of a second order reaction is dependent on reactant concentration. The second order half-life is the time it takes for [A]t in 1/[A]t = 1/[A]o + kt to become half of [A]o. Substituting in [A]o/2 for [A]t yields that the half-life is 1/k[A]o. That is, the half life is inversely proportional to the initial concentration of the reactant A.
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