For this problem, we use the integrated rate law for first order decay which is expressed as follows: An = Aoe^-kt where An is the amount left after time t, Ao is the initial amount and k is a constant. We, first, need to calculate for the constant k by using the given ratio of An and Ao at a given time. We calculate k as follows:An = Aoe^-kt .25 =e^-k(60)k = 0.023 / min At half-life, the ratio of An and Ao is equal to 1/2 or .50. We calculate the half-life as follows: An = Aoe^-kt 0.5 = e^-0.023 (t)t = 30 minutes The half-life of the compound would be 30 minutes.
A compound decomposes by a first-order process. if 25.0% of the compound decomposes in 60.0 minutes, the half-life of the compound is __________.