Question

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 __________.

Answer 1

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.