Question

1. For a first order decay of [A], if 525 mg remains of an initial sample of 1.3079 g after 361 min, what is the half life (in minutes)?

2. The decay of antimony-131 is first order with a half life is 23.03 minutes. How much of 1.4228 g sample would remain after 1.368 hours?

3. The decay of antimony-131 is first order with a half life is 23.03 minutes. How long (in minutes) would it take for a 0.8893 g sample to be reduced to 0.3082 g?

Answer 1

1)
we have:
[A]o = 1.3079 g
[A] = 525 mg = 0.525 g
t = 361 min


use integrated rate law for 1st order reaction
ln[A] = ln[A]o - k*t
ln(0.525) = ln(1.308) - k*3.61*10^2
-0.6444 = 0.2684 - k*3.61*10^2
k*3.61*10^2 = 0.9128
k = 2.528*10^-3 min-1
Given:
k = 2.528*10^-3 min-1
use relation between rate constant and half life of 1st order reaction

t1/2 = (ln 2) / k
= 0.693/(k)
= 0.693/(2.528*10^-3)
= 2.741*10^2 min
Answer: 274.1 min

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