Question

Please explain procedure. The first-order decay of radon has a half-life of 3.823 days. How many grams of radon remain after 7.22 days if the sample initially weighs 250.0 grams?

Answer 1

Given:

Half life = 3.823 days

All decays are 1st order reaction

use relation between rate constant and half life of 1st order reaction

k = (ln 2) / k

= 0.693/(half life)

= 0.693/(3.823)

= 0.1813 days-1

we have:

[Radon]o = 250.0 gram

t = 7.22 days

k = 0.1813 days-1

Given:

[Radon]o = 250 M

use integrated rate law for 1st order reaction

ln[Radon] = ln[Radon]o - k*t

ln[Radon] = ln(250) - 0.1813*7.22

ln[Radon] = 5.521461 - 0.1813*7.22

ln[Radon] = 4.212682

[Radon] = 67.54 grams

Answer: 67.54 grams