Question

10. The half life of 18F is 1.83 hours. How long before 99.99% of the initial 18F has decayed in this first order reaction?

Answer 1

Given:

Half life = 1.83 hr

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

k = (ln 2) / k

= 0.693/(half life)

= 0.693/(1.83)

= 0.3787 hr-1

we have:

[18F]o = 100 M (Let initial concentration be 100 M)

since 99.99 % has decomposed, remaining is 100 - 99.99 = 0.01 %

[18F] = 0.01% of 100 M = 0.01 M

k = 0.3787 hr-1

use integrated rate law for 1st order reaction

ln[18F] = ln[18F]o - k*t

ln(0.01) = ln(100) - 0.3787*t

-4.6052 = 4.6052 - 0.3787*t

0.3787*t = 9.2103

t = 24.3 hr

Answer: 24.3 hr