After 41.0 min, 22.0% of a compound has decomposed. What is the half‑life of this reaction assuming first‑order kinetics?

Question

How many minutes would it take?

Answer 1

For any first order reaction a simple formula to use is the following:

Fraction remaining (FR) = 0.5ⁿ where n = the number of half lives elapsed

In this problem, we need to find n first, and then convert that to minutes.

FR = 100% - 22% = 78% - 0.78 (as a fraction)

0.78 = 05ⁿ

log 0.78 = n log 0.5

-0.1079 = -0.301 n

n = 0.358 half lives have elapsed

Since this is equal to 41.0 minutes, we can find the value of 1 half life.

41/x = 0.358 / 1

x = 115 minutes is the half life