34% decomposition means that 66% of the compound remained, meaning the ratio of current to initial concentration after 43 minutes was 0.66. The decomposition equation:
ln[A] = ln[Ao] - kt
ln( [A] / [Ao] ) = -kt
Now, we substitute the given values:
ln(0.66) = -k(43)
k = 9.66 x 10⁻³
half life = ln(2) / k
half life = 71.8 minutes.
