Question

After 54.0 min, 34.0% of a compound has decomposed. What is the half-life of this reaction assuming first-order kinetics?

Answer 1

\[\ln[A]t = -kt + \ln[A]_{0}\\ \ln[1-0.34] - \ln[1] = -kt\\ln[\frac{0.34}] = \]

Answer 2

\[\ln[0.66] = -k(54\min) \\ k = \frac{\ln(0.66)}{54\min} = 0.00769 \]

Answer 3

\[t_\frac{1}{2} = \frac{\ln2}{k} = \frac{0.693}{0.00769} = 90.136 \min\]