The half life of a first order reaction is 100 seconds at 280K. If the temperature coefficient is 3.0 its rate constant at 290 K in s^–1 is

Temperature coefficient = 3

for every 10⁰ rise or fall in temperature rate either increases or decreases by a factor 3

${\mathrm{K}}_{290}={\mathrm{K}}_{280}\times 3$

$$\begin{gathered} {\mathrm{K}}_{290}=\frac{0.693}{100}\times 3 \\ =2.079\times {10}^{-2}\cong 2.08\times {10}^{-2} \end{gathered}$$