Chemistry - Chemical Kinetics Question with Solution | TestHub

For a first order reaction, the rate constant $k$ is inversely proportional to the half-life $t_{1/2}$:

$k=\frac{0.693}{t_{1/2}}$

Given the half-lives of reactions A and B:

$(t_{1/2}{)}_A=75$ min

$(t_{1/2}{)}_B=2.5$ hour $=2.5\times 60=150$ min

The ratio of the rate constants is:

$\frac{r_B}{r_A}=\frac{k_B}{k_A}=\frac{(t_{1/2}{)}_A}{(t_{1/2}{)}_B}$

$\frac{r_B}{r_A}=\frac{75}{150}=0.5$

Answer: $0.5$