Question

the rate law for the reaction $3a\
ightarrow 2b$ is rate=$ka$ with a rate constant of $0.0447\\ h^{-1}$. what is the half-life of this reaction?
0.0645 h
22.4 h
0.0224 h
44.7 h
15.5 h

Explanation:

Step1: Identify reaction order

The rate law $\text{rate}=k[\text{A}]$ shows this is a first-order reaction.

Step2: Recall first-order half-life formula

For first-order reactions, $t_{\frac{1}{2}}=\frac{\ln 2}{k}$

Step3: Substitute values and calculate

Substitute $k=0.0447\ \text{h}^{-1}$ and $\ln 2\approx0.693$:
$t_{\frac{1}{2}}=\frac{0.693}{0.0447\ \text{h}^{-1}}\approx15.5\ \text{h}$

Answer:

15.5 h