For a first-order reaction, the rate law is given by $\text{Rate} = k[A]$. Given: $\text{Rate} = 1.5 \times 10^{-2} \text{ mol L}^{-1} \text{ min}^{-1}$ Concentration $[A] = 0.5 \text{ M}$

First, we calculate the rate constant ($k$): $k = \frac{\text{Rate}}{[A]} = \frac{1.5 \times 10^{-2}}{0.5} = 3.0 \times 10^{-2} \text{ min}^{-1}$

The half-life ($t_{1/2}$) of a first-order reaction is related to the rate constant by the formula: $t_{1/2} = \frac{0.693}{k}$

Substituting the value of $k$: $t_{1/2} = \frac{0.693}{3.0 \times 10^{-2}} = 23.1 \text{ min}$.