The initial concentration of $N_2O_5$ in the first order reaction,$N_2O_5 \rightarrow 2NO_{2(g)} + \frac{1}{2}O_{2(g)}$ was $1.24 \times 10^{-2} \ mol \ L^{-1}$ at $300 \ K$ temperature. The concentration of $N_2O_5$ after $60 \ min$ was $0.20 \times 10^{-2} \ mol \ L^{-1}.$ Calculate the rate constant of the reaction.

(N/A) For a first order reaction,the rate constant $k$ is given by the formula: $k = \frac{2.303}{t} \log \frac{[A]_0}{[A]_t}$
Given:
Initial concentration $[A]_0 = 1.24 \times 10^{-2} \ mol \ L^{-1}$
Final concentration $[A]_t = 0.20 \times 10^{-2} \ mol \ L^{-1}$
Time $t = 60 \ min$
Substituting the values:
$k = \frac{2.303}{60} \log \frac{1.24 \times 10^{-2}}{0.20 \times 10^{-2}}$
$k = \frac{2.303}{60} \log(6.2)$
$k = \frac{2.303}{60} \times 0.7924$
$k \approx 0.0304 \ min^{-1}$