Question

In a first order reaction, $N_2O_5(g) \rightarrow 2NO_2(g) + \frac{1}{2}O_2(g)$, the initial concentration of $N_2O_5$ was $1.6 \times 10^{-3} mol\,lit^{-1}$ at $300\,K$. The concentration of $N_2O_5$ after 23 minutes was $0.8 \times 10^{-3} mol\,lit^{-1}$. ($\log 2 = 0.3010$). Find the rate constant.

• A. $0.04\,min^{-1}$
• B. $0.06\,min^{-1}$
• C. $0.3\,min^{-1}$
• D. $0.6\,min^{-1}$
• E. $0.03\,min^{-1}$

Hint:

For first order reactions, half-life concept simplifies calculations.

Answer 1

Answer: (E)

Concept: \[ k = \frac{2.303}{t} \log \frac{[A]_0}{[A]} \]

Step 1: Substitute values
\[ k = \frac{2.303}{23} \log \frac{1.6\times10^{-3}}{0.8\times10^{-3}} = \frac{2.303}{23} \log 2 \]

Step 2: Solve
\[ k = \frac{2.303 \times 0.3010}{23} \approx \frac{0.693}{23} \approx 0.03 \] Final Conclusion:
Option (E)