Question

Reaction given below follows first order kinetics.
2N\(_2\)O\(_5\) \(\rightarrow\) 4NO\(_2\) + O\(_2\)
Calculate rate constant of reaction if concentration of N\(_2\)O\(_5\) is 0.05 M and rate of reaction is \(1.5 \times 10^{-6}\) mol L\(^{-1}\) s\(^{-1}\).

• A. \(3.0 \times 10^{-5}\ \text{s}^{-1}\)
• B. \(2.0 \times 10^{-5}\ \text{s}^{-1}\)
• C. \(2.5 \times 10^{-5}\ \text{s}^{-1}\)
• D. \(1.5 \times 10^{-5}\ \text{s}^{-1}\)

Hint:

For first order reactions, rate constant is obtained by dividing rate by concentration.

Answer 1

The Correct Option is A

Step 1: Write the rate law for first order reaction.
\[ \text{Rate} = k[\mathrm{N_2O_5}] \]
Step 2: Substitute given values.
\[ 1.5 \times 10^{-6} = k \times 0.05 \]
Step 3: Solve for rate constant \(k\).
\[ k = \frac{1.5 \times 10^{-6}}{0.05} \]
\[ k = 3.0 \times 10^{-5}\ \text{s}^{-1} \]
Step 4: Conclusion.
The rate constant of the reaction is \(3.0 \times 10^{-5}\ \text{s}^{-1}\).