Question

The rate of first order reaction \( A \rightarrow B \) is \( 6.3 \times 10^{-6} \, \text{M s}^{-1} \). If \( [A] = 0.3 \, \text{M} \), what is the rate constant of the reaction?

• A. \( 2.1 \times 10^{-5} \, \text{s}^{-1} \)
• B. \( 1.2 \times 10^{-5} \, \text{s}^{-1} \)
• C. \( 1.3 \times 10^{-5} \, \text{s}^{-1} \)
• D. \( 1.6 \times 10^{-5} \, \text{s}^{-1} \)

Hint:

For first order reactions, the unit of rate constant is always \( \text{s}^{-1} \).

Answer 1

The Correct Option is A

Step 1: Writing the rate law for first order reaction.
For a first order reaction, the rate law is:
\[ \text{Rate} = k[A] \]

Step 2: Substituting given values.
Given:
\[ \text{Rate} = 6.3 \times 10^{-6} \, \text{M s}^{-1}, \quad [A] = 0.3 \, \text{M} \]

Step 3: Calculating rate constant.
\[ k = \frac{\text{Rate}}{[A]} = \frac{6.3 \times 10^{-6}}{0.3} = 2.1 \times 10^{-5} \, \text{s}^{-1} \]

Step 4: Conclusion.
The correct value of the rate constant is option (A).