The rate of a first-order reaction is $5.6 \times 10^{-4}$ mol L$^{-1}$s$^{-1}$ when the concentration of reactant is $0.2$ mol L$^{-1}$. The rate constant $k$ is:
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- $5.6 \times 10^{-3}$ s$^{-1}$
- $2.8 \times 10^{-4}$ s$^{-1}$
- $2.8 \times 10^{-5}$ s$^{-1}$
- $2.8 \times 10^{-3}$ s$^{-1}$
The Correct Option is D
Solution and Explanation
For a first-order reaction, the rate law is: $\text{Rate} = k[A]^1$.
Step 2: Analysis
Rearranging: $k = \dfrac{\text{Rate}}{[A]}$.
Step 3: Calculation
$k = \dfrac{5.6 \times 10^{-4}}{0.2} = \dfrac{5.6 \times 10^{-4}}{2 \times 10^{-1}} = 2.8 \times 10^{-3}$ s$^{-1}$.
Final Answer: (D)
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