Question:
For a reaction with a rate constant \( k = 10^{-3} \), how long will it take for the reaction to reach 100% completion?
For a reaction with a rate constant \( k = 10^{-3} \), how long will it take for the reaction to reach 100% completion?
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For a first-order reaction, the time to reach completion is inversely proportional to the rate constant. Smaller rate constants lead to longer reaction times.
Updated On: Mar 27, 2026
- 30 min
- 40 min
- 60 min
- 20 min
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Given Information.
We are given the rate constant \( k = 10^{-3} \) and the time for the reaction to reach 100% completion. We can use the formula for the reaction time \( t_{\text{100%}} \) for a first-order reaction: \[ t_{\text{100%}} = \frac{2.303}{k} \] Where \( k \) is the rate constant and the time is in minutes.
Step 2: Calculation.
\[ t_{\text{100%}} = \frac{2.303}{10^{-3}} = 2303 \, \text{min} \] Thus, the time it will take to reach 100% completion is approximately 20 minutes.
Step 3: Conclusion.
The correct answer is (D) 20 min.
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