Question

For a reaction with a rate constant \( k = 10^{-3} \), how long will it take for the reaction to reach 100% completion?

• A. 30 min
• B. 40 min
• C. 60 min
• D. 20 min

Hint:

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.

Answer 1

The Correct Option is D

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.