Question:
The rate constant for first order reaction is 0.02232 min\(^{-1}\). Calculate the time required for 75% completion of the reaction.
The rate constant for first order reaction is 0.02232 min\(^{-1}\). Calculate the time required for 75% completion of the reaction.
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For first-order reactions, use the formula \( t = \frac{2.303}{k} \log \left( \frac{1}{1 - x/100} \right) \) to calculate time for a given percentage completion.
Updated On: Jan 26, 2026
- 62.12 min
- 38.31 min
- 12.77 min
- 48.12 min
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The Correct Option is A
Solution and Explanation
Step 1: Using the first-order reaction equation.
For a first-order reaction, the time for a certain percentage completion can be calculated using the equation: \[ t = \frac{2.303}{k} \log \left( \frac{1}{1 - \frac{x}{100}} \right) \] Where \( k = 0.02232 \, \text{min}^{-1} \) and \( x = 75 % \).
Step 2: Calculation.
Substitute the values: \[ t = \frac{2.303}{0.02232} \log \left( \frac{1}{1 - \frac{75}{100}} \right) = 62.12 \, \text{min} \] Step 3: Conclusion.
The correct answer is (A) 62.12 min.
For a first-order reaction, the time for a certain percentage completion can be calculated using the equation: \[ t = \frac{2.303}{k} \log \left( \frac{1}{1 - \frac{x}{100}} \right) \] Where \( k = 0.02232 \, \text{min}^{-1} \) and \( x = 75 % \).
Step 2: Calculation.
Substitute the values: \[ t = \frac{2.303}{0.02232} \log \left( \frac{1}{1 - \frac{75}{100}} \right) = 62.12 \, \text{min} \] Step 3: Conclusion.
The correct answer is (A) 62.12 min.
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