Question

The rate constant for first order reaction is 0.02232 min\(^{-1}\). Calculate the time required for 75% completion of the reaction.

• A. 62.12 min
• B. 38.31 min
• C. 12.77 min
• D. 48.12 min

Hint:

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.

Answer 1

The Correct Option is A

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.