Question

The half life period of a first order chemical reaction is 6.93 minutes. The time required for the completion of 99% of the chemical reaction will be

• A. 23.03 minutes
• B. 46.06 minutes
• C. 460.6 minutes
• D. 230.03 minutes

Hint:

For a first-order reaction, the time required for a specific percentage of completion can be calculated using the integrated rate law.

Answer 1

The Correct Option is B

Step 1: Use the first-order reaction half-life formula.
For a first-order reaction, the half-life (\( t_{1/2} \)) is given by: \[ t_{1/2} = \frac{0.693}{k} \] where \( k \) is the rate constant. For 99% completion, the time can be calculated using: \[ t = \frac{2.303}{k} \log \left(\frac{1}{1-0.99}\right) \]
Step 2: Conclusion.
The time required for 99% completion of the reaction is 46.06 minutes.
Final Answer: \[ \boxed{46.06 \, \text{minutes}} \]