Question

Calculate the half-life of a first-order reaction if the rate constant is \(0.693\, \text{min}^{-1}\).

• A. \(10\) min
• B. \(1\) min
• C. \(0.5\) min
• D. \(6.93\) min

Hint:

For first-order reactions, remember that the half-life formula is \(t_{1/2} = \frac{0.693}{k}\). The half-life does not depend on the initial concentration of reactants.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
We are required to determine the time taken for the concentration of a reactant to reduce to half its initial value for a first-order kinetics process.
Step 2: Key Formula or Approach:
For a first-order reaction, the half-life (\( t_{1/2} \)) is related to the rate constant (\( k \)) by the expression:
\[ t_{1/2} = \frac{\ln(2)}{k} \approx \frac{0.693}{k} \]
Step 3: Detailed Explanation:
The given rate constant \( k = 0.693 \, \text{min}^{-1} \).
Plugging this into the half-life formula:
\[ t_{1/2} = \frac{0.693}{0.693 \, \text{min}^{-1}} \]
\[ t_{1/2} = 1 \, \text{min} \]
Step 4: Final Answer:
The half-life of the reaction is \( 1 \) minute.