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

Concept: For a first-order reaction, the half-life is independent of the initial concentration and is given by the formula: \[ t_{1/2} = \frac{0.693}{k} \] where \(t_{1/2}\) = half-life of the reaction, \(k\) = rate constant of the reaction.

Step 1: Substitute the given value of the rate constant. \[ k = 0.693 \, \text{min}^{-1} \] \[ t_{1/2} = \frac{0.693}{0.693} \]

Step 2: Simplify the expression. \[ t_{1/2} = 1 \, \text{min} \]