Question

Calculate the half-life of a first order reaction if the rate constant of the reaction is $2.772 \times 10^{-3}\,\text{s}^{-1}$.

• A. 125 s
• B. 250 s
• C. 100 s
• D. 150 s

Hint:

Kinetics Tip: Note that for a first-order reaction, the half-life is constant and does not depend on the initial concentration of the reactant.

Answer 1

The Correct Option is B

Concept: Chemistry (Chemical Kinetics) - Half-life of First Order Reactions.

Step 1: Identify the given value. Rate constant ($k$) = $2.772 \times 10^{-3} s^{-1}$.

Step 2: State the formula for half-life. For a first-order reaction, the half-life ($t_{1/2}$) is calculated using: $$ t_{1/2} = \frac{0.693}{k} \text{} $$

Step 3: Substitute and calculate. $$ t_{1/2} = \frac{0.693}{2.772 \times 10^{-3} s^{-1}} \text{} $$ $$ t_{1/2} = \frac{0.693}{0.002772} s \text{} $$ $$ t_{1/2} = 250 \text{ s} \text{} $$ $$ \therefore \text{The half-life of the reaction is 250 seconds.} $$