The half-life of a first order reaction is 25 minutes. Its rate constant is:
Answer & explanation
Correct answer: option 4
The correct answer is option 4. \(2.8 × 10^{-2} min^{-1}\).
The half-life (\(t_{1/2}\)) of a first-order reaction is related to the rate constant (\(k\)) by the equation:
\(t_{1/2} = \frac{0.693}{k}\)
Given that the half-life (\(t_{1/2}\)) of the reaction is 25 minutes, we can rearrange the equation to solve for the rate constant (\(k\)):
\(k = \frac{0.693}{t_{1/2}} \)
Substituting the given value of \(t_{1/2}\) into the equation, we get:
\( k = \frac{0.693}{25\, \text{min}} \)
\( k \approx 0.02772 \, \text{min}^{-1} \)
Rounding to the appropriate number of significant figures, we get:
\(k \approx 2.8 \times 10^{-2} \, \text{min}^{-1} \)
So, the correct answer is: (4) \(2.8 \times 10^{-2} \, \text{min}^{-1}\)