Question

The half-life of a first-order reaction is \(20\) minutes. What is the rate constant (in min\(^{-1}\)) for this reaction?

• A. \(0.0347\)
• B. \(0.5\)
• C. \(13.86\)
• D. \(34.67\)

Hint:

Use \(k = 0.693/t_{1/2}\).

Answer 1

The Correct Option is A

Step 1: Via the integrated law:
At the half life, $[A] = [A]_0/2$, so $kt_{1/2} = \ln 2$.
\[ k = \frac{\ln 2}{20} = \frac{0.6931}{20} = 0.0347\ \text{min}^{-1} \]

Final Answer:
The rate constant is $0.0347$ min$^{-1}$, option (A). \[ \boxed{0.0347\ \text{min}^{-1}} \]