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: Key Formula:
For a first order reaction, \(t_{1/2} = \dfrac{0.693}{k}\).

Step 2: Calculate:
\[ k = \frac{0.693}{20\ \text{min}} = 0.03465\ \text{min}^{-1} \approx 0.0347\ \text{min}^{-1} \]

Step 3: Other options:
\(13.86\) is \(0.693\times20\), which multiplies instead of dividing. \(34.67\) is the same mistake with a factor of \(1000\) slip. \(0.5\) has no link to \(0.693/20\), and it would give a half life of only about \(1.4\) min.

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