A first-order reaction has a half-life of 20 seconds. Calculate the rate constant for this reaction. GIve your answer to 3 decimal places.

1. Break Down the Problem

To find the rate constant ($k$) for a first-order reaction, we use the relationship between the half-life ($t_{1/2}$) and the rate constant.

2. Relevant Concepts

For a first-order reaction, the half-life is given by the formula: $t_{1/2} = \frac{0.693}{k}$ where:

• $t_{1/2}$ is the half-life,
• $k$ is the rate constant.

3. Analysis and Detail

Given that the half-life $t_{1/2}$ is 20 seconds, we can rearrange the formula to solve for $k$: $k = \frac{0.693}{t_{1/2}}$ Now substituting $t_{1/2}$: $k = \frac{0.693}{20 \, \text{s}}$

Calculating the value: $k = 0.03465 \, \text{s}^{-1}$

4. Verify and Summarize

Rounding $k$ to three decimal places: $k \approx 0.035 \, \text{s}^{-1}$

Final Answer

The rate constant for the reaction is $k = 0.035 \, \text{s}^{-1}$.