The half life of a first order reaction is 69.35 sec. The value of the rate constant of the reaction is

Options

A. `1.0 sec^(-1)`
B. `0.1 sec^(-1)`
C. `0.01 sec^(-1)`
D. `0.001 sec^(-1)`

Answer

To find the value of the rate constant (k) for a first-order reaction given its half-life (t₁/₂), we can use the relationship between half-life and the rate constant for first-order reactions. The formula for the half-life of a first-order reaction is:

\[ t_{1/2} = \frac{0.693}{k} \]

### Step-by-Step Solution:

1. **Identify the given data**:
- Half-life (t₁/₂) = 69.35 seconds.

2. **Use the half-life formula for first-order reactions**:
- Rearranging the formula to solve for k gives:
\[ k = \frac{0.693}{t_{1/2}} \]

3. **Substitute the value of half-life into the equation**:
- Substitute t₁/₂ = 69.35 seconds into the equation:
\[ k = \frac{0.693}{69.35} \]

4. **Calculate the value of k**:
- Performing the calculation:
\[ k = \frac{0.693}{69.35} \approx 0.00997 \, \text{s}^{-1} \]

5. **Round the value**:
- Rounding to two decimal places gives:
\[ k \approx 0.01 \, \text{s}^{-1} \]

6. **Final answer**:
- The value of the rate constant k is approximately **0.01 s⁻¹**.