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 rate constant of a first-order reaction given its half-life, we can use the relationship between half-life and the rate constant for first-order reactions.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- The half-life (\( t_{1/2} \)) of the reaction is given as 69.35 seconds.

2. **Use the Formula for Half-Life of a First-Order Reaction:**
- The formula for the half-life of a first-order reaction is:
\[ t_{1/2} = \frac{0.693}{k} \]
where \( k \) is the rate constant.

3. **Rearrange the Formula to Solve for \( k \):**
- To find the rate constant \( k \), we can rearrange the formula:
\[ k = \frac{0.693}{t_{1/2}} \]

4. **Substitute the Given Half-Life into the Formula:**
- Now, substitute \( t_{1/2} = 69.35 \) seconds into the rearranged formula:
\[ k = \frac{0.693}{69.35} \]

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

6. **Round the Value Appropriately:**
- Rounding \( 0.00997 \) gives approximately \( 0.01 \, \text{s}^{-1} \).

7. **Final Answer:**
- Therefore, the value of the rate constant \( k \) is:
\[ k \approx 0.01 \, \text{s}^{-1} \]