A first order reaction has `t_(1//2) = 6.93 min`. The rate constant is……….. .

Answer

To find the rate constant (k) for a first-order reaction given the half-life (t₁/₂), we can use the formula for the half-life of a first-order reaction:

### Step-by-Step Solution:

1. **Identify the formula for half-life of a first-order reaction:**
The half-life (t₁/₂) for a first-order reaction is given by the formula:
\[ t_{1/2} = \frac{0.693}{k} \]

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

3. **Substitute the given half-life into the equation:**
We are given that the half-life (t₁/₂) is 6.93 minutes. Substitute this value into the equation:
\[ k = \frac{0.693}{6.93 \text{ min}} \]

4. **Calculate the value of k:**
Now, perform the calculation:
\[ k = \frac{0.693}{6.93} \approx 0.1 \text{ min}^{-1} \]

5. **Final result:**
The rate constant (k) for the reaction is approximately:
\[ k \approx 0.1 \text{ min}^{-1} \]