The rate first order reaction is `2.4 xx 10^(-3) mol L^(-1) s^(-1)`, when the initial concentration is `0.2 mol L^(-1)`. The rate constant is…………. .

Answer

To find the rate constant (k) for a first-order reaction, we can use the relationship between the rate of the reaction (R), the rate constant (k), and the concentration of the reactant (A). The formula for a first-order reaction is given by:

\[ R = k \cdot [A] \]

Where:
- \( R \) is the rate of the reaction,
- \( k \) is the rate constant,
- \( [A] \) is the concentration of the reactant.

### Step-by-Step Solution:

1. **Identify the given values:**
- Rate of reaction (R) = \( 2.4 \times 10^{-3} \, \text{mol L}^{-1} \text{s}^{-1} \)
- Initial concentration ([A]) = \( 0.2 \, \text{mol L}^{-1} \)

2. **Substitute the values into the equation:**
\[ R = k \cdot [A] \]
\[ 2.4 \times 10^{-3} = k \cdot 0.2 \]

3. **Rearrange the equation to solve for k:**
\[ k = \frac{R}{[A]} = \frac{2.4 \times 10^{-3}}{0.2} \]

4. **Calculate the value of k:**
\[ k = \frac{2.4 \times 10^{-3}}{0.2} = 12 \times 10^{-3} \, \text{s}^{-1} \]

5. **Final answer:**
\[ k = 1.2 \times 10^{-2} \, \text{s}^{-1} \]

### Summary:
The rate constant \( k \) for the first-order reaction is \( 1.2 \times 10^{-2} \, \text{s}^{-1} \).