The half life for a zero order reaction having 0.02M initial concentration of reactant is 100s. The rate constant (in `molL^(-1)S^(-1)`) for the reaction is

Options

A. `1.0xx10^(-4)`
B. `2.0xx10^(-4)`
C. `2.0xx10^(-3)`
D. `1.0xx10^(-2)`

Answer

To find the rate constant \( k \) for a zero-order reaction given the half-life and initial concentration, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Zero-Order Reactions:**
The half-life (\( T_{1/2} \)) for a zero-order reaction is given by the formula:
\[ T_{1/2} = \frac{A_0}{2k} \]
where \( A_0 \) is the initial concentration and \( k \) is the rate constant.

2. **Rearranging the Formula:**
We can rearrange the formula to solve for the rate constant \( k \):
\[ k = \frac{A_0}{2T_{1/2}} \]

3. **Substituting the Given Values:**
We are given:
- Initial concentration \( A_0 = 0.02 \, \text{M} \)
- Half-life \( T_{1/2} = 100 \, \text{s} \)

Now substitute these values into the rearranged formula:
\[ k = \frac{0.02}{2 \times 100} \]

4. **Calculating the Rate Constant:**
Performing the calculation:
\[ k = \frac{0.02}{200} = 0.0001 \, \text{mol L}^{-1} \text{s}^{-1} \]

5. **Expressing in Scientific Notation:**
We can express \( 0.0001 \) in scientific notation:
\[ k = 1 \times 10^{-4} \, \text{mol L}^{-1} \text{s}^{-1} \]

### Final Answer:
The rate constant \( k \) for the reaction is:
\[ k = 1 \times 10^{-4} \, \text{mol L}^{-1} \text{s}^{-1} \]