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 solve the problem, we need to find the rate constant \( k \) for a zero-order reaction given the half-life and the initial concentration of the reactant.

### Step-by-Step Solution

1. **Understand the Formula for Half-Life of a Zero-Order Reaction**:
The half-life (\( T_{1/2} \)) for a zero-order reaction is given by the formula:
\[ T_{1/2} = \frac{R_0}{2k} \]
where \( R_0 \) is the initial concentration of the reactant and \( k \) is the rate constant.

2. **Identify Given Values**:
From the problem, we have:
- Initial concentration (\( R_0 \)) = 0.02 M
- Half-life (\( T_{1/2} \)) = 100 s

3. **Substitute the Values into the Formula**:
We can rearrange the half-life formula to solve for \( k \):
\[ k = \frac{R_0}{2T_{1/2}} \]
Now substitute the known values:
\[ k = \frac{0.02 \, \text{mol/L}}{2 \times 100 \, \text{s}} \]

4. **Calculate the Rate Constant**:
Simplifying the equation:
\[ k = \frac{0.02}{200} \]
\[ k = 0.0001 \, \text{mol/L/s} = 1 \times 10^{-4} \, \text{mol/L/s} \]

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