For a zero order reaction, the half-life periof is independent of the initial concentration.

Answer

To determine whether the statement "For a zero-order reaction, the half-life period is independent of the initial concentration" is true or false, we need to analyze the half-life expression for a zero-order reaction.

### Step-by-Step Solution:

1. **Understanding Zero-Order Reactions**:
- A zero-order reaction is one where the rate of reaction is constant and does not depend on the concentration of the reactants. The rate law for a zero-order reaction can be expressed as:
\[ \text{Rate} = k \]
where \( k \) is the rate constant.

2. **Deriving the Half-Life Expression**:
- The integrated rate law for a zero-order reaction is given by:
\[ [A] = [A]_0 - kt \]
where \([A]\) is the concentration of the reactant at time \( t \), \([A]_0\) is the initial concentration, and \( k \) is the rate constant.

3. **Finding Half-Life**:
- The half-life (\( t_{1/2} \)) is the time required for the concentration of the reactant to decrease to half of its initial concentration. Setting \([A] = \frac{1}{2}[A]_0\) in the integrated rate equation gives:
\[ \frac{1}{2}[A]_0 = [A]_0 - kt_{1/2} \]
- Rearranging this equation leads to:
\[ kt_{1/2} = [A]_0 - \frac{1}{2}[A]_0 = \frac{1}{2}[A]_0 \]
- Thus, we can solve for \( t_{1/2} \):
\[ t_{1/2} = \frac{[A]_0}{2k} \]

4. **Analyzing the Result**:
- From the derived expression \( t_{1/2} = \frac{[A]_0}{2k} \), we can see that the half-life (\( t_{1/2} \)) is directly proportional to the initial concentration \([A]_0\). This means that as the initial concentration increases, the half-life also increases.

5. **Conclusion**:
- Therefore, the statement "For a zero-order reaction, the half-life period is independent of the initial concentration" is **false**. In fact, the half-life is dependent on the initial concentration.