For a first order reaction, the half-life period is independent of

Options

A. initial concentration
B. cube root of initial concentration
C. first power of final concentration
D. square root of final concentration

Explanation

To solve the question regarding the half-life period of a first-order reaction and its independence from various factors, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Half-Life in First-Order Reactions**:
- The half-life (\( t_{1/2} \)) of a reaction is the time required for the concentration of a reactant to decrease to half of its initial value.
- For a first-order reaction, the half-life is given by the formula:
\[ t_{1/2} = \frac{0.693}{k} \]
where \( k \) is the rate constant of the reaction.

2. **Analyzing the Formula**:
- From the formula, we can observe that \( t_{1/2} \) depends only on the rate constant \( k \) and is independent of the initial concentration of the reactant.
- This means that regardless of how much reactant you start with, the half-life remains constant as long as the rate constant \( k \) is unchanged.

3. **Identifying Independence from Concentrations**:
- The question asks about the independence of the half-life period from various forms of concentration:
- Initial concentration
- Cube root of initial concentration
- First power of final concentration
- Square root of final concentration
- Since the half-life does not depend on any of these concentrations, we can conclude that it is indeed independent of them.

4. **Conclusion**:
- Therefore, the half-life period of a first-order reaction is independent of the initial concentration, cube root of initial concentration, first power of final concentration, and square root of final concentration.

### Final Answer:
The half-life period of a first-order reaction is independent of:
- Initial concentration
- Cube root of initial concentration
- First power of final concentration
- Square root of final concentration