when initial concentration of the reactant is doubled, the half-life period of a zero order reaction

Options

A. Is tripled
B. Is doubled
C. Is halved
D. Remains unchanged

Explanation

To solve the question regarding the effect of doubling the initial concentration on the half-life period of a zero-order reaction, we can follow these steps:

### Step-by-Step Solution:

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

2. **Define Initial Conditions**:
Let the initial concentration of the reactant be \([A_0]\). Therefore, the half-life for this concentration is:
\[ T_1 = \frac{[A_0]}{2k} \]

3. **Consider the New Concentration**:
When the initial concentration is doubled, the new concentration becomes:
\[ [A_0'] = 2[A_0] \]
Now, we can calculate the new half-life (T_2) using the doubled concentration:
\[ T_2 = \frac{[A_0']}{2k} = \frac{2[A_0]}{2k} = \frac{[A_0]}{k} \]

4. **Relate the Two Half-Lives**:
We can express \(T_2\) in terms of \(T_1\):
\[ T_2 = \frac{[A_0]}{k} = 2 \cdot \frac{[A_0]}{2k} = 2T_1 \]
This shows that the new half-life \(T_2\) is twice the original half-life \(T_1\).

5. **Conclusion**:
Therefore, when the initial concentration of the reactant is doubled, the half-life period of a zero-order reaction also doubles.

### Final Answer:
When the initial concentration of the reactant is doubled, the half-life period of a zero-order reaction is doubled.

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