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

Options

A. is halved
B. is doubled
C. is tripled
D. remains unchanged.

Explanation

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

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

### Step 2: Write the Integrated Rate Equation
For a zero-order reaction, the integrated rate equation is given by:
\[ [A] = [A_0] - kt \]
where:
- \( [A] \) is the concentration of the reactant at time \( t \),
- \( [A_0] \) is the initial concentration,
- \( k \) is the rate constant,
- \( t \) is the time.

### Step 3: Define Half-Life for Zero-Order Reactions
The half-life (\( t_{1/2} \)) is defined as the time required for the concentration of the reactant to decrease to half of its initial value. For a zero-order reaction, the half-life can be calculated as:
\[ t_{1/2} = \frac{[A_0]}{2k} \]

### Step 4: Analyze the Effect of Doubling the Initial Concentration
If the initial concentration is doubled, we set:
\[ [A_0] = 2A \]
Then, the new half-life becomes:
\[ t'_{1/2} = \frac{2A}{2k} = \frac{A}{k} \]

### Step 5: Compare the Two Half-Lives
Now, we can compare the original half-life and the new half-life:
- Original half-life: \( t_{1/2} = \frac{A}{2k} \)
- New half-life: \( t'_{1/2} = \frac{A}{k} \)

From this comparison, we see that:
\[ t'_{1/2} = 2 \times t_{1/2} \]
Thus, when the initial concentration is doubled, the half-life of the zero-order reaction is also doubled.

### Conclusion
When the initial concentration of the reactant in a zero-order reaction is doubled, the half-life period is doubled.

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