If the half-life of a reaction increases as the initial concentration of substance increases, the order of the reaction is :

Options

A. zero
B. First
C. second
D. third

Answer

To determine the order of the reaction based on the given condition that the half-life of a reaction increases as the initial concentration of the substance increases, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Half-Life**: The half-life (t₁/₂) of a reaction is the time required for the concentration of a reactant to decrease to half of its initial concentration. The relationship between half-life and concentration can vary depending on the order of the reaction.

2. **Rate Law Expression**: The rate of a reaction can be expressed as:
\[ \text{Rate} = k [A]^n \]
where \(k\) is the rate constant, \([A]\) is the concentration of the reactant, and \(n\) is the order of the reaction.

3. **Differential Rate Expression**: We can express the rate of change of concentration as:
\[ -\frac{d[A]}{dt} = k [A]^n \]

4. **Integrating the Rate Law**: To find the relationship between concentration and time, we integrate the rate law. Rearranging gives:
\[ -\frac{d[A]}{[A]^n} = k dt \]
Integrating both sides will yield different expressions based on the value of \(n\).

5. **Half-Life Expressions**:
- For **Zero Order Reaction** (\(n = 0\)):
\[ t_{1/2} = \frac{[A]_0}{2k} \]
Here, \(t_{1/2}\) is directly proportional to the initial concentration \([A]_0\). As \([A]_0\) increases, \(t_{1/2}\) increases.

- For **First Order Reaction** (\(n = 1\)):
\[ t_{1/2} = \frac{0.693}{k} \]
Here, \(t_{1/2}\) is independent of the initial concentration. Thus, increasing \([A]_0\) does not affect \(t_{1/2}\).

- For **Second Order Reaction** (\(n = 2\)):
\[ t_{1/2} = \frac{1}{k[A]_0} \]
Here, \(t_{1/2}\) is inversely proportional to the initial concentration. As \([A]_0\) increases, \(t_{1/2}\) decreases.

6. **Conclusion**: Since the problem states that the half-life increases with increasing initial concentration, the only scenario that fits this condition is for a zero-order reaction. Therefore, the order of the reaction is **zero order**.

### Final Answer:
The order of the reaction is **zero order**.