Which order reaction obeys the expression `t_(1//2)prop1[A]` ?

Options

A. (a) First
B. (b) Second
C. (c) Third
D. (d) Zero

Answer

To determine which order of reaction obeys the expression \( t_{1/2} \propto \frac{1}{[A]} \), we can analyze the relationship between half-life (\( t_{1/2} \)) and the concentration of the reactant (\( [A] \)) for different orders of reactions.

### Step-by-Step Solution:

1. **Understanding Half-Life**:
The half-life 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 varies with the order of the reaction.

2. **General Relation**:
The general relation for half-life in terms of concentration for a reaction of order \( n \) is given by:
\[ t_{1/2} \propto \frac{1}{[A]^{n-1}} \]
Here, \( n \) is the order of the reaction.

3. **Analyzing Different Orders**:
- **Zero Order Reaction** (\( n = 0 \)):
\[ t_{1/2} \propto \frac{1}{[A]^{-1}} \quad \text{(directly proportional to [A])} \]
- **First Order Reaction** (\( n = 1 \)):
\[ t_{1/2} \propto \frac{1}{[A]^{0}} \quad \text{(independent of concentration)} \]
- **Second Order Reaction** (\( n = 2 \)):
\[ t_{1/2} \propto \frac{1}{[A]^{1}} \quad \text{(inversely proportional to [A])} \]
- **Third Order Reaction** (\( n = 3 \)):
\[ t_{1/2} \propto \frac{1}{[A]^{2}} \quad \text{(more complex relationship)} \]

4. **Conclusion**:
From the analysis, we see that the expression \( t_{1/2} \propto \frac{1}{[A]} \) holds true for a **second order reaction**. Therefore, the answer to the question is that the reaction that obeys the expression is a **second order reaction**.