……………………… reaction obeys the expresison `t_(1//2) = 1//ka` in chemical kinetics.

Answer

To solve the question regarding which reaction obeys the expression \( t_{1/2} = \frac{1}{k[A_0]} \) in chemical kinetics, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Expression**: The expression \( t_{1/2} = \frac{1}{k[A_0]} \) represents the half-life of a reaction, where:
- \( t_{1/2} \) is the half-life,
- \( k \) is the rate constant,
- \( [A_0] \) is the initial concentration of the reactant.

2. **Identify the Order of Reaction**: In chemical kinetics, different orders of reactions have different expressions for their half-lives:
- **Zero-order reactions**: \( t_{1/2} = \frac{[A_0]}{2k} \)
- **First-order reactions**: \( t_{1/2} = \frac{0.693}{k} \)
- **Second-order reactions**: \( t_{1/2} = \frac{1}{k[A_0]} \)

3. **Match the Expression to Reaction Order**: From the above information, we can see that the expression \( t_{1/2} = \frac{1}{k[A_0]} \) specifically corresponds to second-order reactions.

4. **Conclusion**: Therefore, the reaction that obeys the expression \( t_{1/2} = \frac{1}{k[A_0]} \) is a **second-order reaction**.

### Final Answer:
The reaction that obeys the expression \( t_{1/2} = \frac{1}{k[A_0]} \) is a **second-order reaction**.