The reaction that obeys the expression `t_(1/2) = 1/(Ka)` the order of reaction

Options

A. 0
B. 1
C. 2
D. 3

Explanation

To determine the order of the reaction given the expression for half-life \( t_{1/2} = \frac{1}{k_a} \), we will analyze the relationship between the half-life and the rate constant for different orders of reactions.

### Step-by-Step Solution:

1. **Understanding Half-Life Expressions**:
- The half-life of a reaction is the time required for the concentration of a reactant to reduce to half its initial value. The expression for half-life varies depending on the order of the reaction.

2. **General Expression for Half-Life**:
- For different orders of reactions, the half-life expressions are:
- **Zero-order reaction**:
\[ t_{1/2} = \frac{[A]_0}{2k} \]
- **First-order reaction**:
\[ t_{1/2} = \frac{0.693}{k} \]
- **Second-order reaction**:
\[ t_{1/2} = \frac{1}{k[A]_0} \]

3. **Comparing Given Expression**:
- The given expression is \( t_{1/2} = \frac{1}{k_a} \). This expression does not include the concentration of the reactant \( [A] \).

4. **Testing Different Orders**:
- **Zero-order**: The half-life depends on the initial concentration, so it cannot be equal to \( \frac{1}{k_a} \).
- **First-order**: The half-life is independent of concentration but is expressed as \( \frac{0.693}{k} \), which does not match the given expression.
- **Second-order**: The half-life is given by \( t_{1/2} = \frac{1}{k[A]_0} \), which indicates that it depends on the initial concentration. However, if we consider the scenario where the concentration is constant or not specified, we can simplify to \( t_{1/2} = \frac{1}{k} \) when we assume \( [A]_0 = 1 \).

5. **Conclusion**:
- The only scenario where \( t_{1/2} = \frac{1}{k_a} \) holds true without any concentration dependence is for a second-order reaction when we assume a specific initial concentration. Thus, the order of the reaction is **second order**.

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