Which of the following does not represent a first order reation?

Options

A. Hydrogenation of ethene
B. radioactive decay
C. decomposition of `H_(2)O_(2)`
D. Alkaline hydrolysis of ester

Explanation

To determine which of the given reactions does not represent a first-order reaction, we need to analyze each option based on the rate law and how the rate of reaction depends on the concentration of reactants.

### Step-by-Step Solution:

1. **Understanding First-Order Reactions**:
- A first-order reaction is one where the rate of reaction is directly proportional to the concentration of one reactant. The rate law can be expressed as:
\[ \text{Rate} = k[A] \]
- Here, \( k \) is the rate constant and \( [A] \) is the concentration of the reactant.

2. **Analyzing the Hydrogenation of Ethene**:
- The reaction can be written as:
\[ \text{C}_2\text{H}_4(g) + \text{H}_2(g) \rightarrow \text{C}_2\text{H}_6(g) \]
- The rate expression is:
\[ \text{Rate} = k[\text{C}_2\text{H}_4] \]
- This indicates that the rate depends only on the concentration of ethene, thus it is a first-order reaction.

3. **Analyzing Radioactive Decay**:
- For radioactive decay, the general form is:
\[ \text{Rate} = k[N] \]
- Where \( N \) is the quantity of the radioactive substance. This also shows that the rate depends on a single concentration term, confirming that it is a first-order reaction.

4. **Analyzing the Decomposition of H2O2**:
- The decomposition reaction can be represented as:
\[ 2 \text{H}_2\text{O}_2 \rightarrow 2 \text{H}_2\text{O} + \text{O}_2 \]
- The rate expression is:
\[ \text{Rate} = k[\text{H}_2\text{O}_2] \]
- This indicates that the rate depends only on the concentration of hydrogen peroxide, confirming it is also a first-order reaction.

5. **Analyzing Alkaline Hydrolysis of an Ester**:
- For the hydrolysis of an ester, consider the reaction:
\[ \text{CH}_3\text{COOC}_2\text{H}_5 + \text{NaOH} \rightarrow \text{CH}_3\text{COONa} + \text{C}_2\text{H}_5\text{OH} \]
- The rate expression can be written as:
\[ \text{Rate} = k[\text{CH}_3\text{COOC}_2\text{H}_5][\text{NaOH}] \]
- Here, the rate depends on the concentrations of both the ester and sodium hydroxide, indicating that it is not a first-order reaction.

### Conclusion:
- The reaction that does not represent a first-order reaction is the **alkaline hydrolysis of the ester**.