Which of the following reaction `(s)` is `//` are of the first order ?

Options

A. The decompoistion of ammonium nitrate in an aqueous solution.
B. The inverison of cane sugar in the presence of an acid.
C. The acidic hydrolyiss of ethyl acetate.
D. All radioactive decays.

Answer

To determine which of the given reactions are of the first order, we need to understand the characteristics of first-order reactions. A first-order reaction is defined as one where the rate of reaction depends on the concentration of one reactant raised to the power of one.

Let's analyze the reactions one by one:

1. **Decomposition of Ammonium Nitrate (NH4NO3)**:
- The reaction can be represented as:
\[ NH4NO3 \rightarrow N2O + 2 H2O \]
- In this reaction, the rate depends on the concentration of ammonium nitrate. Since it depends on one reactant and the power is one, this is a first-order reaction.

2. **Inversion of Cane Sugar (C12H22O11)**:
- The reaction can be represented as:
\[ C12H22O11 + H2O \rightarrow C6H12O6 + C6H12O6 \]
- In this case, the reaction occurs in the presence of an acid, and water is in excess. Therefore, the rate depends primarily on the concentration of sucrose. This makes it a first-order reaction as well.

3. **Hydrolysis of Ethyl Acetate (CH3COOCH2CH3)**:
- The reaction can be represented as:
\[ CH3COOCH2CH3 + H2O \rightarrow CH3COOH + CH3OH \]
- Similar to the previous reactions, water is in excess, and the rate depends on the concentration of ethyl acetate. Hence, this is also a first-order reaction.

4. **Radioactive Decay**:
- Radioactive decay can be represented as:
\[ N \rightarrow N - \text{decay products} \]
- All radioactive decay processes are inherently first-order reactions, as the rate of decay is proportional to the number of undecayed nuclei present.

Based on the analysis above, all the reactions listed (A, B, C, and D) are first-order reactions.

### Final Answer:
All of the reactions (A, B, C, and D) are of the first order.