Which of the following isomerization reactions is/are of the first order?

Options

A. `"Cylopropane" rarr "Propane"`
B. cis-But-`2`-ene`rarr`Trans-but-`2`-ene
C. Vinyl allyl ether `rarr` Pent-`4`-enal
D. `CH_(3)NCrarrCH_(3)CN`

Answer

To determine which of the given isomerization reactions are of the first order, we need to understand the definition of isomerization reactions and first-order kinetics.

### Step-by-Step Solution:

1. **Understanding Isomerization Reactions**:
- Isomerization reactions involve the conversion of one isomer into another. Isomers are compounds that have the same molecular formula but different structural arrangements.

2. **Identifying the Reactions**:
- The question provides four options of isomerization reactions. We need to analyze each reaction to see if it fits the criteria for first-order kinetics.

3. **Criteria for First-Order Reactions**:
- A reaction is classified as first order if the rate of the reaction depends on the concentration of one reactant raised to the power of one. This means that the rate law can be expressed as:
\[ \text{Rate} = k[\text{A}]^1 \]
- Here, \(k\) is the rate constant, and \([\text{A}]\) is the concentration of the reactant.

4. **Analyzing Each Option**:
- For each of the provided isomerization reactions, we check if they have only one reactant and if the rate can be expressed as a function of that reactant's concentration raised to the first power.
- For example:
- **Cyclopropane to Propene**: The reaction can be expressed as Rate = k[cyclopropane]^1, indicating it is first order.
- **Cis-Butyrene to Trans-Butyrene**: Similarly, this can be expressed as Rate = k[cis-butyrene]^1, indicating it is first order.
- **Other reactions**: The same analysis applies to the remaining options.

5. **Conclusion**:
- Since all the reactions provided in the options have only one reactant and follow the first-order rate law, we conclude that all options (A, B, C, and D) are first-order reactions.

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