Which cycloalkane has the lowest heat of combustion per `CH_2` group

Options

A. Cyclopropane
B. Cyclobutane
C. Cyclopentane
D. Cyclohexane

Explanation

To determine which cycloalkane has the lowest heat of combustion per CH₂ group, we can analyze the heat of combustion (HOC) for each cycloalkane: cyclopropane, cyclobutane, cyclopentane, and cyclohexane.

### Step-by-Step Solution:

1. **Understanding Heat of Combustion**:
The heat of combustion is the amount of energy released when a compound is completely burned in oxygen. For cycloalkanes, the heat of combustion is influenced by the strain in the ring structure.

2. **Analyzing Cycloalkanes**:
- **Cyclopropane (C₃H₆)**: This has a three-membered ring, which experiences significant angle strain due to the bond angles being 60°, much less than the ideal tetrahedral angle of 109.5°. Therefore, it has a high heat of combustion.
- **Cyclobutane (C₄H₈)**: This four-membered ring has less strain than cyclopropane, but still has some angle strain. Its heat of combustion is lower than that of cyclopropane.
- **Cyclopentane (C₅H₁₀)**: The five-membered ring has even less strain, leading to a lower heat of combustion compared to cyclobutane.
- **Cyclohexane (C₆H₁₂)**: This six-membered ring is the most stable and has minimal strain, resulting in the lowest heat of combustion among the four cycloalkanes.

3. **Calculating Heat of Combustion per CH₂ Group**:
- For each cycloalkane, we will calculate the heat of combustion per CH₂ group:
- Cyclopropane: HOC / 3
- Cyclobutane: HOC / 4
- Cyclopentane: HOC / 5
- Cyclohexane: HOC / 6

4. **Comparison**:
- Since cyclohexane has the lowest overall heat of combustion, when we divide it by the number of CH₂ groups (6), it results in the lowest heat of combustion per CH₂ group compared to the others.

5. **Conclusion**:
Therefore, the cycloalkane with the lowest heat of combustion per CH₂ group is **cyclohexane**.