In which of these cyclic compounds you find the minimum angle strain?

Options

A. `C_3H_6`
B. `C_4H_8`
C. `C_5H_10`
D. `C_6H_12`

Answer

To determine which cyclic compound has the minimum angle strain, we need to analyze the angle strain associated with each of the given cyclic compounds: C3H6 (cyclopropane), C4H8 (cyclobutane), C5H10 (cyclopentane), and C6H12 (cyclohexane).

### Step-by-step Solution:

1. **Identify the Compounds:**
- C3H6 is cyclopropane.
- C4H8 is cyclobutane.
- C5H10 is cyclopentane.
- C6H12 is cyclohexane.

2. **Determine the Hybridization:**
- All the compounds are made up of carbon atoms that are sp³ hybridized since they are cycloalkanes. Each carbon in these compounds forms four sigma bonds and has no lone pairs.

3. **Calculate the Ideal Bond Angle:**
- For sp³ hybridized carbon, the ideal bond angle is approximately 109.5 degrees.

4. **Analyze Each Compound:**
- **Cyclopropane (C3H6):**
- The structure is triangular, and the bond angles are 60 degrees.
- Angle strain = Ideal angle (109.5°) - Actual angle (60°) = 49.5°.

- **Cyclobutane (C4H8):**
- The structure is square-like, and the bond angles are approximately 90 degrees.
- Angle strain = Ideal angle (109.5°) - Actual angle (90°) = 19.5°.

- **Cyclopentane (C5H10):**
- The structure is pentagonal, and the bond angles are approximately 108 degrees.
- Angle strain = Ideal angle (109.5°) - Actual angle (108°) = 1.5°.

- **Cyclohexane (C6H12):**
- The structure can adopt a chair conformation, which allows for bond angles close to 109.5 degrees.
- Angle strain is minimal, effectively 0° in the chair form.

5. **Conclusion:**
- Among the compounds analyzed, cyclohexane (C6H12) has the least angle strain due to its ability to adopt a stable chair conformation with bond angles very close to the ideal angle of 109.5 degrees.

Thus, the cyclic compound with the minimum angle strain is **C6H12 (cyclohexane)**.