Which of the following is the most stable cycloalkane ?

Options

A.
B.
C.
D.

Answer

To determine which cycloalkane is the most stable among the given options, we need to analyze the angle strain associated with each cycloalkane. Here's a step-by-step solution:

### Step 1: Understand Angle Strain
Angle strain occurs when the bond angles in a molecule deviate from the ideal bond angles of the hybridization involved. For sp³ hybridized carbon, the ideal bond angle is 109.5°.

### Step 2: Identify the Cycloalkanes
Let's consider the following cycloalkanes:
- Cyclopropane (C3H6)
- Cyclobutane (C4H8)
- Cyclopentane (C5H10)
- Cyclohexane (C6H12)

### Step 3: Determine the Bond Angles
- **Cyclopropane**: The bond angle is 60°.
- **Cyclobutane**: The bond angle is approximately 90°.
- **Cyclopentane**: The bond angle is approximately 108°.
- **Cyclohexane**: The bond angle is approximately 109.5° in its chair conformation.

### Step 4: Calculate Angle Strain
Now, we calculate the angle strain for each cycloalkane by comparing their bond angles to the ideal angle of 109.5°:
- **Cyclopropane**: 109.5° - 60° = 49.5° (high strain)
- **Cyclobutane**: 109.5° - 90° = 19.5° (moderate strain)
- **Cyclopentane**: 109.5° - 108° = 1.5° (low strain)
- **Cyclohexane**: 109.5° - 109.5° = 0° (no strain)

### Step 5: Determine Stability
The stability of cycloalkanes is inversely proportional to their angle strain. Therefore, the cycloalkane with the least angle strain is the most stable:
- Cyclohexane has no angle strain and is the most stable.
- Cyclopentane has very low strain.
- Cyclobutane has moderate strain.
- Cyclopropane has high strain and is the least stable.

### Conclusion
Thus, the most stable cycloalkane among the given options is **Cyclohexane**.