The angle strain in cyclohexane is :

Options

A. `9^(@), 44'`
B. `0^(@), 44'`
C. `-5^(@), 36'`
D. `5^(@), 36'`

Answer

To determine the angle strain in cyclohexane, we can follow these steps:

### Step 1: Understand the Structure of Cyclohexane
Cyclohexane is a cyclic alkane with the molecular formula C6H12. Its structure allows for a chair conformation, which minimizes strain.

### Step 2: Identify the Ideal Bond Angle
In a perfect tetrahedral geometry, the ideal bond angle is approximately 109.5 degrees (or 109 degrees 28 minutes). This is the angle that carbon atoms prefer to adopt when they are sp3 hybridized.

### Step 3: Determine the Actual Bond Angle in Cyclohexane
In the chair conformation of cyclohexane, the bond angles are close to 109.5 degrees. However, in some representations, it may appear that the bond angles are around 120 degrees due to the way the molecule is drawn.

### Step 4: Calculate the Angle Strain
According to Baeyer's strain theory, the angle strain can be calculated using the formula:

\[ \text{Angle Strain} = \frac{1}{2} \left( \text{Ideal Bond Angle} - \text{Actual Bond Angle} \right) \]

Here, we will consider the ideal bond angle as 109 degrees 28 minutes (which is approximately 109.5 degrees) and the actual bond angle as 120 degrees.

### Step 5: Perform the Calculation
1. Convert the angles to a consistent format if necessary:
- Ideal Bond Angle = 109 degrees 28 minutes
- Actual Bond Angle = 120 degrees

2. Calculate the difference:
\[ \text{Difference} = 109^\circ 28' - 120^\circ = -10^\circ 72' \]

3. Convert the difference to decimal if needed:
- -10 degrees 72 minutes can be converted to -11 degrees (since 72 minutes = 1 degree).

4. Now, apply the formula:
\[ \text{Angle Strain} = \frac{1}{2} \times (-11^\circ) = -5.5^\circ \]

### Step 6: Conclusion
The angle strain in cyclohexane is approximately -5.5 degrees, indicating that there is a slight strain due to the deviation from the ideal tetrahedral angle.

### Final Answer
The angle strain in cyclohexane is approximately -5 degrees 36 minutes.

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