Question

In Baeyer strain theory, which cycloalkane is more stable?

• A. Cyclopropane
• B. Cyclobutane
• C. Cyclopentane
• D. Cyclooctane

Hint:

Remember: Cyclopentane has minimal angle strain and is considered most stable according to Baeyer's angle strain theory — important for understanding ring stability in GPAT.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Baeyer strain theory says a cycloalkane ring is most stable when its internal bond angle is closest to the natural tetrahedral angle of carbon, about 109.5 degrees. Moving away from this angle in either direction adds angle strain and lowers stability.

Step 2: Key Formula or Approach:
For a flat regular polygon ring with n sides, the internal angle can be estimated using
\[ \text{Internal angle} = \frac{(n-2) \times 180^{\circ}}{n} \]
Comparing this angle for each ring size against 109.5 degrees shows which ring has the least strain.

Step 3: Detailed Explanation:
For cyclopropane, n is 3, giving an internal angle of 60 degrees, far below the ideal value and producing large angle strain.
For cyclobutane, n is 4, giving an internal angle of 90 degrees, closer to ideal than cyclopropane but still noticeably strained.
For cyclopentane, n is 5, giving an internal angle of 108 degrees, within about 1.5 degrees of the ideal tetrahedral angle, so this ring carries almost no angle strain.
For cyclooctane, n is 8, and the flat polygon formula gives an internal angle of 135 degrees, well above the ideal value, though real cyclooctane puckers out of plane and also picks up torsional strain from its larger, flexible structure.

Step 4: Final Answer:
Cyclopentane has an internal angle closest to the ideal tetrahedral value, making it the most stable cycloalkane among the four according to Baeyer strain theory.