Question

Cycloalkanes are a group of cyclic saturated hydrocarbons with a general formula of ${\mathrm{C}}_n{\mathrm{H}}_3$. Which of the following compounds will display the LEAST amount of free rotation around a $\mathrm{C}-\mathrm{C}$ single bond? A. alkanes, which are relatively inert chemically B. alkanes, which are able to form numerous types of isomers C. cycloalkanes, which are limited by geometric constraints D. cycloalkanes, which are polar and water soluble

Short answer

C. cycloalkanes, which are limited by geometric constraints

Step-by-step solution

- Understand the question

Identify which type of compound will display the least amount of free rotation around a carbon-carbon single bond.

- Analyze the options

Evaluate each option to determine its characteristics related to free rotation around a C-C bond.

- Review characteristics of alkanes

Recognize that alkanes are saturated hydrocarbons with free rotation around C-C single bonds, and thus do not have restrictions on rotation unless there are large substituents or constraints.

- Review characteristics of cycloalkanes

Understand that cycloalkanes are cyclic, meaning the carbon atoms form a ring. This ring structure imposes geometric constraints that restrict the rotation around C-C bonds.

- Analyze the constraints imposed on cycloalkanes

Consider that the ring structure of cycloalkanes significantly limits the free rotation around the C-C bonds due to the fixed angles in the cyclic structure.

- Identify the correct choice

Given the constraints on rotation in cycloalkanes due to their ring structure, determine that cycloalkanes (especially choice C) will display the least amount of free rotation around a C-C single bond.

Key concepts

Free Rotation in Organic Molecules

In organic chemistry, the term 'free rotation' refers to the ability of atoms in a molecule to rotate around a single bond. Generally, single bonds (sigma bonds) allow such rotation because they create an axis that lets atoms turn around freely. For example, in alkanes, carbon atoms connected by single bonds can rotate with ease.
However, if there are large substituents or specific structural constraints, this rotation can be hindered. Free rotation is important in determining the flexibility and shape of the molecule. A molecule with unrestricted rotation can adopt various conformations, which influences its properties and behavior.

Cyclic Hydrocarbons

Cyclic hydrocarbons are organic compounds where carbon atoms are connected in a ring. This group includes cycloalkanes, which are saturated (only single bonds) and have the general formula of ${\text{C}}_n{\text{H}}_{2}n$. The ring structure of cyclic hydrocarbons differentiates them from alkanes, which have an open chain structure.
Because the atoms form a closed loop, the structure imposes certain geometric constraints that affect the molecule’s physical and chemical properties. For example, the ring can result in stability differences and different kinds of reactivity, in contrast to open-chain hydrocarbons.

Geometric Constraints in Cycloalkanes

Cycloalkanes have unique geometric constraints due to their ring structure. The carbon atoms in a ring are forced into specific angles to maintain the cyclic formation. This limits the free rotation about the C-C single bonds found in cycloalkanes.
In smaller rings like cyclopropane or cyclobutane, the bond angles deviate significantly from the ideal tetrahedral angle (109.5 degrees), causing strain. This strain further restricts the rotation of the C-C bonds. Larger rings like cyclohexane have less angle strain and might adopt conformations like chair or boat forms to relieve it, but still, the constraints are more rigid than in alkanes.
This geometric rigidity is a key reason why cycloalkanes display the least amount of free rotation around carbon-carbon single bonds among the given options in the exercise.