Question

Draw the five cycloalkanes with the formula \(\mathrm{C}_{5} \mathrm{H}_{10}\) -

Short answer

Draw cyclopentane, a methyl-substituted cyclobutane, and ethyl or dimethyl-substituted cyclopropanes.

Step-by-step solution

Understand the Cycloalkane Formula

For cycloalkanes, the general formula is \\(\mathrm{C}_n\mathrm{H}_{2n}\). Since we are given \(\mathrm{C}_5\mathrm{H}_{10}\), \it confirms that we are dealing with rings (not straight chains or alkenes). This means there will be five carbon atoms forming a ring.

Identify Possible Cycloalkane Structures

Since we need to draw cycloalkanes with the formula \(\mathrm{C}_5\mathrm{H}_{10}\), \we will explore different ways to form five carbon rings, including possible geometric and conformational isomers.

Draw Cyclopentane

The simplest cycloalkane is cyclopentane, which is a five-carbon ring with no branches or substitutions. Draw a pentagon to represent this ring.

Consider Methyl-Substituted Cyclobutanes

Another possibility is to have four carbon atoms in a square (cyclobutane) with a methyl group (\(\mathrm{CH}_3\)) attached to one of the carbons. Draw the square and add a methyl group as a branch.

Contemplate Ethyl or Dimethyl-Substituted Cyclopropanes

Similarly, you can have three carbon atoms in a triangle (cyclopropane) with two carbon atoms as substituents. This can be either an ethyl group or two methyl groups on any of the carbons in cyclopropane. Draw the triangle and add the branches accordingly.

Key concepts

Cyclopentane

Cyclopentane is one of the simplest and most fundamental cycloalkanes, made up solely of carbon and hydrogen atoms. It is comprised of a ring of five carbon atoms, each bonded to two hydrogen atoms, forming a total of ten hydrogen atoms. The structure resembles a regular pentagon, though in reality, the molecule is not perfectly planar due to the natural spatial orientations of the atoms involved.

• The formula of cyclopentane is \(\mathrm{C}_5\mathrm{H}_{10}\), ensuring its classification as a cycloalkane because it fits the general formula \(\mathrm{C}_n\mathrm{H}_{2n}\).
• Cyclopentane is notable for the fact it does not have any branches or substitutions, making it a simple and clear representation of a five-membered cyclic structure.

Cyclopentane is known for having a certain degree of flexibility, allowing it to adopt slight variations in its conformation, such as envelope or half-chair conformations. These conformations help reduce the angle strain and torsional strain that may arise in cyclic compounds.

Methyl-Substituted Cyclobutane

Methyl-substituted cyclobutane illustrates another way to conform to the cycloalkane formula of \(\mathrm{C}_5\mathrm{H}_{10}\). In this structure, the core is a cyclobutane ring – a square made up of four carbon atoms. By adding a methyl group \((\mathrm{CH}_3)\) as a substituent to any of the carbon atoms, we keep the carbon count at five, fitting the molecular composition.

• The core cyclobutane structure contributes four carbons to the structure, while the methyl group provides the fifth carbon required.
• This type of substitution offers room for various geometric isomers, depending on which carbon the methyl group attaches to.

The cyclobutane ring itself is known for having substantial angle strain because its internal angles are significantly less than the ideal tetrahedral angle. However, by opening up the ring and attaching a methyl group, some of this strain can be relieved, allowing it to exist as a viable compound.

Cyclopropane Isomers

Cyclopropane is the smallest cycloalkane, containing only three carbon atoms linked in a triangular formation. To reach the formula \(\mathrm{C}_5\mathrm{H}_{10}\), cyclopropane must have extra groups appended to its structure, such as ethyl or dimethyl.

• An ethyl-substituted cyclopropane involves one ethyl group \((\mathrm{CH}_2\mathrm{CH}_3)\) attached to one of the carbons in the cyclopropane ring.
• Alternatively, using two methyl groups \((\mathrm{CH}_3)\) as branches can form isomeric structures if these are placed on different or the same carbon atom.

The cyclopropane ring itself tends to have significant angle strain due to the compact triangle shape, which severely limits its flexibility and stability. Despite this, the addition of substituents can create interesting structural diversity and render the molecule more accessible for certain chemical reactions, leading to various isomeric forms.