Question

The total number of isomers of molecular formula \(\mathrm{C}_{4} \mathrm{H}_{6}\) containing at least one ring is (A) 3 (B) 5 (C) 2 (D) 4

Short answer

The molecular formula C4H6 has a degree of unsaturation of 2, meaning it can have a ring with a double bond, two rings, or two double bonds. Since we are only considering isomers with at least one ring, there are 4 possible isomers: cyclobutene, methylcyclopropane, 1,2-dimethylcyclopropane, and bicyclo[1.1.0] butane (which has two rings). Each structure is unique and thus is an individual isomer of C4H6. So, the answer is (D) 4.

Step-by-step solution

Understand the general structure of the molecule

A molecule with the formula C4H6 will have a degree of unsaturation of 2. This means it can either have a ring and a double bond, two rings, or two double bonds. However, since this exercise is focused on isomers containing at least one ring, we can rule out the scenario of two double bonds.

Draw initial structure of the molecule

Start with drawing a simple ring of the four carbon atoms, and assign the remaining hydrogens in a way that each carbon atom is tetravalent (forming four bonds), which is the standard in organic chemistry.

Identify possible variations

Now, in order to generate isomers, we can either modify the internal structure (arrangement of atoms), add an additional ring, or add a double bond within the ring or outside of it.

Draw all possible structures

Carefully draw out all the possibilities identified in the previous step. Remember to not create structures that result in any carbon atoms forming more than four bonds.

Determine the isomers

There are 4 possible isomers with at least one ring: cyclobutene, methylcyclopropane, 1,2-dimethylcyclopropane and bicyclo[1.1.0] butane (which has two rings). Each structure is unique and thus is an individual isomer of C4H6. So, the answer is (D) 4.

Key concepts

Degree of Unsaturation

The degree of unsaturation in a molecular formula refers to the total number of pi bonds and rings in the structure. An easy way to determine this is to use the formula: \[ \text{Degree of Unsaturation} = \frac{2C + 2 + N - X - H}{2} \] where \( C \) is the number of carbon atoms, \( N \) is the number of nitrogen atoms, \( X \) is the number of halogens, and \( H \) is the number of hydrogens. For the compound \( \mathrm{C}_{4}\mathrm{H}_{6} \), applying this formula gives: \[ \frac{2(4) + 2 - 6}{2} = 2 \] This indicates there are two unsaturation units, which could be either two double bonds, a ring and a double bond, or two rings. This information helps us identify possible structures you might draw for isomers.

Ring Structures

Ring structures are closed loops of atoms, typically carbon. In organic chemistry, these are called cyclic compounds. Rings create interesting possibilities for shape and properties. In the context of C4H6, creating ring structures can involve forming:

• Cyclobutene, a four-membered ring with a double bond.
• Methylcyclopropane, which is a three-membered ring with a methyl group attached.
• 1,2-Dimethylcyclopropane, another three-membered ring but with two methyl groups.
• Bicyclo[1.1.0]butane, a two-ring system where two rings are fused together.

Each of these variations contributes a distinct isomer for the chemical formula, highlighting the diversity of cyclic molecular structures.

Isomer Identification

Isomers are molecules with the same chemical formula but different structures. Identifying isomers involves recognizing the different possible arrangements of atoms. For C4H6, we must ensure each potential isomer adheres to the chemical formula and satisfies the degree of unsaturation. Isomer identification starts by deciding whether an isomer will contain rings or double bonds and then exploring possibilities within those choices. To be precise:

• Check if the total bonds (including rings and double bonds) match the unsaturation degree.
• Modify positions of atoms like methyl groups within the ring.
• Don’t overlook stereochemistry when relevant, as it can also yield different isomers.

Efficient isomer identification leads to discovering all unique structural possibilities for the molecular formula.

Carbon Bonding Rules

Understanding carbon bonding rules is crucial when drawing and identifying organic molecules. Carbon generally forms four bonds, which can be a mix of single, double, or triple bonds. For every carbon atom in a molecule, check the surrounding atoms to ensure no carbon exceeds four bonds. This is because carbon has a valency of four. When drawing molecules like isomers of C4H6, ensure:

• All carbons have a complete octet (i.e., they are surrounded by four bonds).
• Double check that no carbons make more than four bonds by mistake.
• Pay attention to the potential formation of radical species, which are usually avoided in stable compounds.

By applying these rules, one ensures structural correctness which simplifies the process of identifying valid isomers.