Question

The total number of possible acyclic isomers of molecular formula \(\mathrm{C}_{5} \mathrm{H}_{10}\) is (A) 7 (B) 6 (C) 5 (D) 4

Short answer

The total number of possible acyclic isomers of molecular formula C5H10 can be found by calculating the degrees of unsaturation and then enumerating all possible structures. In this case, the degree of unsaturation equals 0, meaning there are no double bonds, triple bonds, or rings in the molecule. Generating the isomers, we find the following structures: n-pentane, 2-methylbutane, 2,2-dimethylpropane, 3-methylpentane, and 2-methylpentane. Only these 5 isomers fulfill the given molecular formula C5H10, so the correct option is (C) 5.

Step-by-step solution

Calculate the Degrees of Unsaturation

Calculate the degrees of unsaturation for the given molecular formula using the formula: \(Degrees~of~Unsaturation = \frac{(2 * number~of~Carbons + 2 - number~of~Hydrogens)}{2}\). In this case, that would be: \[\frac{(2 * 5 + 2 - 10)}{2}\] Degrees of Unsaturation = \(\frac{10 - 10}{2}\) = 0. This means that the molecular formula has 0 double bonds, 0 triple bonds, and no rings.

Generate the Isomers

Enumerate all the possible structures with 5 carbon atoms and 10 hydrogen atoms, with a degree of unsaturation equal to 0. Keep in mind that we are considering only acyclic structures. 1. n-pentane: \(CH_{3}-CH_{2}-CH_{2}-CH_{2}-CH_{3}\) 2. 2-methylbutane: \(CH_{3}-CH_{2}-CH(CH_{3})-CH_{3}\) 3. 2,2-dimethylpropane: \(CH_{3}-C(CH_{3})_{2}-CH_{3}\) 4. 3-methylpentane: \(CH_{3}-CH_{2}-CH(CH_{3})-CH_{2}-CH_{3}\) 5. 2-methylpentane: \(CH_{3}-CH(CH_{3})-CH_{2}-CH_{2}-CH_{3}\) 6. n-hexane: \(CH_{3}-CH_{2}-CH_{3}-CH_{2}-CH_{2}-CH_{3}\) From the above isomers, only the first 5 isomers fit the given molecular formula C5H10. As a result, we have a total of 5 possible acyclic isomers.

Select the Correct Option

From the number of isomers we counted, we can now choose the correct option from the list provided in the exercise. 5 isomers correspond to option (C). So, the final answer is (C) 5.

Key concepts

Degrees of Unsaturation

Understanding how to calculate the degrees of unsaturation is crucial in organic chemistry, especially for identifying the bonding structure of a molecule. The degrees of unsaturation refer to the number of pi bonds or rings that a molecule can potentially accommodate based on its molecular formula.

To compute the degrees of unsaturation, you can use the simple formula: \[\begin{equation}Degrees~of~Unsaturation = \frac{2n + 2 - h}{2}\end{equation}\]where n stands for the number of carbon atoms and h for the number of hydrogen atoms. In our example with the molecular formula \[\begin{equation}\mathrm{C}_{5}\mathrm{H}_{10}\end{equation}\], we obtain a result of zero, signifying that the molecule has no double bonds, triple bonds, or rings that would indicate saturation. This initial step is very helpful for setting the foundation for the structural isomer enumeration, as it limits the types of bonds that need to be considered in the molecule's structure.

Structural Isomer Enumeration

The process of structural isomer enumeration involves counting all possible unique molecules that have the same molecular formula but different structural arrangements. Isomers are compounds that share the same chemical formula yet differ in the arrangement of atoms in space, leading to different properties.

In the case of \[\begin{equation}\mathrm{C}_{5}\mathrm{H}_{10}\end{equation}\], with the knowledge that there are no degrees of unsaturation, we focus only on acyclic isomers - molecules without rings. This limitation simplifies the task, as you only create structures with single bonds connecting carbon atoms.

Strategies for Enumeration

1. Start with the longest chain possible and then rearrange the bonds to form side groups or branches.
2. Be systematic to avoid repetition; perhaps employ the IUPAC nomenclature to keep track and ensure that all possible variations are considered.
3. Review each isomer for uniqueness to guarantee that all counted forms are distinct from one another.

After generating the isomer list, we can see that there are five distinct acyclic isomers for \[\begin{equation}\mathrm{C}_{5}\mathrm{H}_{10}\end{equation}\], as any additional enumerations either repeat earlier structures or do not fit the molecular formula.

Molecular Formula Analysis

The molecular formula analysis is the starting point before diving deeper into specific details such as isomer enumeration. It represents a compound's composition in terms of the type and number of atoms present but without specifying the structural layout.

By analyzing the molecular formula \[\begin{equation}\mathrm{C}_{5}\mathrm{H}_{10}\end{equation}\], we gather that there are five carbon atoms and ten hydrogen atoms. This information, coupled with the calculated degrees of unsaturation, provides a blueprint that guides us when considering the possible structures of the molecule. From the initial analysis of the molecular formula, we've determined that due to a lack of unsaturation, these atoms should be linked in chains with no double bonds or rings, which is an essential insight for constructing structural isomers.In educational practice, students are advised first to understand the significance of a molecular formula and then to apply its implications in further calculations or structural predictions. This analytic approach aids in visualizing the potential skeleton of a molecule before delving into more complex steps such as isomer enumeration.