Problem 4 - Chemistry and Chemical Reactivity

Question

Which of the following compounds can be a cycloalkane? (a) \(\mathrm{C}_{3} \mathrm{H}_{5}\) (b) \(\mathrm{C}_{5} \mathrm{H}_{10}\) (c) \(\mathrm{C}_{14} \mathrm{H}_{30}\) (d) \(\mathrm{C}_{8} \mathrm{H}_{8}\)

Step-by-Step Solution

Answer

(b) \(\mathrm{C}_5\mathrm{H}_{10}\) can be a cycloalkane.

Step 1: Understanding Cycloalkanes

Cycloalkanes are saturated hydrocarbons arranged in a ring and general formula for a cycloalkane is \(\mathrm{C}_n\mathrm{H}_{2n}\). This means that the number of hydrogen atoms is double the number of carbon atoms.

Step 2: Examining Option (a)

Given \(\mathrm{C}_3\mathrm{H}_5\), apply the formula \(\mathrm{C}_n\mathrm{H}_{2n}\). It should be \(\mathrm{C}_3\mathrm{H}_6\) to be a cycloalkane. Since \(\mathrm{H}_5\) is less than \(\mathrm{H}_6\), this compound cannot be a cycloalkane.

Step 3: Examining Option (b)

Given \(\mathrm{C}_5\mathrm{H}_{10}\), apply the formula \(\mathrm{C}_n\mathrm{H}_{2n}\). It matches with the formula \(\mathrm{C}_5\mathrm{H}_{10}\), which fits the cycloalkane general structure. Thus, this compound can be a cycloalkane.

Step 4: Examining Option (c)

Given \(\mathrm{C}_{14}\mathrm{H}_{30}\), apply the formula \(\mathrm{C}_n\mathrm{H}_{2n}\). It should be \(\mathrm{C}_{14}\mathrm{H}_{28}\) to be a cycloalkane. Since \(\mathrm{H}_{30}\) is more than \(\mathrm{H}_{28}\), this compound cannot be a cycloalkane.

Step 5: Examining Option (d)

Given \(\mathrm{C}_8\mathrm{H}_8\), apply the formula \(\mathrm{C}_n\mathrm{H}_{2n}\). It should be \(\mathrm{C}_8\mathrm{H}_{16}\) to be a cycloalkane. Since \(\mathrm{H}_8\) is less than \(\mathrm{H}_{16}\), this compound cannot be a cycloalkane.

Step 6: Conclusion

Considering the above steps, only \(\mathrm{C}_5\mathrm{H}_{10}\) matches the cycloalkane formula \(\mathrm{C}_n\mathrm{H}_{2n}\). So, it is the compound that can be a cycloalkane.

Key Concepts

Chemical Formula

In the context of cycloalkanes, the chemical formula is an essential tool for determining the compounds' structural possibilities. Cycloalkanes are part of the larger family of hydrocarbons and their distinctive feature is that they are organized in a ring-like formation. By using the formula \(C_nH_{2n}\), you can quickly decide if a compound could be a cycloalkane. Here, \(n\) represents the number of carbon atoms, and the number of hydrogen atoms should be exactly twice the number of carbon atoms.
For example, in cycloalkanes, if we have a compound with 5 carbon atoms, then it should have 10 hydrogen atoms to fit the formula. If there's a mismatch, like having more or fewer hydrogen atoms than required, the compound might not form a proper cycloalkane. This is why knowing and applying the chemical formula is a great way to quickly assess possible cycloalkane structures.

Organic Chemistry

Organic chemistry is the study of carbon-containing compounds, and cycloalkanes fit neatly into this category. These structures, along with other hydrocarbons, form the foundation of organic molecules.
Organic chemistry looks at how carbon atoms can link together and form various architectures, including chains and rings. Cycloalkanes specifically are rings of carbon atoms and represent a crucial subclass of hydrocarbons known as alkanes. These are characterized by single carbon-carbon bonds, forming robust structural backbones ideal for studying many reactions and transformations in organic chemistry.
Understanding organic chemistry principles allows you to identify how cycloalkanes can interact with other molecules, react under different conditions, and transform into other useful compounds. This makes the study of cycloalkanes particularly insightful in broader chemical synthesis and industrial applications.

Saturated Hydrocarbons

Saturated hydrocarbons are hydrocarbons with single bonds only between carbon atoms, which is precisely why cycloalkanes belong to this group. These compounds have all their carbon atoms bonded with hydrogen atoms or with other carbon atoms, without any unsaturated (double or triple) bonds.
In cycloalkanes, all the bonds present are single bonds, which makes them saturated. This results in certain chemical stability, as the single bonds create a less reactive backbone compared to unsaturated counterparts like alkenes and alkynes. The saturated nature ensures that cycloalkanes don’t easily react with other elements or compounds under normal conditions, making them valuable as non-reactive solvents or in manufacturing processes.
Recognizing that cycloalkanes are saturated hydrocarbons helps in understanding their role in both synthetic chemistry and larger industrial applications.