Question

Which of the following molecular formulas represents an alkane? (a) \(\mathrm{C}_{10} \mathrm{H}_{24}\) (b) \(C_{10} H_{22}\)

Short answer

Option (b) \( C_{10}H_{22} \) is the alkane.

Step-by-step solution

Define an Alkane

Alkanes are hydrocarbons with only single bonds between the carbon atoms. Alkanes follow the general molecular formula \( C_nH_{2n+2} \), where \( n \) is the number of carbon atoms.

Analyze Option (a)

The first option is \( \mathrm{C}_{10}\mathrm{H}_{24} \). For an alkane with 10 carbon atoms, the formula should be \( \mathrm{C}_{10}\mathrm{H}_{22} \). Therefore, \( \mathrm{C}_{10}\mathrm{H}_{24} \) does not match the alkane formula as it has two extra hydrogen atoms.

Analyze Option (b)

The second option is \( \mathrm{C}_{10}\mathrm{H}_{22} \). If we apply the alkane formula \( C_nH_{2n+2} \) with \( n = 10 \), we indeed get \( \mathrm{C}_{10}\mathrm{H}_{22} \). This aligns perfectly with the definition of an alkane.

Conclusion

From the analysis, only option \( \mathrm{C}_{10}\mathrm{H}_{22} \) satisfies the alkane formula \( C_nH_{2n+2} \). Therefore, option (b) is an alkane.

Key concepts

Hydrocarbons

Hydrocarbons are fascinating compounds mainly composed of carbon and hydrogen atoms. These are considered the building blocks of organic chemistry. Alkanes fall under the category of hydrocarbons, and they specifically contain only single carbon-carbon bonds. However, hydrocarbons come in various forms:

• Alkanes: Saturated hydrocarbons with single bonds only. Alkanes are the simplest hydrocarbons.
• Alkenes: These have at least one carbon-carbon double bond. They are unsaturated hydrocarbons.
• Alkynes: They contain at least one carbon-carbon triple bond and are also unsaturated.

Understanding hydrocarbons is integral to grasping their reactions and functions in various chemical processes. In particular, alkanes, due to their single bonds, tend to be less reactive compared to alkenes and alkynes.

Molecular formula

A molecular formula gives insight into the number of each type of atom in a molecule. It's like a recipe indicating exactly what ingredients (atoms) you need to create a particular compound.
For example, when dealing with alkanes, the specific molecular formula is pivotal. The formula for alkanes follows this pattern:

• Formula: \( C_nH_{2n+2} \)
• Explanation: 'n' represents the number of carbon atoms. The number of hydrogen atoms is always two more than twice the number of carbon atoms.

In the exercise, we analyzed which molecular formula aligned with an alkane. Option \( C_{10}H_{22} \) fit the alkane formula perfectly, making it a valid representation of an alkane.

Single bonds

Single bonds are the simplest form of chemical bonds between atoms. They are key in forming the structure of alkanes. Specifically, single bonds involve the sharing of one pair of electrons between two atoms.

• Function: In alkanes, single bonds connect the carbon atoms together in a chain, as well as connect carbon atoms to hydrogen atoms.
• Stability: Single bonds offer stability to molecules because they are not easily broken. This stability is a central feature in the structure of alkanes, contributing to their label as 'saturated' hydrocarbons.

Due to the presence of only single bonds, alkanes do not contain any double or triple bonds, distinguishing them from other hydrocarbons like alkenes and alkynes.