Problem 18 - Chemistry Principles and Practice

Question

Which of the following molecules are noncyclic alkanes? (a) \(\mathrm{C}_{5} \mathrm{H}_{12}\) (b) \(\mathrm{C}_{6} \mathrm{H}_{12}\) (c) \(\mathrm{C}_{3} \mathrm{H}_{6}\) (d) \(\mathrm{C}_{4} \mathrm{H}_{9} \mathrm{Cl}\)

Step-by-Step Solution

Answer

(a) \(\mathrm{C}_{5} \mathrm{H}_{12}\) is a noncyclic alkane.

Step 1: Determine the General Formula for Alkanes

Alkanes are saturated hydrocarbons with the general formula \(\mathrm{C}_n\mathrm{H}_{2n+2}\), where \(n\) is the number of carbon atoms. This formula applies to noncyclic alkanes. Using this formula, we can determine if a molecule is a noncyclic alkane.

Step 2: Check Each Molecule Against the Alkane Formula

Apply the general formula \(\mathrm{C}_n\mathrm{H}_{2n+2}\) to each option: - For (a) \(\mathrm{C}_{5} \mathrm{H}_{12}\): Here, \(n = 5\), so \(2n+2 = 12\). Thus, \(\mathrm{C}_{5} \mathrm{H}_{12}\) satisfies the formula for noncyclic alkanes. - For (b) \(\mathrm{C}_{6} \mathrm{H}_{12}\): Here, \(n = 6\), and \(2n+2 = 14\). Thus, this formula does not satisfy the condition for noncyclic alkanes. - For (c) \(\mathrm{C}_{3} \mathrm{H}_{6}\): Here, \(n = 3\), and \(2n+2 = 8\). This is not a noncyclic alkane. - For (d) \(\mathrm{C}_{4} \mathrm{H}_{9} \mathrm{Cl}\): This formula includes Cl, which means it is not purely a hydrocarbon.

Step 3: Identify Molecules That Match the Criteria

From the application of the general formula, only \(\mathrm{C}_{5} \mathrm{H}_{12}\) fits the criteria for a noncyclic alkane. It meets the formula \(\mathrm{C}_n\mathrm{H}_{2n+2}\) perfectly, indicating it is a saturated, chain hydrocarbon without any cycles or rings.

Key Concepts

Noncyclic hydrocarbons

Noncyclic hydrocarbons are types of compounds that consist solely of hydrogen and carbon atoms, where the carbon atoms are connected in a straight line or branched chains. These compounds do not form rings or closed loops. This structure affects their chemical properties and makes them quite stable.
Noncyclic hydrocarbons can be either saturated or unsaturated, but alkanes, in particular, are saturated hydrocarbons. In alkanes, each carbon atom forms four single covalent bonds, leading to a maximum number of hydrogen atoms bonded to them. These compounds do not include any cyclical structures that might cause them to deviate from their simplistic chain formation. Understanding these basic properties is crucial when identifying noncyclic alkanes from given molecular formulas.

General formula for alkanes

The general formula for alkanes is \( C_nH_{2n+2} \), where \( n \) is the number of carbon atoms present in the molecule. This formula helps to identify noncyclic alkanes because it represents the maximum possible hydrogen atoms that can bond with a given number of carbon atoms in a straight chain.
For example, if the formula of a molecule is \( C_5H_{12} \), we can determine that \( n = 5 \). Substituting the value into the formula \( (2n+2) \) gives \( 12 \), which confirms that it fits the structure of a noncyclic alkane. This systematic approach is instrumental in distinguishing alkanes from other classes of hydrocarbons.

• This formula assumes no branching or cyclization, ensuring each carbon is fully saturated with hydrogen atoms.
• The formula will not hold for hydrocarbons with double bonds, triple bonds, or ring structures.

Saturated hydrocarbons

Saturated hydrocarbons have only single bonds between carbon atoms, ensuring each carbon atom is bonded to the maximum number of hydrogen atoms. This means that these compounds do not have any available capacity for additional hydrogen or other elements without breaking a carbon-hydrogen bond.
Alkanes are the simplest form of saturated hydrocarbons, making them vital in understanding the concept of saturation in organic chemistry. The structure of alkanes led to their other name, 'paraffins', indicating their limited reactivity compared to unsaturated hydrocarbons, which contain double or triple bonds.
The term "saturated" itself reflects this idea of being "full," as no more hydrogen atoms can be added without altering the existing single-bond structure. This property gives alkanes unique characteristics, such as a relatively high level of chemical inertness and stability, allowing them to serve as a fundamental building block in chemistry.