Problem 3 - Chemistry and Chemical Reactivity

Question

Which of the following compounds can be an alkane? (a) \(\mathrm{C}_{2} \mathrm{H}_{4}\) (b) \(\mathrm{C}_{5} \mathrm{H}_{12}\) (c) \(\mathrm{C}_{14} \mathrm{H}_{30}\) (d) \(\mathrm{C}_{7} \mathrm{H}_{8}\)

Step-by-Step Solution

Answer

The compounds \(\mathrm{C}_5\mathrm{H}_{12}\) and \(\mathrm{C}_{14}\mathrm{H}_{30}\) can be alkanes.

Step 1: Understanding Alkane Formula

Alkanes are hydrocarbons with the general formula \( ext{C}_n ext{H}_{2n+2}\), where \(n\) is the number of carbon atoms. This formula determines the number of hydrogen atoms that will be attached to the carbon atoms.

Step 2: Applying Alkane Formula to Option (a)

For \( ext{C}_2 ext{H}_4\): Substituting \(n = 2\) into the formula, the hydrogen count should be \(2n + 2 = 2(2) + 2 = 6\). Since \( ext{C}_2 ext{H}_4\) has only 4 hydrogens, it does not fit the alkane formula.

Step 3: Applying Alkane Formula to Option (b)

For \( ext{C}_5 ext{H}_{12}\): Substituting \(n = 5\) into the formula, the hydrogen count should be \(2n + 2 = 2(5) + 2 = 12\). The hydrogen count matches exactly with \( ext{C}_5 ext{H}_{12}\), making it a valid alkane.

Step 4: Applying Alkane Formula to Option (c)

For \( ext{C}_{14} ext{H}_{30}\): Substituting \(n = 14\) into the formula, the hydrogen count should be \(2n + 2 = 2(14) + 2 = 30\). The hydrogen count matches exactly with \( ext{C}_{14} ext{H}_{30}\), making it a valid alkane.

Step 5: Applying Alkane Formula to Option (d)

For \( ext{C}_7 ext{H}_8\): Substituting \(n = 7\) into the formula, the hydrogen count should be \(2n + 2 = 2(7) + 2 = 16\). The compound \( ext{C}_7 ext{H}_8\) has a hydrogen count of only 8, so it does not fit the alkane formula.

Key Concepts

Hydrocarbon formula

Alkanes belong to a class of compounds known as hydrocarbons. Hydrocarbons are organic compounds made entirely of carbon and hydrogen atoms. The special feature that distinguishes alkanes from other hydrocarbons is their chemical formula. The general formula for alkanes is \( \text{C}_n\text{H}_{2n+2} \). This formula helps determine the relationship between carbon and hydrogen atoms in a given alkane.

• \( n \) is the number of carbon atoms.
• \( \text{H} \) denotes the number of hydrogen atoms, which must always compute to \( 2n + 2 \).

This relationship shows that alkanes are saturated hydrocarbons with single bonds only, meaning all carbon atoms are filled with hydrogen in the simplest form without any double or triple bonds.

Carbon atoms

In organic chemistry, carbon is the central element. Each carbon atom can form four bonds, which is a major aspect of alkane structures. In the context of alkanes, the number of carbon atoms is denoted as \( n \) in the general formula \( \text{C}_n\text{H}_{2n+2} \). By knowing \( n \), you can easily identify how many carbon and hydrogen atoms exist in an alkane molecule.

• A single carbon atom forms the basis for smaller alkanes and as you increase \( n \), the alkane becomes more complex.
• The formation of long carbon chains or rings is just a matter of different values of \( n \).

The structure of carbon chains forms the backbone of alkanes, dictating their physical and chemical properties.

Hydrogen count

The number of hydrogen atoms in alkanes directly ties into the number of carbon atoms present, making it simple to determine if a compound is indeed an alkane. According to the formula \( \text{C}_n\text{H}_{2n+2} \), every carbon bond with the maximum number of hydrogen atoms is satisfied.This makes alkanes saturated hydrocarbons, as all available valence electrons in carbon are fulfilled via hydrogen or other carbon bonds.

• For each carbon in an alkane, add hydrogen according to \( 2n + 2 \).
• This setup ensures that the compound remains stable and fully saturated.

This count also highlights why alkanes are less reactive compared to other hydrocarbon families, as there are no double or triple bonds to break open or react with.

Organic Chemistry

Organic chemistry covers the study of carbon-containing compounds, among which alkanes serve as the basic type. A foundational concept in organic chemistry is understanding the diversity and structure of hydrocarbons. Among hydrocarbons, alkanes are the simplest because they contain only carbon and hydrogen in a straight or branched chain.

• Organic chemistry utilizes alkanes as the basic scaffold for studying more complex substances.
• The anatomy of alkanes—iner of singular carbon-carbon single bonds—serves as a jumping-off point to explore more complicated molecules and reactions.

Learning the particulars of alkanes aids in comprehending broader principles of organic chemistry and their applications in everyday life, such as energy sources and raw materials for plastic and other synthetic products.