Question

Is \(\mathrm{C}_{22} \mathrm{H}_{46}\) an alkane, an alkene, or an alkyne? How can you tell?

Short answer

\(\mathrm{C}_{22} \mathrm{H}_{46}\) is an alkane, as it matches the general formula for alkanes \(\mathrm{C}_n \mathrm{H}_{2n+2}\) with \(n=22\). It does not match the formulas for alkenes or alkynes.

Step-by-step solution

Recall General Formulas for Hydrocarbons

Alkanes have the general formula: \(\mathrm{C}_n \mathrm{H}_{2n+2}\) Alkenes have the general formula: \(\mathrm{C}_n \mathrm{H}_{2n}\) Alkynes have the general formula: \(\mathrm{C}_n \mathrm{H}_{2n-2}\)

Compare the given formula to general formulas

We have \(\mathrm{C}_{22} \mathrm{H}_{46}\), and we want to determine which of the hydrocarbon classes it belongs to. Let's test if it's an alkane: If it is an alkane, then \(2n+2= 46\), with \(n = 22\). Solving for \(n\), we get \(n = \dfrac{46-2}{2} = 22\). Since we get the correct value for n, we can conclude that \(\mathrm{C}_{22} \mathrm{H}_{46}\) is an alkane. However, let's check for the other classes of hydrocarbons: Alkene: If it's an alkene, then \(2n = 46\), with \(n = 22\). In this case, we get \(n = 46/2= 23\), which does not match the given \(n\) value (22). Alkyne: If it's an alkyne, then \(2n-2 = 46\), with \(n = 22\). Solving for \(n\), we get \(n = \dfrac{46+2}{2} = 24\). Again, it does not match the given \(n\) value (22).

Conclusion

Based on the comparison of the given formula to the general formulas for alkanes, alkenes, and alkynes, we can conclude that \(\mathrm{C}_{22} \mathrm{H}_{46}\) is an alkane.

Key concepts

Hydrocarbons

Hydrocarbons are fundamental chemical compounds made up exclusively of hydrogen and carbon atoms. They play a critical role in organic chemistry and form the structural basis for many different types of compounds. These molecules are classified based on the types of bonds between carbon atoms. The three primary categories are:

• Alkanes: Hydrocarbons with only single bonds. They are the simplest type of hydrocarbon and are often called saturated hydrocarbons.
• Alkenes: These hydrocarbons have one or more carbon-carbon double bonds. The presence of a double bond makes them unsaturated.
• Alkynes: Characterized by one or more carbon-carbon triple bonds, making them highly unsaturated.

Alkanes are the most stable due to their single bonds. In contrast, alkenes and alkynes are more reactive due to the presence of double or triple bonds. All hydrocarbons serve as essential energy sources and raw materials for the chemical industry.

General Formula

The general formula for hydrocarbons serves as a straightforward way to determine the type of a hydrocarbon. Each family of hydrocarbons has its own specific formula, which helps in identifying them:

• Alkanes: Represented by the formula \(\mathrm{C}_n \mathrm{H}_{2n+2}\). This formula implies that for every \(n\) carbon atoms, there are \(2n+2\) hydrogen atoms.
• Alkenes: Follow the formula \(\mathrm{C}_n \mathrm{H}_{2n}\). Here, \(n\) carbon atoms are bonded with \(2n\) hydrogen atoms, reflecting the presence of a double bond.
• Alkynes: These use the formula \(\mathrm{C}_n \mathrm{H}_{2n-2}\). This reduction in hydrogen is due to the triple bond between carbon atoms.

These formulas not only help in identifying structures but also in predicting the properties of these hydrocarbons. Understanding these general formulas is crucial, especially when analyzing unknown compounds like \(\mathrm{C}_{22} \mathrm{H}_{46}\), which matches the formula for alkanes.

Organic Chemistry

Organic chemistry is the study of carbon-containing compounds, primarily focusing on hydrocarbons and their derivatives. The field is vast, dealing with the synthesis, structure, and reactions of organic compounds. The study of hydrocarbons is vital since they are the simplest organic compounds and serve as building blocks for more complex molecules.
Each class of hydrocarbons exhibits unique properties and reactivity patterns, making them essential for various applications:

• Alkanes: Mostly used as fuels and lubricants due to their stable nature.
• Alkenes: Their double bonds make them ideal for chemical reactions used in industries, particularly in the production of plastics and alcohols.
• Alkynes: Known for their energy-rich triple bonds, they're used in welding and as starting materials for synthesizing other chemicals.

Understanding hydrocarbons' chemical bonding nature allows chemists to manipulate them into creating an array of new and useful compounds, which is at the heart of organic chemistry.