Problem 55 - Chemistry: Principles and Reactions

Question

The general formula of an alkane is \(\mathrm{C}_{n} \mathrm{H}_{2 n+2}\). What is the general formula of an (a) alkene? (b) alkyne? (c) alcohol derived from an alkane?

Step-by-Step Solution

Answer

Answer: The general formulas for these compounds are as follows: - Alkene: \(\mathrm{C}_{n} \mathrm{H}_{2 n}\) - Alkyne: \(\mathrm{C}_{n} \mathrm{H}_{2 n-2}\) - Alcohol derived from alkane: \(\mathrm{C}_{n} \mathrm{H}_{2 n+2}\) (with a hydroxyl (OH) group instead of one hydrogen atom)

Step 1: (Step 1: Alkene general formula)

In alkenes, there is a carbon-carbon double bond. Because the double bond uses up two hydrogen atoms (compared to a carbon-carbon single bond in alkanes), the general formula for alkenes becomes \(\mathrm{C}_{n} \mathrm{H}_{2 n}\).

Step 2: (Step 2: Alkyne general formula)

In alkynes, there is a carbon-carbon triple bond. The triple bond replaces two carbon-hydrogen bonds (compared to a carbon-carbon single bond in alkanes), so we need to subtract another two hydrogen atoms from the alkane general formula. The general formula for alkynes becomes \(\mathrm{C}_{n} \mathrm{H}_{2 n-2}\).

Step 3: (Step 3: Alcohol derived from alkane general formula)

In alcohols, there is a hydroxyl (OH) group connected to a carbon atom. To derive an alcohol from an alkane, we need to replace one of the hydrogen atoms in an alkane with an OH group. Therefore, the general formula for an alcohol derived from an alkane remains the same as the general formula for alkanes, which is \(\mathrm{C}_{n} \mathrm{H}_{2 n+2}\). The difference between alkanes and alcohol is the functional group (OH) instead of one hydrogen atom, but the general formula stays the same.

Key Concepts

Alkane

Alkanes are the simplest type of hydrocarbons. They consist of carbon and hydrogen atoms joined by single bonds. Each carbon atom forms four single covalent bonds, allowing for a variety of chain lengths and structures. The general formula for alkanes is \(\mathrm{C}_{n} \mathrm{H}_{2n+2}\), indicating that every carbon atom supports two hydrogen atoms, with an additional two at the ends of the chain.

• Features only single bonds.
• Known as saturated hydrocarbons because they contain no double or triple bonds.
• Common examples include methane (\(\mathrm{CH}_4\)), ethane (\(\mathrm{C}_2\mathrm{H}_6\)), and propane (\(\mathrm{C}_3\mathrm{H}_8\)).

Alkanes are relatively unreactive due to their strong carbon-carbon and carbon-hydrogen bonds. As a result, they are commonly used as fuels and are a key component of natural gas and petroleum.

Alkene

Alkenes are hydrocarbons that contain carbon-carbon double bonds. The presence of this double bond enables alkenes to engage in various chemical reactions, such as addition reactions. The general formula for alkenes is \(\mathrm{C}_{n} \mathrm{H}_{2n}\).

• Contains one or more carbon-carbon double bonds.
• Considered unsaturated hydrocarbons due to the double bond enabling further chemical reactions.
• Examples include ethene (\(\mathrm{C}_2\mathrm{H}_4\)) and propene (\(\mathrm{C}_3\mathrm{H}_6\)).

Because of the double bonds, alkenes are more reactive than alkanes. These double bonds also result in an important aspect of alkenes called isomerism, which allows for multiple structural forms of the same molecular formula.

Alkyne

Alkynes are hydrocarbons known for containing carbon-carbon triple bonds. This characteristic makes them very distinct in their reactivity and properties compared to alkanes and alkenes. They adhere to the general formula \(\mathrm{C}_{n} \mathrm{H}_{2n-2}\).

• Possess at least one carbon-carbon triple bond.
• Due to the presence of the triple bond, alkynes are highly reactive.
• Examples include ethyne (also known as acetylene, \(\mathrm{C}_2\mathrm{H}_2\)) and propyne (\(\mathrm{C}_3\mathrm{H}_4\)).

The linear structure induced by the triple bond constrains alkynes compared to their counterparts with single and double bonds. They are typically used in organic synthesis and have applications in industrial processes.

Alcohol Functional Group

Alcohols are organic compounds featuring one or more hydroxyl (OH) groups attached to a carbon atom. To derive an alcohol from an alkane, we replace one hydrogen atom with the OH group, but the base carbon-hydrogen framework remains the same, resulting in a similar molecular formula \(\mathrm{C}_{n} \mathrm{H}_{2n+2}\).

• Contains one or more hydroxyl functional groups (OH).
• Hydrophilic (water-attracting) due to the polar nature of the OH group.
• Common examples include methanol (\(\mathrm{CH}_3\mathrm{OH}\)) and ethanol (\(\mathrm{C}_2\mathrm{H}_5\mathrm{OH}\)).

Alcohols have a wide range of uses in everyday life, from being beverages to solvents and fuel. Their distinctive functional group makes them pivotal in chemical reactions and synthesis in organic chemistry.