Question

The general formula \(\mathrm{C}_{n} \mathrm{H}_{2 n-2}\) may represent (A) Allene (B) Alkyne (C) Bicycloalkane (D) Cycloalkene

Short answer

The general formula \(\mathrm{C}_{n} \mathrm{H}_{2 n-2}\) can represent multiple types of hydrocarbons, including allene, alkyne, bicycloalkane, and cycloalkene. However, it is not sufficient to uniquely determine a single type of hydrocarbon from this formula, as each type has unique structural characteristics.

Step-by-step solution

Analyze the molecular formula of each option

The first step is to understand the molecular formulas of the given hydrocarbon options. Let's find out the general formula for each type: (A) Allene: An allene has at least one carbon-carbon double bond. The general formula for an allene is \(\mathrm{C}_{n} \mathrm{H}_{2n-2}\). (B) Alkyne: An alkyne has at least one carbon-carbon triple bond. The general formula for an alkyne is \(\mathrm{C}_{n} \mathrm{H}_{2n-2}\). (C) Bicycloalkane: A bicycloalkane contains two adjacent rings that share two carbon atoms and have no other common atoms. The general formula for a bicycloalkane is \(\mathrm{C}_{n} \mathrm{H}_{2n-2}\). (D) Cycloalkene: A cycloalkene contains one carbon-carbon double bond and is a cyclic hydrocarbon. The general formula for a cycloalkene is \(\mathrm{C}_{n} \mathrm{H}_{2n-2}\). We notice that allene, alkyne, bicycloalkane, and cycloalkene have the same general molecular formula.

Compare general formula with given formula

The general formula given in the problem is \(\mathrm{C}_{n} \mathrm{H}_{2 n-2}\). Comparing this formula with the general formulas for allene, alkyne, bicycloalkane, and cycloalkene, we can conclude that this general formula can represent multiple types of hydrocarbons.

Conclusion

Based on the comparison in step 2, we can conclude that the general formula \(\mathrm{C}_{n} \mathrm{H}_{2 n-2}\) can represent: (A) Allene (B) Alkyne (C) Bicycloalkane (D) Cycloalkene However, we know that each type of hydrocarbon has unique structural characteristics, and the molecular formula alone may not be sufficient to differentiate between the types. Therefore, we cannot uniquely determine a single type of hydrocarbon from the given general molecular formula.

Key concepts

Allene

Allenes are fascinating hydrocarbons known for their unique molecular structure. They contain two carbon-carbon double bonds ( =C=C= ) adjacent to each other. This distinct feature is what sets them apart from other hydrocarbons. The simplest allene is propadiene ( C_3H_4 ).

Allenes are generally represented by the formula C_nH_{2n-2} , which implies that they are less saturated than alkanes. In allene, the central carbon is sp-hybridized, while the terminal carbons are sp^2-hybridized. This hybridization pattern gives them a linear or planar geometry across the double bonds.

• Form: C_nH_{2n-2}
• Structure: Two adjacent double bonds
• Example: Propadiene ( C_3H_4 )

Alkyne

Alkynes are a class of hydrocarbons characterized by at least one carbon-carbon triple bond ( ≡ ). This triple bond is what makes alkynes unique, leading them to be highly reactive compared to other hydrocarbons. The simplest alkyne is ethyne, commonly known as acetylene ( C_2H_2 ).

The general formula for alkynes is C_nH_{2n-2} , indicating they have fewer hydrogen atoms than either alkanes or alkenes. In alkynes, the carbon atoms in the triple bond are sp-hybridized, resulting in linear geometry.

• Form: C_nH_{2n-2}
• Structure: At least one triple bond
• Example: Acetylene ( C_2H_2 )

Bicycloalkane

Bicycloalkanes are complex hydrocarbons composed of two connected ring structures. These rings share two or more carbon atoms, giving rise to a unique configuration. An example is bicyclo[2.2.1]heptane, known as norbornane.

The general formula C_nH_{2n-2} applies to bicycloalkanes when the rings are small and simple. These structures are prevalent in natural and synthetic chemistry due to their stability and reactivity.

• Form: C_nH_{2n-2}
• Structure: Two interconnected rings
• Example: Norbornane

Cycloalkene

Cycloalkenes are cyclic hydrocarbons containing at least one carbon-carbon double bond within the ring. This double bond introduces a point of unsaturation, which can lead to increased reactivity. Cyclohexene ( C_6H_{10} ) is a simple example of a cycloalkene.

With the general formula C_nH_{2n-2} , cycloalkenes demonstrate a decrease in hydrogen atoms compared to cycloalkanes. The geometry around the double bond is typically planar, granting the molecule a degree of rigidity.

• Form: C_nH_{2n-2}
• Structure: Cyclic with a double bond
• Example: Cyclohexene ( C_6H_{10} )