Question

The C-H bond distance is longest in (a) \(\mathrm{C}_{2} \mathrm{H}_{2}\) (b) \(\mathrm{C}_{2} \mathrm{H}_{4}\) (c) \(\mathrm{C}_{2} \mathrm{H}_{6}\) (d) \(\mathrm{C}_{2} \mathrm{H}_{2} \mathrm{Br}_{2}\)

Short answer

The longest C-H bond distance is in \(\mathrm{C}_{2}\mathrm{H}_{6}\).

Step-by-step solution

Understand the Question

We need to determine in which of the given compounds the carbon-hydrogen (C-H) bond length is the longest.

Consider the Saturation

Identify the types of bonds in each compound. In alkanes (single bonds, e.g., \(\mathrm{C}_{2}\mathrm{H}_{6}\)), alkenes (double bonds, e.g., \(\mathrm{C}_{2}\mathrm{H}_{4}\)), and alkynes (triple bonds, e.g., \(\mathrm{C}_{2}\mathrm{H}_{2}\)), the level of saturation increases as the number of bonds between carbons increases. More saturated (fewer multiple bonds) tends to have longer C-H bonds.

Analyze Each Option

- \(\mathrm{C}_{2}\mathrm{H}_{2}\) (alkyne) with a triple bond: typically has the shortest C-H bonds because of higher \(sp\) character. - \(\mathrm{C}_{2}\mathrm{H}_{4}\) (alkene) with a double bond: has \(sp^2\) character. - \(\mathrm{C}_{2}\mathrm{H}_{6}\) (alkane) with single bonds: has \(sp^3\) character leading to longer C-H bonds. - \(\mathrm{C}_{2}\mathrm{H}_{2}\mathrm{Br}_{2}\): it's similar in C-H bond nature to \(\mathrm{C}_{2}\mathrm{H}_{2}\) but with substitutions affecting the carbon, not the hydrogen.

Determine Most Saturated Compound

The compound with the highest level of saturation (all single bonds) typically has the longest C-H bond, which is \(\mathrm{C}_{2}\mathrm{H}_{6}\) as it has \(sp^3\) hybridization.

Conclusion

Based on the bond types and hybridizations, \(\mathrm{C}_{2}\mathrm{H}_{6}\) should have the longest C-H bond compared to the others.

Key concepts

Bond Saturation

Bond saturation refers to the type, number, and arrangement of bonds between carbon atoms in a molecule. The concept of saturation helps us understand how compounds like alkanes, alkenes, and alkynes differ in terms of their hydrogen bonding and reactivity.

• **Saturated hydrocarbons**: These are alkanes, with only single bonds between carbon atoms. This configuration allows more hydrogen atoms to bond, resulting in longer C-H bonds.
• **Unsaturated hydrocarbons**: These include alkenes and alkynes, with double and triple bonds respectively. The presence of multiple bonds reduces hydrogen atoms, leading to shorter C-H bonds.

Understanding saturation is key to determining the chemical properties and behaviors of organic compounds.

Alkane

Alkanes are the simplest type of hydrocarbons, consisting solely of carbon and hydrogen atoms connected by single bonds. This group of compounds is known as saturated hydrocarbons, which means they have the maximum number of hydrogen atoms bonded to carbon. Their general formula is \(C_{n}H_{2n+2}\).

• **Structure**: Characterized by a straight or branched chain of single-bonded carbon atoms.
• **Examples**: Methane (\(CH_4\)), ethane (\(C_2H_6\)), and propane (\(C_3H_8\)).
• **Physical properties**: They typically exhibit lower boiling points and are less dense than water.

Due to their saturation, alkanes generally have the longest C-H bond lengths among hydrocarbons.

Hybridization

Hybridization in chemistry refers to the mixing of atomic orbitals to form new hybrid orbitals. These are suitable for the pairing of electrons to form chemical bonds in molecules.It's crucial in understanding the shape and bonding in organic compounds.

• **spHybridization**: Found in alkynes like acetylene (\(C_2H_2\)), where one s and two p orbitals combine to form two sp orbitals. This results in a linear structure with a shorter C-H bond distance due to higher bond energy.
• **sp^2 Hybridization**: Occurs in alkenes like ethylene (\(C_2H_4\)). One s and two p orbitals mix to create three sp^2 orbitals, leading to a trigonal planar structure.
• **sp^3 Hybridization**: Characteristic of alkanes such as ethane (\(C_2H_6\)), combining one s and three p orbitals, resulting in a tetrahedral shape. This hybridization has longer C-H bonds due to the reduced bond energy.

The hybridization state significantly impacts the bond lengths and angles in a molecule, helping predict structural properties.

Alkene

Alkenes are a class of hydrocarbons characterized by at least one carbon-carbon double bond, making them unsaturated. Their general formula is \(C_{n}H_{2n}\).

• **Structure**: Contain sp^2 hybridized carbon atoms, resulting in a planar configuration.
• **Examples**: Ethylene (\(C_2H_4\)) and propylene (\(C_3H_6\)).
• **Reactivity**: More reactive than alkanes due to the presence of the double bond, which can easily participate in addition reactions.

The sp^2 hybridization causes alkenes to have shorter C-H bonds than alkanes, as the carbon atoms pull electrons closer.

Alkyne

Alkynes are hydrocarbons with at least one carbon-carbon triple bond. They belong to the group of unsaturated hydrocarbons.This group is known for having higher energy and shorter C-H bonds compared to alkanes and alkenes.

• **Structure**: Characterized by sp hybridized carbon atoms in a linear arrangement.
• **Examples**: Acetylene (\(C_2H_2\)) and propyne (\(C_3H_4\)).
• **Reactivity**: Typically more reactive than alkanes, slightly more reactive than alkenes, due to the high bond energy of the triple bond.

The triple bond leads to stronger but shorter C-H bonds, which influences the physical and chemical properties of alkynes.