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

Step-by-step solution

Identify Types of Hydrocarbons

Look at the compounds provided: (a) \( \mathrm{C}_{2} \mathrm{H}_{2} \), (b) \( \mathrm{C}_{2} \mathrm{H}_{4} \), (c) \( \mathrm{C}_{2} \mathrm{H}_{6} \), (d) \( \mathrm{C}_{2} \mathrm{H}_{2} \mathrm{Br}_{2} \). Classify these compounds based on the type of bonds present in the carbon atoms: (a) \( \mathrm{C}_{2} \mathrm{H}_{2} \) is a molecule with a triple bond (alkyne), (b) \( \mathrm{C}_{2} \mathrm{H}_{4} \) with a double bond (alkene), (c) \( \mathrm{C}_{2} \mathrm{H}_{6} \) with single bonds (alkane), and (d) \( \mathrm{C}_{2} \mathrm{H}_{2} \mathrm{Br}_{2} \) is an alkene with additional bromine atoms.

Understand Bond Lengths in Bond Types

Recall that the length of C-H bonds is affected by the nature of the carbon-hydrogen interaction. Generally, the bond length increases from carbon in triple bonds to single bonds. Therefore: \( \mathrm{C}_{2} \mathrm{H}_{2} \) with C-H in a sp hybridization (triple bond) has the shortest bond, \( \mathrm{C}_{2} \mathrm{H}_{4} \) with sp2 hybridization (double bond) has a medium length, and \( \mathrm{C}_{2} \mathrm{H}_{6} \) with sp3 hybridization (single bond) has the longest C-H bond.

Compare and Choose the Longest C-H Bond

Based on the knowledge that bond length increases as the number of bonds between carbons decreases, the longest bond distance is in \( \mathrm{C}_{2} \mathrm{H}_{6} \) which is an alkane with only single bonds, leading to the most extended bond length due to sp3 hybridization.

Key concepts

Hybridization

Hybridization is a concept used to describe the mixing of atomic orbitals in an atom to form new hybrid orbitals. These hybrid orbitals have different energies, shapes, and other characteristics compared to the original atomic orbitals. In the context of hydrocarbons, hybridization plays a significant role in determining the structure and properties of the molecule.
Carbon atoms can hybridize in three main ways, depending on how many regions of electron density surround the carbon:

• sp Hybridization: Involves the mixing of one s orbital and one p orbital. This results in two sp orbitals and is found in molecules with triple bonds, such as alkynes like \( \mathrm{C}_{2} \mathrm{H}_{2} \) (acetylene).
• sp2 Hybridization: Involves mixing one s orbital and two p orbitals to create three sp2 orbitals. This type of hybridization is typical for molecules with double bonds like alkenes, such as \( \mathrm{C}_{2} \mathrm{H}_{4} \) (ethylene).
• sp3 Hybridization: Involves mixing one s orbital with three p orbitals to form four sp3 hybrid orbitals. It's seen in molecules with single bonds like alkanes, such as \( \mathrm{C}_{2} \mathrm{H}_{6} \) (ethane).

Hybridization affects not only the geometry of the molecule but also the bond lengths and strengths, as we'll see when discussing bond length comparison.

Types of Hydrocarbons

Hydrocarbons are organic compounds made solely of carbon and hydrogen atoms. Based on the types of bonds between the carbon atoms, hydrocarbons are classified into different categories:

• Alkanes: These have only single bonds between carbon atoms. They are also known as saturated hydrocarbons. An example is \( \mathrm{C}_{2} \mathrm{H}_{6} \) (ethane).
• Alkenes: These hydrocarbons contain at least one double bond between carbon atoms, like \( \mathrm{C}_{2} \mathrm{H}_{4} \) (ethylene). They are referred to as unsaturated hydrocarbons.
• Alkynes: These consist of at least one triple bond between carbon atoms, such as \( \mathrm{C}_{2} \mathrm{H}_{2} \) (acetylene). Like alkenes, they are also unsaturated hydrocarbons.

Understanding the types of hydrocarbons is important because the types of bonds (single, double, or triple) directly influence properties such as bond strength and bond length. It also determines molecules' physical and chemical properties, including reactivity.

Bond Length Comparison

The bond length in hydrocarbons is influenced by the type of hybridization and the nature of the bonding between carbon atoms.

• Triple bonds, as found in alkynes (\( \mathrm{C}_{2} \mathrm{H}_{2} \)), result in sp hybridization and tend to have the shortest bond lengths. This is because the bonds involve more s character, pulling the bonded atoms closer.
• Double bonds, seen in alkenes (\( \mathrm{C}_{2} \mathrm{H}_{4} \)), exhibit sp2 hybridization. These bonds are longer than those in alkynes but shorter than single bonds due to less s character.
• Single bonds, present in alkanes (\( \mathrm{C}_{2} \mathrm{H}_{6} \)), involve sp3 hybridization and have the longest bond lengths. This occurs because of the least s character, resulting in a more extended bond.

In general, as the bond order increases (from single to triple), the bond length decreases. Thus, bond length comparison allows us to understand the stability and reactivity of different hydrocarbons. Single bonds allow for more flexibility in the molecule's shape, while multiple bonds constrain movement but increase strength and stability.