Question

Among the following which has the shortest C-C single bond length? (a) \(\mathrm{H}_{3} \mathrm{C}-\mathrm{CH}_{3}\) (b) \(\mathrm{H}_{2} \mathrm{C}=\mathrm{CH}-\mathrm{CH}=\mathrm{CH}_{2}\) (c) \(\mathrm{HC} \equiv \mathrm{C}-\mathrm{C} \equiv \mathrm{CH}\) (d) \(\mathrm{H}_{2} \mathrm{C}=\mathrm{CH}-\mathrm{CH}_{2}-\mathrm{CH}_{3}\)

Short answer

a) CH3-CH3 b) CH2=CH-CH=CH2 c) HC≡C-C≡CH d) CH3-CH=CH2 Answer: (c) HC≡C-C≡CH

Step-by-step solution

Analyze the C-C bonds in the molecules

For each molecule, we need to identify the C-C single bond and determine its hybridization. We will also consider the electron cloud repulsions caused by nearby multiple bonds in the molecule.

Determine hybridization and repulsions for option (a)

In this molecule, both C-C bonds are single bonds, and each carbon atom is sp3 hybridized. There are no nearby multiple bonds creating additional repulsions, so the length of this bond depends purely on the hybridization of the carbon atoms.

Determine hybridization and repulsions for option (b)

In this molecule, the C-C single bond occurs between two double-bonded carbon atoms. Each of the single-bonded carbon atoms is sp2 hybridized, and the electron cloud repulsions from the neighboring C=C double bonds will cause the single bond to be somewhat shorter.

Determine hybridization and repulsions for option (c)

In this molecule, the C-C single bond occurs between two triple-bonded carbon atoms. The single-bonded carbon atoms are sp hybridized. The electron cloud repulsions from the neighboring C≡C triple bonds will cause the single bond to become even shorter than in option (b).

Determine hybridization and repulsions for option (d)

In this molecule, the C-C single bond occurs between an sp3 hybridized carbon and an sp2 hybridized carbon. The electron cloud repulsions from the neighboring C=C double bond will cause this bond to be shorter than a normal sp3-sp3 bond. However, it should still be longer than the bond in option (b) due to the sp3 hybridization of one of the carbon atoms.

Compare the bond lengths

Based on the hybridization and electron cloud repulsions, option (c) should have the shortest C-C single bond, as it has the highest level of s-character and the strongest repulsion from neighboring triple bonds. Option (a) should have the longest C-C single bond, while options (b) and (d) will have somewhat shorter bond lengths due to the electron cloud repulsion from their neighboring multiple bonds. Therefore, the molecule with the shortest C-C single bond length is: (c) \(\mathrm{HC} \equiv \mathrm{C}-\mathrm{C} \equiv \mathrm{CH}\)

Key concepts

Chemical Bonding

Chemical bonding is the fundamental process through which atoms combine to form molecules. A bond is formed due to the electrostatic force of attraction between the oppositely charged electrons and nuclei. The types of chemical bonds include ionic, covalent, and metallic bonds, and within covalent bonds, there can be single, double, or triple bonds.

A single covalent bond, like the C-C bond, involves the sharing of one pair of valence electrons between two atoms. However, the length of a C-C single bond is not a fixed value and can vary based on factors such as hybridization of the carbon atoms and electronic repulsions, which are the focus points of the exercise in question. For instance, an sp3 hybridized carbon typically forms longer single bonds, while an sp2 or sp hybridized carbon forms shorter single bonds due to increased s-character, which pulls electrons closer to the nucleus and shortens the bond length.

Hybridization in Chemistry

Hybridization in chemistry is the concept used to describe the mixing of atomic orbitals within an atom to form new hybrid orbitals of equivalent energy. It provides insight into molecule geometry and bond lengths.

There are three main types of hybridization relevant to carbon atoms in organic molecules: sp3, sp2, and sp. An sp3 hybridized carbon has four sigma (single) bonds and forms a tetrahedral geometry. An sp2 hybridized carbon has one double bond and two single bonds, leading to a trigonal planar arrangement. An sp hybridized carbon has one triple bond and one single bond, which results in a linear geometry.

Different hybridizations involve different proportions of the s and p orbitals. An sp3 hybridization includes less s-character (25%) than sp2 (33%) or sp (50%), affecting properties such as bond angles and bond lengths. When comparing C-C bond lengths, the sp hybridized carbons form the shortest bonds because the higher s-character brings the binding electrons closer to the nucleus.

Molecular Geometry

Molecular geometry refers to the three-dimensional arrangement of atoms within a molecule. Not only does molecular geometry provide insight into the shape of a molecule, but it also impacts physical and chemical properties, including reactive site availability, polarity, and bond length.

The geometry around a carbon atom can be understood through VSEPR (Valence Shell Electron Pair Repulsion) theory, which states that electron pairs around a central atom repel each other and arrange themselves as far apart as possible. For example, a linear geometry is found in molecules with sp hybridized atoms, where the bond angles are 180 degrees.

Returning to the exercise scenario, the electron cloud repulsion between multiple bonds has a significant role in determining bond lengths. In a molecule dominated by sp hybridized atoms, with strong s-character, not only does the molecular geometry tend toward a linear shape but the surrounding electron cloud repulsions also contribute to minimizing the single bond length, resulting in the shortest C-C bond as seen in molecule (c).