Question

With appropriate sketches, represent chemical bonding in terms of the overlap of hybridized and unhybridized atomic orbitals in the following molecules. (a) ${\mathrm{C}}_4{\mathrm{H}}_{10};$ (b) ${\mathrm{H}}_2\mathrm{C}=\mathrm{CHCl};$ (c) ${\mathrm{CH}}_3\mathrm{C}\equiv \mathrm{CH}$.

Short answer

The molecules C4H10, H2C=CHCl, and CH3C≡CH contain sp3, sp2, and sp hybrid orbitals respectively from carbon atoms involved in sigma bonding. While C4H10 contains only sigma bonds, H2C=CHCl and CH3C≡CH also contain pi bonds from the overlap of unhybridized carbon p orbitals.

Step-by-step solution

- Understanding Chemical Bonding

Knowing that chemical bonding occurs when the atoms' orbitals overlap, it will be crucial to recognize the types of orbitals involved in each molecule. An understanding of hybrid orbitals will be particularly necessary.

- Orbitals in C4H10

In butane (C4H10), carbon atoms form sigma bonds with both hydrogen and other carbon atoms. The carbon atoms utilize sp3 hybrid orbitals for this bonding, while the hydrogen atoms utilize their 1s atomic orbitals. For the unhybridized p orbitals, you'll note that there are none in this molecule due to all carbon electrons being involved in sigma bonding.

- Orbitals in H2C=CHCl

In H2C=CHCl, there are both sigma and pi bonds. The carbon atoms use sp2 hybrid orbitals to form sigma bonds with hydrogen and other carbon or chlorine atoms, while they use unhybridized 2p orbitals to form the pi bond that constitutes the double bond between the two carbon atoms. Hydrogen uses 1s atomic orbitals, and chlorine uses 3p.

- Orbitals in CH3C≡CH

In CH3C≡CH, there are sigma and pi bonds due to the presence of a triple bond. The carbon atoms connected by the triple bond use their sp hybrid orbitals to form the sigma bonds and two sets of unhybridized p orbitals to make two pi bonds. Hydrogen atoms again use 1s atomic orbitals to form bonds with the carbon atoms.

Key concepts

Hybrid Orbitals

Hybrid orbitals are a fascinating concept helping us to understand how atoms form bonds in molecules. When atoms prepare to bond, their existing atomic orbitals can "mix" or "hybridize" to form new orbitals that better accommodate the pairing of electrons. These new orbitals are known as hybrid orbitals.

For example, in the molecule of butane (C${}_4$H${}_{10}$), carbon atoms undergo sp${}^3$ hybridization. This means that one s orbital and three p orbitals blend together to form four equivalent sp${}^3$ hybrid orbitals. These orbital hybrids facilitate the formation of strong sigma bonds (explored below) with both carbon and hydrogen atoms.

Each type of hybridization determines the geometry of the molecule. For instance:

• sp${}^3$ hybridization: Results in a tetrahedral shape and involves four sigma bonds, as seen in C${}_4$H${}_{10}$.
• sp${}^2$ hybridization: Leaves one p orbital unhybridized and gives rise to a trigonal planar shape, useful for forming double bonds such as in H${}_2$C=CHCl.
• sp hybridization: Leaves two p orbitals unhybridized, resulting in a linear shape, appropriate for triple bonds like in CH${}_3$C≡CH.

An understanding of hybrid orbitals enables us to predict the geometry and bonding behavior of molecules, forming the bedrock of molecular chemistry.

Sigma Bonds

Sigma (σ) bonds are the strongest type of covalent chemical bond due to the end-to-end overlap of atomic orbitals. These bonds form the backbone of many molecular structures.

In sigma bonds, the overlap occurs along the axis connecting two bonded nuclei. This overlap can involve hybrid orbitals or atomic s orbitals. In butane (C${}_4$H${}_{10}$), for instance, each carbon atom's sp${}^3$ hybrid orbitals overlap with the 1s orbitals of hydrogen, forming strong σ bonds.

The features of sigma bonds include:

• Single Bonds: Sigma bonds form every time you have a single bond, making them present in all molecular structures.
• Strength and Stability: The direct overlap results in strong and stable bonds, crucial for constructing a molecule's framework.
• Rotation Allowed: Unlike pi bonds, sigma bonds allow free rotation of bonded atoms because the orbital overlap is symmetrical around the bond axis.

Understanding sigma bonds is fundamental to grasping how atoms stick together so firmly to form stable compounds.

Pi Bonds

Pi (π) bonds are a type of covalent bond that form after a sigma bond during the creation of double or triple bonds. Unlike sigma bonds, pi bonds involve the sideways overlap of unhybridized p orbitals.

Pi bonds are responsible for producing multiple bonds between atoms. For example, in H${}_2$C=CHCl, each carbon forms a pi bond by overlapping a p orbital with another carbon's unhybridized p orbital. This sideways overlap leads to the formation of a double bond, consisting of one sigma and one pi bond.

Characteristics of pi bonds include:

• Secondary Bonding: Pi bonds are always present in addition to a sigma bond, never alone.
• Restricted Rotation: The nature of pi bonds restricts the rotational freedom of bonded atoms, affecting the molecule's overall shape.
• Weaker Than Sigma Bonds: With only partial orbital overlap, pi bonds are generally weaker than sigma bonds.

In molecules with triple bonds like CH${}_3$C≡CH, two pi bonds accompany a sigma bond, showcasing the capacity for multiple bonding overlaps, which create intriguing molecular properties.