Question

(a) Draw a picture showing how two \(p\) orbitals on two different atoms can be combined to make a \(\sigma\) bond. (b) Sketch a \(\pi\) bond that is constructed from \(p\) orbitals. (c) Which is generally stronger, a \(\sigma\) bond or a \(\pi\) bond? Explain. (d) Can two \(s\) orbitals combine to form a \(\pi\) bond? Explain.

Short answer

A \(\sigma\) bond is formed by the head-to-head overlap of orbitals, like two \(p\) orbitals aligned along the axis between the two nuclei. A \(\pi\) bond results from the side-to-side overlap of two \(p\) orbitals, with electron density above and below the plane of the nuclei. \(\sigma\) bonds are generally stronger than \(\pi\) bonds due to greater electron density between the nuclei. Two \(s\) orbitals cannot form a \(\pi\) bond, as their spherical nature only allows head-to-head overlap, resulting in a \(\sigma\) bond.

Step-by-step solution

Understand \(\sigma\) and \(\pi\) bonds

A \(\sigma\) bond is a type of covalent bond formed by the direct head-to-head overlap of orbitals, resulting in electron density along the axis joining the nuclei of both atoms. A \(\pi\) bond, on the other hand, forms by the side-to-side overlap of orbitals resulting in electron density above and below the plane of the nuclei, leading to a weaker bond than the \(\sigma\) bond.

Drawing a \(\sigma\) bond with \(p\) orbitals

To draw a \(\sigma\) bond formed by the combination of two \(p\) orbitals: 1. Draw two \(p\) orbitals from two different atoms, one from each atom. \(p\) orbitals look like dumbbell-shaped lobes, with two equal-sized lobes on either side of the nucleus. 2. Align the orbitals so that they overlap along the axis joining their nuclei, effectively sharing electron density along the axis.

Sketching a \(\pi\) bond with \(p\) orbitals

To draw a \(\pi\) bond formed by the combination of two \(p\) orbitals: 1. Draw the same two \(p\) orbitals from two different atoms, one from each atom. 2. In this case, instead of aligning them head-to-head, align them so that a lobe from each orbital overlaps side-to-side. 3. Show the resulting electron density above and below the plane of the two nuclei, depicting the \(\pi\) bond.

Comparing the strengths of \(\sigma\) and \(\pi\) bonds

A \(\sigma\) bond is generally stronger than a \(\pi\) bond. This is because the head-to-head overlap in \(\sigma\) bonds results in greater electron density between the nuclei, providing a stronger force of attraction between the atoms. Conversely, the side-to-side overlap in \(\pi\) bonds results in electron density above and below the plane of the nuclei, leading to a weaker bond.

Can two \(s\) orbitals form a \(\pi\) bond?

Two \(s\) orbitals cannot combine to form a \(\pi\) bond. \(s\) orbitals are spherical and symmetric around their nucleus, and when two \(s\) orbitals overlap, they result in a \(\sigma\) bond, with the electron density concentrated along the axis between the nuclei. The nature of \(s\) orbitals does not allow for the side-to-side overlap necessary to create a \(\pi\) bond.

Key concepts

Chemical Bonding

Chemical bonding is a fundamental concept in chemistry that explains how atoms combine to form molecules. The force that holds atoms together in molecules is a result of the interactions between their electrons. There are several types of chemical bonds, including ionic, covalent, and metallic bonds. Covalent bonding, in particular, involves the sharing of electron pairs between atoms. These shared electrons contribute to the formation of a stable electronic configuration for each atom involved, leading to the creation of a molecule.

When discussing covalent bonds, we often refer to 'sigma () and 'pi' () bonds. A bond, as mentioned in the solution, is the result of end-to-end overlapping of atomic orbitals, while a bond is formed by the side-to-side overlap of orbitals. Having a visual understanding of these overlapping processes, as accomplished through drawing, enhances comprehension of these concepts.

Molecular Orbital Theory

Molecular orbital theory (MOT) provides a more comprehensive understanding of how atoms bind together to form molecules. According to MOT, atomic orbitals combine to form molecular orbitals. These molecular orbitals are distributed over the entire molecule, rather than belonging to a single atom. Electrons occupying these orbitals thus influence the entire molecule's structure and properties.

In this theory, when two atomic orbitals overlap, they create two molecular orbitals: a bonding molecular orbital (lower in energy and more stable), and an antibonding molecular orbital (higher in energy and less stable). bonds are associated with the bonding molecular orbitals, while bonds correspond to the situations where the p orbitals overlap sideways, which is not as energetically favorable. Knowing the difference between bonding and antibonding orbitals is crucial for understanding the stability of molecules and predicting their behavior.

Covalent Bonding

Covalent bonding is characterized by the sharing of electron pairs between atoms. The shared electrons allow each atom to achieve an electron configuration that is typically more stable, often resembling that of the nearest noble gas. This type of bonding is a key feature in organic molecules and many other compounds.

The strength of a covalent bond is influenced by the overlap between the atomic orbitals. As you've learned from the exercise, a bond is stronger than a bond because the overlap is more significant in a head-to-head orientation. It's helpful for students to visualize covalent bonds not just as static connections but as the dynamic sharing of electron pairs, which can be influenced by the nature of the atomic orbitals involved and the presence of other atoms or bonds nearby.

Orbital Hybridization

Orbital hybridization is a concept that describes the mixing of atomic orbitals to form new hybrid orbitals. These hybrid orbitals accommodate the formation of covalent bonds in molecules, explaining geometrical structures that otherwise would not be justified by the simple arrangement of atomic orbitals.

For example, the sp3 hybridization in methane (CH4) results in four equivalent hybrid orbitals arranged in a tetrahedral geometry. Orbital hybridization significantly enriches our understanding of molecular shapes and the distribution of electrons within molecules. It is directly connected to the types of bonds a single atom can form, such as a bond formed by an sp3 hybridized carbon with another sp3 hybridized carbon.