Question

In the hybrid orbital model, compare and contrast \(\sigma\) bonds with \(\pi\) bonds. What orbitals form the \(\sigma\) bonds and what orbitals form the \(\pi\) bonds? Assume the \(z\) -axis is the internuclear axis.

Short answer

In the hybrid orbital model, \(\sigma\) bonds are formed by the axial overlap of s and p orbitals along the internuclear axis, resulting in strong, stable, and polar bonds due to significant orbital overlap and electron density between the nuclei. On the other hand, \(\pi\) bonds are formed by the lateral overlap of parallel p orbitals above and below the internuclear axis, leading to weaker, less polar bonds with less significant orbital overlap.

Step-by-step solution

Understanding sigma (\(\sigma\)) bonds and their formation

A \(\sigma\) bond is formed when two orbitals, one from each atom, overlap end-to-end along the internuclear axis (the line connecting the two nuclei). This overlap is called axial overlap. The resulting bond is strong and stable because of the significant overlap of orbitals along the internuclear axis. In general, s and p orbitals can form \(\sigma\) bonds. For example, an s-s, s-p, or p-p overlap could lead to the formation of a \(\sigma\) bond.

Understanding pi (\(\pi\)) bonds and their formation

A \(\pi\) bond is formed when two parallel p orbitals, one from each atom, overlap side-to-side above and below the internuclear axis. This overlap is called lateral overlap. The resulting bond is weaker than a \(\sigma\) bond because the overlap between the orbitals is not as significant (less electron density between the nuclei). In general, only p orbitals can form \(\pi\) bonds, such as a p-p overlap.

Comparing and contrasting sigma (\(\sigma\)) and pi (\(\pi\)) bonds

There are several ways in which \(\sigma\) and \(\pi\) bonds can be compared and contrasted: 1. Formation: While \(\sigma\) bonds are formed by the axial overlap of orbitals, \(\pi\) bonds are formed by the lateral overlap of parallel p orbitals. 2. Strength: \(\sigma\) bonds are generally stronger than \(\pi\) bonds, due to the greater orbital overlap and the electron density situated between the nuclei. 3. Orbitals involved: \(\sigma\) bonds can be formed by the overlap of s and p orbitals, whereas \(\pi\) bonds are only formed by the overlap of p orbitals. 4. Polarity: \(\sigma\) bonds are usually more polar than \(\pi\) bonds, as they allow for more charge distribution between the atoms involved. #Conclusion# In summary, \(\sigma\) bonds are stronger, more stable, and polar bonds formed by the axial overlap of s and p orbitals along the internuclear axis. On the other hand, \(\pi\) bonds are weaker, less polar bonds formed by the lateral overlap of parallel p orbitals above and below the internuclear axis.

Key concepts

sigma bonds

Sigma (\(\sigma\)) bonds are a fundamental concept in chemistry, representing the strongest type of covalent chemical bond. These bonds are formed by the direct, end-to-end overlapping of orbitals along the internuclear axis, which is the imaginary line running through the nuclei of the bonding atoms. The strength and stability of \(\sigma\) bonds arise from this axial overlap, which maximizes electron density between the nuclei.
Common types of orbital overlaps that can form \(\sigma\) bonds include:

• s-s overlap: Two s orbitals overlapping.
• s-p overlap: An s orbital overlapping with a p orbital.
• p-p overlap: Two p orbitals overlapping end-to-end.

The versatility in overlap types explains why \(\sigma\) bonds are found in a variety of chemical compounds, making them a critical part of our understanding of molecular structure.

pi bonds

Pi (\(\pi\)) bonds are another type of covalent bond, distinct from \(\sigma\) bonds, yet they often exist alongside them in molecules containing double or triple bonds. Unlike \(\sigma\) bonds, \(\pi\) bonds arise from side-to-side overlap of two parallel p orbitals above and below the internuclear axis. This lateral overlap is less extensive compared to the axial overlap of \(\sigma\) bonds, leading to a weaker bond.
Pi bonds contribute to the double-bond character in molecules like ethylene (C₂H₄) or the triple-bond character in acetylene (C₂H₂). In a double bond, one is a \(\sigma\) bond and the other is a \(\pi\) bond, whereas in a triple bond, there is one \(\sigma\) bond and two \(\pi\) bonds, which provide rigidity and restrict rotation around the bond axis.

orbital overlap

Orbital overlap is the concept explaining how atoms combine to form covalent bonds based on the spatial orientation and interaction of their atomic orbitals. When two orbitals overlap, they share space, allowing electrons from each atom to occupy overlapping regions. This sharing of space allows for electron pairing and the formation of chemical bonds.
In \(\sigma\) bonds, the overlap is axial, occurring along the internuclear axis, ensuring strong electron density between the nuclei. Conversely, in \(\pi\) bonds, the overlap is lateral, resulting in electron density above and below the axis. The nature of the overlap not only determines the type of bond that forms but also influences the bond's strength, polarity, and overall stability.

internuclear axis

The internuclear axis is a pivotal concept when understanding molecular geometry and bonding, particularly for \(\sigma\) and \(\pi\) bonds. This imaginary line represents the shortest distance between the nuclei of two atoms bonded together. The orientation of overlapping orbitals relative to this axis determines the type of bond formed.
In \(\sigma\) bonds, orbitals overlap along the internuclear axis, creating a strong single bond with distinct electron density directly between the two nuclei. This directional characteristic enhances bond strength. For \(\pi\) bonds, the orbitals overlap perpendicular to the internuclear axis, leading to weaker bonds with electron clouds above and below the axis. Knowing this axis helps in predicting molecular shapes and the nature of chemical bonding.