Question

Draw a picture that shows all three \(2 p\) orbitals on one atom and all three \(2 p\) orbitals on another atom. (a) Imagine the atoms coming close together to bond. How many \(a\) bonds can the two sets of \(2 p\) orbitals make with each other? (b) How many \(\pi\) bonds can the two sets of \(2 p\) orbitals make with each other? (c) How many antibonding orbitals, and of what type, can be made from the two sets of \(2 p\) orbitals?

Short answer

When the two sets of 2p orbitals on two atoms come close together to bond, they can form: (a) 1 σ bond, created by the overlap of the \(2p_z\) orbitals on both atoms. (b) 2 π bonds, formed by the sideways overlap of the \(2p_x\) and \(2p_y\) orbitals on both atoms. (c) 3 antibonding orbitals: 1 σ antibonding orbital (\(\sigma^*\)) from the out-of-phase overlap of the \(2p_z\) orbitals, and 2 π antibonding orbitals (\(\pi^*\)_x and \(\pi^*\)_y) from the out-of-phase overlap of the \(2p_x\) and \(2p_y\) orbitals, respectively.

Step-by-step solution

Sketch the 2p orbitals on both atoms

To begin, we have to draw six 2p orbitals in total – three on each atom. Remember that there are three types of 2p orbitals: \(2p_x\), \(2p_y\), and \(2p_z\). These indicate the Cartesian axes (x, y, and z) to which the orbitals are aligned. Draw three 2p orbitals for each atom, one along each axis.

Determine the number of σ bonds between the two sets of 2p orbitals

When two atoms come together to bond, σ bonds form by end-to-end overlap of atomic orbitals along the axis between two nuclei. In the case of 2p orbitals, a σ bond can only be formed by the overlap of the orbitals aligned on the same axis, i.e., the z-axis (\(2p_z\)). For the two sets of 2p orbitals on the two atoms, they can form only one σ bond, created by the overlap of the \(2p_z\) orbitals on both atoms.

Determine the number of π bonds between the two sets of 2p orbitals

Pi (π) bonds are formed by the sideways overlap of atomic orbitals. For 2p orbitals, π bonds can form between \(2p_x\) and \(2p_y\) orbitals. When combining the \(2p_x\) and \(2p_y\) orbitals on one atom with those on the other atom, we find there can be two possible π bonds: 1. The overlap of the \(2p_x\) orbitals on both atoms 2. The overlap of the \(2p_y\) orbitals on both atoms

Identify the antibonding orbitals and their types

Antibonding orbitals form when the wave functions of combining atomic orbitals are out of phase (destructive interference). The antibonding orbitals have higher energy and cancel out some or all of the bonding effect. From the two sets of 2p orbitals, we can form three antibonding orbitals: 1. A σ antibonding orbital (\(\sigma^*\)) formed from the out-of-phase overlap of the \(2p_z\) orbitals 2. A π antibonding orbital (\(\pi^*\)_x) formed from the out-of-phase overlap of the \(2p_x\) orbitals 3. A π antibonding orbital (\(\pi^*\)_y) formed from the out-of-phase overlap of the \(2p_y\) orbitals In summary, when the two sets of 2p orbitals on the two atoms come close together to bond, they can form: (a) 1 σ bond (b) 2 π bonds (c) 3 antibonding orbitals (1 σ antibonding and 2 π antibonding)

Key concepts

σ Bonds

Sigma (σ) bonds represent the strongest type of covalent chemical bond and are formed by the direct overlap of atomic orbitals between two atoms. Picture two spheres, each representing an atomic orbital, coming together to intersect directly; that intersection area, along the axis connecting the atomic nuclei, is a visual representation of a σ bond.

When looking at p orbitals, specifically the 2p orbitals, they can overlap end-to-end to create a σ bond. This occurs when, for example, the 2p_z orbitals of two different atoms align and combine. The result is a robust bond with a high electron density between the nuclei. Since each set of 2p orbitals has only one orbital (2p_z) that can align this way, the maximum number of σ bonds between two sets of 2p orbitals is one.

π Bonds

Pi (π) bonds show up in many organic and inorganic molecules where a double or triple bond is present between atoms. They are the result of the lateral, or side-by-side, overlap of p orbitals across two atoms.

The unique aspect of π bonds, compared to σ bonds, is that they are not formed along the axis between two atomic nuclei but rather above and below this axis. This is possible because of the specific shapes of the p orbitals (2p_x and 2p_y).
By overlapping a 2p_x orbital from one atom with a 2p_x orbital from another, and the same for the 2p_y orbitals, two separate π bonds can be constructed. This side-by-side bonding arrangement can be more reactive than σ bonds and allows for the unique geometry and electron delocalization found in molecules with double and triple bonds.

Antibonding Orbitals

Antibonding orbitals often puzzle students, but they're essential for understanding molecular stability. They occur when atomic orbitals combine with each other in a way that leads to a decrease in overall stability: the orbitals are out of phase, causing destructive interference. This causes regions of low electron probability, also known as nodes.

For two atoms' 2p orbitals, when they align but are out of phase (imagine waves on the ocean crashing against each other and cancelling out), this results in antibonding orbitals. There are three possible antibonding orbitals between two sets of 2p orbitals: one σ* antibonding orbital from the 2p_z orbitals, and two π* antibonding orbitals from the 2p_x and 2p_y orbitals. These orbitals are higher in energy and overall decrease the bond strength compared to when only bonding orbitals are involved.

Orbital Hybridization

Orbital hybridization can be a challenging concept but it is a fundamental aspect of molecular geometry. It relates to how atomic orbitals mix to create new hybrid orbitals. For instance, carbon atoms in organic molecules often undergo sp3, sp2, or sp hybridization—these notations represent the blending of one s orbital with three, two, or one p orbitals respectively.

Hybrid orbitals form because they can result in more stable, stronger bonding within molecules. Picture the transformation of one s orbital and one p orbital—a round shape and a dumbbell shape—morphing into two identical, oval-shaped hybrid orbitals. These hybrids then bond with other hybrids or atomic orbitals in the molecule, maximizing overlapping and therefore electron sharing between atoms. Hybridization explains why molecules show specific shapes, such as the tetrahedral geometry of methane (CH4) or the planar shape of ethene (C2H4).