Problem 102 - Chemistry: An Atoms-Focused Approach

Question

Make a sketch showing how two \(2 p_{y}\) orbitals overlap "sideways" to form a \(\pi_{2 p}\) bonding molecular orbital and a \(\pi_{2 p}^{*}\) antibonding molecular orbital.

Step-by-Step Solution

Answer

Answer: \(\pi_{2p}\) bonding molecular orbitals are formed when the lobes of the same phase (color) of two \(2p_y\) orbitals overlap sideways, resulting in constructive interference and higher electron density between the nuclei. On the other hand, \(\pi_{2p}^*\) antibonding molecular orbitals are formed when the lobes of opposite phases (colors) of the \(2p_y\) orbitals overlap, resulting in destructive interference and a node between the nuclei.

Step 1: Understand "sideways" overlap

When the \(2p_y\) orbitals interact, they overlap "sideways." This means that their lobes are parallel to the internuclear axis, as opposed to head-on interaction like in sigma bonds. Sideways overlap creates what is known as a pi bond.

Step 2: Visualize Atomic Orbitals

To draw the sketch of the overlapping \(2p_y\) atomic orbitals, first visualize the two separate \(2p_y\) atomic orbitals. Each \(2p_y\) orbital has two lobes on opposite sides of the atom's nucleus, with one lobe above and one below the internuclear axis.

Step 3: Draw the Formation of \(\pi_{2p}\) Bonding MO

Now, represent the two atoms with their \(2p_y\) orbitals approaching each other from opposite sides so that the lobes overlap sidewise. When the lobes of the same phase (color) overlap, constructive interference occurs, and this results in the formation of a \(\pi_{2p}\) bonding molecular orbital, with higher electron density in the region between the nuclei. In the sketch, show the overlapping lobes with the same color (for instance, both positive or both negative phases), and depict the electron density cloud between the nuclei that is formed by this overlap.

Step 4: Draw the Formation of \(\pi_{2p}^{*}\) Antibonding MO

Similarly, when the lobes of opposite phases (colors) overlap, destructive interference occurs, and this results in the formation of a \(\pi_{2p}^*\) antibonding molecular orbital. In the sketch, show the overlapping lobes with different colors (one positive phase and one negative phase). Because of the destructive interference, there will be a node (a plane of zero electron density) perpendicular to the internuclear axis in the region between the nuclei. Now you have a sketch that illustrates the formation of \(\pi_{2p}\) bonding and \(\pi_{2p}^*\) antibonding molecular orbitals due to the sideways overlap of two \(2p_y\) orbitals.

Key Concepts

2p orbitals

The 2p orbitals play a crucial role in the formation of certain molecular bonds, particularly pi bonds. These orbitals are part of the second principal energy level around an atom’s nucleus, and each energy level has three p orbitals traditionally labeled as px, py, and pz. Each 2p orbital is dumbbell-shaped, with two lobes on either side of the nucleus.
The 2p orbitals can overlap in different ways, creating different types of bonds between atoms. For a pi bond to form, the lobes of these p orbitals must align parallel to one another. This arrangement allows for sideways overlap, distinct from the end-to-end overlap seen in sigma bonds.
When sketching or visualizing 2p orbitals, remember that each orbital extends in different directions, with py typically represented as oriented in the horizontal plane. This traditional depiction helps appreciate how these orbitals interact to form complex molecular structures.

molecular orbitals

Molecular orbitals are fundamental to understanding how atoms bond to form molecules. These orbitals arise when atomic orbitals combine, spreading the electrons over several atomic centers in a molecule.
In the case of the pi bond involving the 2p_y orbitals, molecular orbitals are formed through a sideways overlap. Two main types of molecular orbitals are formed: bonding and antibonding.

• Bonding Molecular Orbital (\(\pi_{2p}\)): In the bonding molecular orbital, electrons are more likely to be found in the space between the nuclei. This orbital results from the constructive interference of wave functions, where lobes of the same phase overlap, increasing electron density in the bonding region.
• Antibonding Molecular Orbital (\(\pi_{2p}^{*}\)): On the other hand, the antibonding molecular orbital features nodes, or areas of zero electron density, where wave functions destructively interfere. This occurs when lobes of opposite phases overlap, making the molecular structure weaker and less stable.

The effective bonding depends largely on the occupation of these molecular orbitals, providing insight into the molecule’s stability and reactivity.

bonding and antibonding interactions

In molecular bond formation, interactions between atomic orbitals either strengthen or weaken the resulting molecule, depending on the type of overlap.
Bonding interactions occur when the wave functions of overlapping orbitals are in phase. This in-phase overlap leads to constructive interference, creating a region of increased electron density between the bonded nuclei. Electrons in this region are attracted to both nuclei, forging a strong bond.
Conversely, antibonding interactions involve out-of-phase overlaps, leading to destructive interference. The result is a node, an area with no electron density, within the antibonding molecular orbital. These interactions are less favorable since they destabilize the bond, making it weaker overall.

• Bonding molecular orbital: Higher electron density between atoms, resulting in a strong molecule.
• Antibonding molecular orbital: Lower electron density between atoms with nodes, leading to instability and weakness.

Understanding these interactions is key to predicting the behavior and stability of molecules in various chemical contexts.