Problem 115 - Chemistry The Molecular Nature of Matter

Question

Assume that in the \(\mathrm{NO}\) molecule the molecular orbital energy level sequence is similar to that for \(\mathrm{O}_{2}\). What happens to the NO bond length when an electron is removed from \(\mathrm{NO}\) to give \(\mathrm{NO}^{+} ?\) How would the bond energy of NO compare to that of \(\mathrm{NO}^{+}\) ?

Step-by-Step Solution

Answer

The NO bond length decreases when an electron is removed to form NO+. The bond energy of NO+ is higher compared to NO because of the shorter and stronger bond.

Step 1: Understanding Molecular Orbitals

Understand that in molecular orbitals of diatomic molecules like NO and O2, electrons fill the orbitals starting from the lowest energy level. The order in which these orbitals are filled can affect properties like bond length and bond energy. For NO, which has an odd number of electrons, the last electron is placed in an antibonding orbital (as NO has one more electron than NO+).

Step 2: Considering the Electron Removal

Recognize that removing an electron from NO to form NO+ means removing it from the highest occupied molecular orbital, which is an antibonding orbital. As a result, there's a decrease in the electron density in an antibonding orbital, which typically leads to a decrease in bond length. This is because antibonding orbitals, when occupied, weaken the bond between the two atoms.

Step 3: Comparing Bond Energy

Acknowledge that a shorter bond length results in a stronger (higher energy) bond. Therefore, since NO+ has a shorter bond length due to the removal of an electron from the antibonding orbital, the bond energy in NO+ is greater than in NO.

Key Concepts

Understanding Bond Length

Bond length is a measure of the distance between the nuclei of two bonded atoms. It is a significant factor in the stability and reactivity of a molecule. Generally, when we talk about bond length, we are referring to the equilibrium distance where the forces of attraction and repulsion between the atoms are balanced.

In the case of the NO molecule, when an electron is removed to form NO+, the bond length shortens. This is due to the decrease in electron density in the antibonding orbital. Antibonding orbitals, as their name suggests, work against the bonding process, and when they are populated, they make the bond weaker and longer. By removing an electron from this antibonding orbital, the repulsion between the atoms is reduced, allowing them to come closer together, resulting in a shorter bond length.

It's also important to note that multiple factors influence bond length. Atomic size, the type of bond (single, double, triple), and the presence of different electron orbitals all play a role in determining the precise distance between atoms within a molecule.

The Role of Bond Energy

Bond energy is directly related to the strength of a chemical bond. It is defined as the energy required to break one mole of bonds in a molecule and is usually measured in kilojoules per mole (kJ/mol). High bond energy correlates to a more stable bond as it signifies a stronger attraction between the bonded atoms.

In the context of NO and NO+, removing an electron from the antibonding orbital in NO results in an increase in bond energy when we get NO+. Since NO+ has a shorter bond length, the bond strength is correspondingly higher, which means more energy is needed to break the bonds compared to NO. This concept is crucial for understanding reactivity patterns in chemistry because molecules with higher bond energies are generally less reactive since they require more energy to undergo chemical changes.

Molecular stability and reactivity are influenced by bond energy - molecules with shorter bonds and higher bond energies are often less reactive because the bonded atoms hold onto each other more tightly, displaying lower tendencies to participate in chemical reactions.

Antibonding Orbitals Explained

Antibonding orbitals are a type of molecular orbitals that, when occupied by electrons, weaken the bond between atoms rather than strengthening it. They are denoted by an asterisk symbol (e.g., \(\sigma^*\) or \(\pi^*\)) to distinguish them from bonding orbitals.

In NO, the presence of an electron in an antibonding orbital contributes to a longer bond length and reduced bond energy. As electrons in antibonding orbitals create repulsion between the two atoms, they are said to 'anti-bond' the molecule. When an electron is removed from an antibonding orbital (such as in the formation of NO+), the destabilizing effect is reduced, leading to a stronger and shorter bond.

The concept of antibonding orbitals emphasizes the balance between bonding and antibonding influences in a molecule. It is crucial to understand that for a bond to exist, the number of electrons in bonding orbitals must exceed the number of electrons in antibonding orbitals. Antibonding orbitals are also keys when it comes to absorption of light and electronic transitions, which affect the color and spectroscopic properties of molecules.