Problem 116 - Chemistry Principles and Practice

Question

Ionization energies can be determined for molecules and atoms. Draw the molecular orbital diagrams for \(\mathrm{NO}\) and \(\mathrm{CO}\), and predict which compound has the lower ionization energy.

Step-by-Step Solution

Answer

NO has the lower ionization energy due to its higher-energy HOMO.

Step 1: Understanding the Molecules

To predict which molecule has a lower ionization energy, we need to consider the molecular orbital (MO) diagrams for both \(\mathrm{NO}\) and \(\mathrm{CO}\). Ionization energy depends on the energy of the highest occupied molecular orbital (HOMO); the lower the energy, the higher the ionization energy.

Step 2: Drawing the MO Diagram for NO

The molecule \(\mathrm{NO}\) has 15 electrons. In an MO diagram, we fill MOs using the Aufbau principle, starting from the lowest energy orbital. The order of filling is: \(\sigma_{2s}\), \(\sigma^*_{2s}\), \(\pi_{2p}\), \(\sigma_{2p}\), \(\pi^*_{2p}\). For \(\mathrm{NO}\), the HOMO is \(\pi^*_{2p}\) containing one electron.

Step 3: Drawing the MO Diagram for CO

The molecule \(\mathrm{CO}\) has 14 electrons. The MO diagram is similar to \(\mathrm{NO}\), but \(\mathrm{CO}\) fills up to the \(\pi_{2p}\) orbitals. The \(\sigma_{2p}\) orbital is the HOMO in this case, and it has filled electrons (a \(\sigma\) bond).

Step 4: Comparing the HOMOs

The HOMO of \(\mathrm{NO}\) is a \(\pi^*_{2p}\) orbital, while for \(\mathrm{CO}\) it is a \(\sigma_{2p}\) orbital. Generally, \(\sigma\) orbitals are lower in energy than \(\pi\) orbitals because they are more concentrated along the internuclear axis, hence more stable.

Step 5: Predicting Ionization Energy

Since \(\pi\) orbitals in \(\mathrm{NO}\) are of higher energy than \(\sigma\) orbitals in \(\mathrm{CO}\), \(\mathrm{NO}\) has a lower ionization energy because its electrons are less tightly held compared to \(\mathrm{CO}\).

Key Concepts

Molecular Orbital Theory

Molecular Orbital Theory provides a framework to understand how atomic orbitals combine to form molecular orbitals. This theory aids in predicting the behavior of electrons in a molecule, which in turn affects properties like ionization energy. In this theory, atomic orbitals from each atom, such as the 2s and 2p orbitals, mix to produce molecular orbitals that can hold the electrons of the entire molecule.
The molecular orbitals are formed in different energy levels and are filled using a set of rules. These orbitals can be classified as bonding or antibonding, represented with notations like \(\sigma \) and \(\pi\) for bonding orbitals, and \(\sigma^* \) and \(\pi^*\) for antibonding orbitals. Electrons filling lower energy (bonding) orbitals precedes those entering higher energy (antibonding) orbitals.

• Bonding orbitals, like the \(\sigma_{2s}\), increase molecule stability.
• Antibonding orbitals, such as \(\sigma^*_{2s}\), tend to make the molecule less stable.

This approach allows us to visualize the distribution of electrons in a molecule, providing insight into molecular stability and reactivity.

HOMO

The Highest Occupied Molecular Orbital (HOMO) is a crucial concept in understanding the electron structure of a molecule. HOMO corresponds to the highest energy level that contains electrons.
It is significant because the energy level of the HOMO helps determine the ionization energy of a molecule. If the HOMO is at a high energy level, the electrons are less tightly bound, leading to lower ionization energy. Conversely, a low-energy HOMO indicates a higher ionization energy due to tightly bound electrons.

• In the molecule \(\text{NO}\), the HOMO is represented by a high-energy antibonding \(\pi^*_{2p}\) orbital.
• For \(\text{CO}\), the HOMO is the lower energy \(\sigma_{2p}\) orbital.

The comparison of HOMOs helps predict differences in ionization energies among molecules, providing insights into molecular reactivity and chemical behavior.

Molecular Orbitals

Molecular orbitals (MOs) are the result of the combination of atomic orbitals when atoms bond together to form a molecule. These orbitals extend over the entire molecule and accommodate the shared electrons. MOs are fundamental in determining molecular properties, as they dictate electron distribution and molecular structure.
The formation and filling of MOs follow an order based on energy, influenced by the types of orbitals involved.

• Bonding MOs, like \(\sigma_{2s}\) and \(\pi_{2p}\), have electrons that help stabilize the molecule.
• Antibonding MOs, such as \(\sigma^*_{2s}\) and \(\pi^*_{2p}\), contain electrons that can destabilize a molecule if occupied.

The correct filling of MOs reveals the electronic nature of the molecule, impacting its chemical and physical characteristics such as stability, reactivity, and ionization energy. Thus, understanding and analyzing molecular orbitals is essential for predicting the behavior of molecules.

Aufbau Principle

The Aufbau Principle is a guideline used to determine the electronic configuration of molecules. The core idea is that electrons fill the lowest energy orbitals available before occupying higher energy ones. This process builds the most stable electronic structure for atoms and molecules.
In molecular orbital diagrams for \(\text{NO}\) and \(\text{CO}\), the principle is applied to distribute electrons among different MOs.

• Start filling with the lowest energy \(\sigma_{2s}\) orbital.
• Progress to the \(\sigma^*_{2s}\), followed by \(\pi_{2p}\) and \(\sigma_{2p}\) orbitals.

This sequence continues until all electrons have been placed. Due to this principle, \(\text{CO}\) exhibits a filled \(\sigma_{2p}\) orbital as its HOMO, while \(\text{NO}\) presents an unpaired electron in a \(\pi^*_{2p}\) orbital.
The application of the Aufbau Principle allows for systematic electron configuration, offering insights into molecular behaviors such as ionization energy.