Question

Bond energy has been defined in the text as the amount of energy required to break a chemical bond, so we have come to think of the addition of energy as breaking bonds. However, in some cases the addition of energy can cause the formation of bonds. For example, in a sample of helium gas subjected to a high-energy source, some He_ molecules exist momentarily and then dissociate. Use MO theory (and diagrams) to explain why \(\mathrm{He}_{2}\) molecules can come to exist and why they dissociate.

Short answer

According to Molecular Orbital Theory, He2 molecules momentarily exist under high-energy conditions due to the formation of a σ bonding molecular orbital. However, the presence of an equal number of electrons in the σ* antibonding molecular orbital leads to rapid dissociation, as the stabilization energy from bonding is canceled out by the destabilization energy from the antibonding orbital. This explanation is supported by the MO diagram for the He2 molecule and its electron configuration (σ2σ*2).

Step-by-step solution

Understanding Molecular Orbital Theory

Molecular Orbital Theory (MO theory) is a method to describe the electronic structure of molecules. It combines atomic orbitals from individual atoms to form molecular orbitals that belong to the entire molecule. These molecular orbitals can have different shapes, energies, and their occupation by electrons determines the stability of the molecule.

Constructing the MO diagram for Helium Molecule (He2)

For constructing the MO diagram, we need to consider atomic orbitals of the two Helium atoms (He). Each He atom has two electrons, occupying the 1s orbital. When the two He atoms come close to each other, their atomic orbitals interact, and due to their overlapping, they form two molecular orbitals: 1. Bonding Molecular Orbital (σ): This molecular orbital has lower energy than the parent atomic orbitals and is formed by the in-phase combination of the atomic orbitals. 2. Antibonding Molecular Orbital (σ*): This molecular orbital has higher energy than the parent atomic orbitals and is formed by the out-of-phase combination of the atomic orbitals. The MO diagram for He2 molecule is shown as follows: - Atomic orbitals from two He atoms are on the left and right sides. - Molecular orbitals are represented in the middle. The lower energy bonding molecular orbital (σ) is at the bottom and the higher energy antibonding molecular orbital (σ*) is at the top.

Determining the electron configuration for He2

Each Helium atom has 2 electrons in its 1s orbital. When forming He2, there are a total of 4 electrons to be placed in the molecular orbitals. According to Aufbau principle, electrons fill the molecular orbitals in order of increasing energy. So, two electrons will go into the bonding molecular orbital (σ) and the remaining two electrons will go into the antibonding molecular orbital (σ*). Hence, electron configuration of He2 is: σ2σ*2

Explaining the momentary existence and dissociation of He2 molecules

From the electron configuration of He2 (σ2σ*2), we can observe that the number of electrons in bonding orbital is equal to the number of electrons in antibonding orbital. This means that the stabilization energy provided by the electrons in bonding molecular orbital is exactly canceled by the destabilization energy due to electrons in the antibonding molecular orbital. So, when Helium gas is subjected to a high-energy source, some He2 molecules can come to exist momentarily due to the formation of σ bonding molecular orbital. However, the destabilizing effect of the electrons in σ* antibonding molecular orbital leads to the rapid dissociation of these He2 molecules. In conclusion, MO theory and MO diagrams help us understand the momentary existence and dissociation of He2 molecules under high-energy conditions. The formation of bonding and antibonding molecular orbitals and their occupation by electrons dictate the overall stability of the molecule.

Key concepts

Chemical Bonding

Chemical bonding is the force that holds atoms together to form molecules. It's a fundamental concept in chemistry, explaining how atoms combine and interact with each other. In the case of the helium molecule (\(\text{He}_2\)), bonds form between helium atoms through interactions of their electrons.
There are several types of chemical bonds: ionic, covalent, and metallic. For the purpose of discussing \(\text{He}_2\), we focus on covalent bonding, where electrons are shared between atoms. However, with \(\text{He}_2\), the situation is slightly more complex because these bonds are momentarily formed and not stable under normal conditions.

• Ionic Bonds: Formed when electrons are transferred from one atom to another, creating charged ions that attract each other.
• Covalent Bonds: Formed when atoms share electrons; common in organic molecules.
• Metallic Bonds: Involve a 'sea of electrons' that move freely between metallic atoms.

In the context of Molecular Orbital (MO) Theory, rather than thinking about individual bonds, we look at how atomic orbitals combine to form molecular orbitals, which belong to the whole molecule rather than a single atom. Understanding this concept helps explain why \(\text{He}_2\) can form under certain conditions, even if only for a fleeting moment.

Bond Energy

Bond energy is crucial to understanding molecule stability. It refers to the amount of energy required to break a bond between two atoms. Essentially, bond energy reflects the strength of the bond - higher bond energy indicates stronger bonds.
When discussing the helium molecule (\(\text{He}_2\)), the consideration of bond energy becomes slightly different. In helium’s case, the bond energy associated with the short-lived molecule gives insight into its instability. High energy inputs, such as from a high-energy source, are necessary to form any bonds.
### Factors influencing Bond Energy

• Atomic Size: Larger atoms tend to have lower bond energies due to increased distance between nuclei.
• Electron Configuration: Stability of electron orbitals influences bond energy. Filled or empty orbitals create different levels of interaction.
• Environmental Conditions: Temperature and pressure can affect bond energies and hence stability of molecules.

Understanding bond energy helps chemists predict how molecules will behave in reactions and under varying conditions, as seen with \(\text{He}_2\).

He2 Molecule Stability

The stability of the \(\text{He}_2\) molecule is an intriguing subject. While it exists momentarily under high-energy conditions, it quickly dissociates.
Molecular stability is ultimately affected by the balance between bonding and antibonding forces within a molecule. In the \(\text{He}_2\) molecule, the electrons found in the bonding molecular orbital (σ) are countered by an equal number in the antibonding molecular orbital (σ*).
This leads to zero bond order, calculated as:\[\text{Bond Order} = \frac{\text{Number of Bonding Electrons} - \text{Number of Antibonding Electrons}}{2} = \frac{2 - 2}{2} = 0\]With a bond order of zero, the \(\text{He}_2\) molecule has no net stabilization from electron sharing, leading to instability.
### Factors explaining He2 Instability

• Electron Pair Cancellation: Equal numbers of electrons in bonding and antibonding orbitals result in neutralizing each other's effects.
• Initial Conditions: Requires high-energy environments to form, indicative of an inherently unstable configuration.
• Zero Bond Order: Reflects the lack of net attractive force to maintain the bond.

Thus, while \(\text{He}_2\)'s brief formation is a fascinating result of electronic interactions, it remains unstable and transient.

MO Diagrams

Molecular Orbital (MO) diagrams are a visual representation that helps us understand the electronic structure of molecules. By using MO diagrams, we can deduce a molecule’s stability and reactivity.
### Constructing the MO Diagram for He2MO diagrams illustrate how atomic orbitals combine to form molecular orbitals. For \(\text{He}_2\):

• Each helium atom starts with the 1s orbital containing two electrons.
• These orbitals merge to form two new molecular orbitals: the bonding (σ) and antibonding (σ*).
• Electrons fill these molecular orbitals from lowest to highest energy according to the Aufbau principle.

This process results in the following electron configuration: σ²σ*².
### Significance of MO Diagrams

• Identify Bonding vs. Antibonding: MO diagrams reveal the distribution of electrons, aiding in understanding molecular strength.
• Calculate Bond Order: The difference in population between bonding and antibonding orbitals determines stability.
• Visualize Orbital Interactions: Helps visualize how individual atomic orbitals contribute to the molecular orbitals.

In the case of \(\text{He}_2\), the MO diagram clearly illustrates why the molecule doesn’t last under normal conditions, due to the electron cancellation in bonding interactions.