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 \(\mathrm{He}_{2}\) 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

Using Molecular Orbital (MO) theory, we can explain the temporary formation and dissociation of He2 molecules when subjected to high-energy sources. When two helium atoms combine, they form two molecular orbitals, a lower energy bonding orbital (\( \sigma_{1s} \)) and a higher energy antibonding orbital (\( \sigma_{1s}^{*} \)). Both orbitals are filled with 2 electrons, resulting in a bond order of zero, which means there is no net bond formation and the molecule is not stable. When a high-energy source is applied to the helium gas, it can excite some He atoms and momentarily form He2 molecules. However, the He2 molecules will dissociate back into individual He atoms due to the zero bond order and no net bonding, making He2 a transient and unstable species.

Step-by-step solution

Atomic Orbitals of Helium

Before analyzing the molecular orbitals of He2, we need to understand the atomic orbitals involved in forming He2. Helium has 2 electrons in the 1s orbital. So, considering two helium atoms, there are a total of 4 electrons in the system.

Molecular Orbitals for He2

Now, we will construct the molecular orbitals for He2. We can form two molecular orbitals – a lower energy bonding orbital (\( \sigma_{1s} \)) and a higher energy antibonding orbital (\( \sigma_{1s}^{*} \)). The combination of two 1s atomic orbitals will form these molecular orbitals.

Filling the Molecular Orbitals

He2 has a total of 4 electrons. According to the Aufbau principle, we'll fill the molecular orbitals with these electrons, starting with the lowest energy orbital. So, the four electrons will be distributed between the \( \sigma_{1s} \) and \( \sigma_{1s}^{*} \) orbitals. In this case, both orbitals will be filled with 2 electrons.

Analyzing the Bond Formation

Now, let's determine the bond order for the He2 molecule. The bond order is given by the following formula: Bond Order = \(\frac{1}{2}\) (Number of Electrons in Bonding Orbitals - Number of Electrons in Antibonding Orbitals) For He2, the bond order becomes: Bond Order = \(\frac{1}{2}\) (2 - 2) = 0 Since the bond order is zero, this implies that there is no net bond formation in the He2 molecule, and the molecule is not stable.

Momentary Existence and Dissociation

When a high-energy source is applied to a sample of helium gas, it can excite some He atoms, causing the temporary formation of He2 molecules. However, due to the fact that the bond order of He2 is zero and there is no net bonding, the He2 molecules formed will dissociate back into individual He atoms. This process of formation and dissociation occurs rapidly, making He2 a transient and unstable species.