Question

Which of the following are predicted by the molecular orbital model to be stable diatomic species? a. \(\mathrm{H}_{2}+, \mathrm{H}_{2}, \mathrm{H}_{2}^{-}, \mathrm{H}_{2}^{2-}\) b. \(\mathrm{He}_{2}^{2+}, \mathrm{He}_{2}^{+}, \mathrm{He}_{2}\)

Short answer

In conclusion, the stable diatomic species predicted by the molecular orbital model are H₂⁺, H₂, H₂⁻, He₂²⁺, and He₂⁺.

Step-by-step solution

Molecular orbitals for H₂ species

For Hydrogen, we have the 1s orbitals which combine to form the σ(1s) bonding orbital and the σ*(1s) antibonding orbital. Let's calculate the bond order for each H₂ species. a. For H₂⁺ species: - We have 1 electron in σ(1s) bonding orbital and 0 electrons in σ*(1s) antibonding orbital.

Calculate bond order for H₂⁺

Bond Order = \(\frac{(1-0)}{2}\) = \(\frac{1}{2}\) Since the bond order is greater than zero, H₂⁺ is a stable diatomic species. a. For H₂: - We have 2 electrons in σ(1s) bonding orbital and 0 electrons in σ*(1s) antibonding orbital.

Calculate bond order for H₂

Bond Order = \(\frac{(2-0)}{2}\) = 1 Since the bond order is greater than zero, H₂ is a stable diatomic species. a. For H₂⁻: - We have 2 electrons in σ(1s) bonding orbital and 1 electron in σ*(1s) antibonding orbital.

Calculate bond order for H₂⁻

Bond Order = \(\frac{(2-1)}{2}\) = \(\frac{1}{2}\) Since the bond order is greater than zero, H₂⁻ is a stable diatomic species. a. For H₂²⁻: - We have 2 electrons in σ(1s) bonding orbital and 2 electrons in σ*(1s) antibonding orbital.

Calculate bond order for H₂²⁻

Bond Order = \(\frac{(2-2)}{2}\) = 0 Since the bond order is equal to zero, H₂²⁻ is not a stable diatomic species.

Molecular orbitals for He₂ species

For Helium, we have the 1s orbitals which combine to form the σ(1s) bonding orbital and the σ*(1s) antibonding orbital, similar to the hydrogen species. Let's calculate the bond order for each He₂ species. b. For He₂²⁺: - We have 2 electrons in σ(1s) bonding orbital and 0 electrons in σ*(1s) antibonding orbital.

Calculate bond order for He₂²⁺

Bond Order = \(\frac{(2-0)}{2}\) = 1 Since the bond order is greater than zero, He₂²⁺ is a stable diatomic species. b. For He₂⁺: - We have 2 electrons in σ(1s) bonding orbital and 1 electron in σ*(1s) antibonding orbital.

Calculate bond order for He₂⁺

Bond Order = \(\frac{(2-1)}{2}\) = \(\frac{1}{2}\) Since the bond order is greater than zero, He₂⁺ is a stable diatomic species. b. For He₂: - We have 2 electrons in σ(1s) bonding orbital and 2 electrons in σ*(1s) antibonding orbital.

Calculate bond order for He₂

Bond Order = \(\frac{(2-2)}{2}\) = 0 Since the bond order is equal to zero, He₂ is not a stable diatomic species. In conclusion, the stable diatomic species are H₂⁺, H₂, H₂⁻, He₂²⁺, and He₂⁺.

Key concepts

Bond Order

Bond order is a crucial concept in molecular orbital theory, helping determine the stability of diatomic molecules. It is defined as the difference between the number of electrons in bonding orbitals and antibonding orbitals, divided by two. This gives a useful way to predict the existence and stability of a molecule.
For instance, when considering a diatomic species, calculating the bond order involves:

• Counting the electrons in bonding orbitals
• Counting the electrons in antibonding orbitals
• Applying the formula: Bond Order = \(\frac{(\text{electrons in bonding orbitals} - \text{electrons in antibonding orbitals})}{2}\)

A positive bond order generally indicates a stable molecule, as more electrons reside in bonding orbitals than antibonding ones. For example, a bond order of 1 for hydrogen's diatomic molecule \(H_2\) signifies stability, as there's more bonding than antibonding interaction.

Diatomic Species

Diatomic species consist of molecules that have two atoms, either of the same or different chemical elements. This simplicity makes them ideal for understanding molecular interactions and bonding through molecular orbital theory. Each atom contributes its atomic orbitals to the molecular orbitals of the molecule.
The diatomic species in our study include molecules like \(H_2\), \(He_2\), and their ionized forms, such as \(H_2^+\) or \(He_2^{2+}\). The molecular orbital approach allows us to predict the stability of these species based on their electronic configurations. For instance, the exact nature of the interaction in \(H_2\) is explored by analyzing how the filled and unfilled orbitals relate to bond order, affecting their stability as a molecule. To recap, the molecular orbital model shines in its ability to predict the stability of these simple diatomic species by examining how atoms share and redistribute electrons to form bonds.

Bonding and Antibonding Orbitals

In molecular orbital theory, understanding bonding and antibonding orbitals is key to predicting molecule stability. When atomic orbitals overlap, they form molecular orbitals, which can be of two types: bonding or antibonding.

• Bonding Orbitals: These orbitals result from the constructive interference of atomic wave functions. Electrons in these orbitals act to stabilize the molecule by increasing attractive interactions between the atomic nuclei.
• Antibonding Orbitals: These orbitals arise from destructive interference, where the atomic wave functions subtract from one another. Electrons in these orbitals decrease stability as they increase repulsive forces within the molecule.

An important takeaway is the balance between these orbitals. If a diatomic species has more electrons in bonding orbitals than antibonding ones, it tends to be stable. This balance is pivotal for explaining why some diatomic molecules like \(H_2\) are stable, whereas others like \(He_2\) are not. Thus, understanding both bonding and antibonding interactions is vital for assessing the stability of diatomic species using molecular orbital theory.