Question

Bond order graph from 0 to 20 electron species

Answer 1

The solution is the provided graph and its interpretation, showing the trend of bond order for species with 0 to 20 electrons.

Answer 2

The bond order graph illustrates the relationship between the total number of electrons in homonuclear diatomic species and their bond order, as predicted by Molecular Orbital Theory. The bond order is calculated as half the difference between bonding and antibonding electrons ($BO = \frac{1}{2}(N_b - N_a)$). The graph's shape is determined by the sequential filling of molecular orbitals, with a key change in energy ordering around 10-14 electrons due to s-p mixing. The graph shows a peak bond order of 3 at 14 electrons (N₂), zero bond order at 4, 8, and 20 electrons (He₂, Be₂, Ne₂), and fractional bond orders for ions.

The bond order of a diatomic molecule or ion is a measure of the number of chemical bonds between two atoms and is determined using Molecular Orbital Theory (MOT). It is calculated using the formula:

$\text{Bond Order (BO)} = \frac{1}{2} (N_b - N_a)$

where $N_b$ is the number of electrons in bonding molecular orbitals and $N_a$ is the number of electrons in antibonding molecular orbitals.

The energy ordering of molecular orbitals (MOs) for diatomic species formed from the first and second-period elements depends on the total number of electrons.

1. For species with $\le 10$ electrons (e.g., Li₂ to N₂): Due to s-p mixing, the $\pi_{2p}$ orbitals are lower in energy than the $\sigma_{2p}$ orbital. The order is: $\sigma_{1s} < \sigma^*_{1s} < \sigma_{2s} < \sigma^*_{2s} < \pi_{2p} < \sigma_{2p} < \pi^*_{2p} < \sigma^*_{2p}$

2. For species with $> 10$ electrons (e.g., O₂ to Ne₂): s-p mixing is less significant, and the $\sigma_{2p}$ orbital is lower in energy than the $\pi_{2p}$ orbitals. The order is: $\sigma_{1s} < \sigma^*_{1s} < \sigma_{2s} < \sigma^*_{2s} < \sigma_{2p} < \pi_{2p} < \pi^*_{2p} < \sigma^*_{2p}$

The graph of bond order versus the total number of electrons (from 0 to 20) illustrates the trend in bond strength and stability for these species.

Bond Order Graph (0-20 Electrons)

The following graph visualizes the bond order for species with 0 to 20 total electrons, considering both neutral molecules and ions.

Explanation of the Graph

The graph shows the following key features:

• Increasing Bond Order: As electrons are added to bonding orbitals, the bond order generally increases, indicating stronger bonds.
• Decreasing Bond Order: As electrons are added to antibonding orbitals, the bond order decreases, indicating weaker bonds and reduced stability.
• Peak Bond Order: The maximum bond order of 3 is observed for species with 14 electrons, such as N₂. This is because N₂ has a stable configuration with filled bonding orbitals and only 4 electrons in antibonding orbitals.
• Zero Bond Order: Species with 4, 8, and 20 electrons (e.g., He₂, Be₂, Ne₂) have a bond order of 0. This means the number of electrons in bonding and antibonding orbitals is equal, resulting in no net bond formation and thus instability (these species do not exist as stable molecules under normal conditions).
• Fractional Bond Orders: Many ions (e.g., H₂⁺, O₂⁻) have fractional bond orders, which are still indicative of bonding but generally represent weaker bonds than those with integer values.
• Change in Trend around 10-14 Electrons: The shape of the graph changes around the 10-14 electron range due to the shift in the energy ordering of $\pi_{2p}$ and $\sigma_{2p}$ MOs caused by s-p mixing.

Key Species and Their Bond Orders:

• 0-1 e⁻: BO = 0 to 0.5 (e.g., H₂⁺ has BO = 0.5)
• 2 e⁻: BO = 1 (e.g., H₂)
• 3 e⁻: BO = 0.5 (e.g., He₂⁺, H₂⁻)
• 4 e⁻: BO = 0 (e.g., He₂)
• 6 e⁻: BO = 1 (e.g., Li₂)
• 8 e⁻: BO = 0 (e.g., Be₂)
• 10 e⁻: BO = 1 (e.g., B₂)
• 12 e⁻: BO = 2 (e.g., C₂)
• 14 e⁻: BO = 3 (e.g., N₂)
• 16 e⁻: BO = 2 (e.g., O₂)
• 18 e⁻: BO = 1 (e.g., F₂)
• 20 e⁻: BO = 0 (e.g., Ne₂)