Animated Solution for Chemistry - Chemical Bonding and Molecular Structure: Of the species, $\text{NO}$, ${\text{NO}}^{+}$, ${\text{NO}}^{2+}$ and ${\text{NO}}^{-}$, the one with minimum bond strength is

Bonding vs. Antibonding

Imagine a microscopic tug-of-war between two atoms. The bonding electrons are the team members pulling the atoms together, creating a stable, strong connection. On the other side, the antibonding electrons are actively trying to push the atoms apart. The net result of this struggle is what we call the Bond Order (BO).

According to Molecular Orbital Theory, the bond order is calculated by taking the difference between the number of bonding electrons ($N_b$) and antibonding electrons ($N_a$), and dividing by two:

The fundamental rule here is simple: Bond strength is directly proportional to bond order. A higher bond order means a stronger, tighter bond. Conversely, a lower bond order means a weaker bond that is easier to break.

Let's start with the neutral Nitrogen Monoxide ($\text{NO}$) molecule. Nitrogen brings 7 electrons, and Oxygen brings 8, giving us a total of 15 electrons.

When we fill these electrons into the molecular orbitals according to their energy sequence, we get:

Counting them up, we have 10 electrons in bonding orbitals and 5 in antibonding orbitals.

What happens if we remove an electron to form ${\text{NO}}^{+}$? The electron is removed from the highest energy orbital, which is the antibonding ${\pi }_{2p_x}^{\ast }$ orbital.

By removing an "enemy" from the antibonding team, the net bonding effect increases! We now have 10 bonding and only 4 antibonding electrons.

If we remove yet another electron to form ${\text{NO}}^{2+}$, we must take it from the next highest orbital, which is the bonding ${\pi }_{2p_y}$ orbital. Now we have 9 bonding and 4 antibonding electrons.

Now, let's see what happens when we add an electron to neutral $\text{NO}$ to form ${\text{NO}}^{-}$. This 16th electron must go into the next available orbital, which is the antibonding ${\pi }_{2p_y}^{\ast }$ orbital.

Adding a member to the antibonding team weakens the overall bond. We now have 10 bonding and 6 antibonding electrons.

Let's line up our competitors based on their bond orders:

${\text{NO}}^{+}$: BO = 3 $\text{NO}$: BO = 2.5 ${\text{NO}}^{2+}$: BO = 2.5 ${\text{NO}}^{-}$: BO = 2

Since bond strength is directly proportional to bond order, the species with the lowest bond order will have the minimum bond strength. That title goes to ${\text{NO}}^{-}$, making it the weakest link in this lineup!