Animated Solution for Chemistry - Chemical Bonding and Molecular Structure: Increasing order of bond strength of $O_2$, $O_2^{-}$, $O_2^{2-}$ and $O_2^{+}$ is

Bond Strength and Bond Order

When we talk about the strength of a chemical bond, we are essentially asking: How tightly are these two atoms holding onto each other? In the realm of Molecular Orbital (MO) Theory, this grip is quantified by a simple yet powerful number called the Bond Order.

The fundamental rule you must engrave in your mind is this: Bond strength is directly proportional to bond order. The higher the bond order, the stronger and more stable the bond. Conversely, a higher bond order also means the atoms are pulled closer together, resulting in a shorter bond length.

To find the bond order, we could draw the entire molecular orbital diagram, fill in the electrons using Aufbau's principle, and then use the formula: where $N_b$ is the number of bonding electrons and $N_a$ is the number of anti-bonding electrons.

However, for competitive exams like JEE, we need speed. There is a brilliant shortcut for diatomic molecules containing between 10 and 18 electrons. We simply count the total number of electrons!

Let's look at our reference point: the nitrogen molecule ($N_2$) has 14 electrons and a maximum bond order of 3.0. For every electron you add or remove from 14, the bond order decreases by exactly 0.5.

Alternatively, using the oxygen molecule ($O_2$) as a reference: $O_2$ has 16 electrons and a bond order of 2.0. Let's apply this to our given species.

Let's break down the total electron count for each species in the question:

1. $O_2$ (Dioxygen): Each oxygen atom has 8 electrons. Total = $8+8=16$ electrons. - From our trick, 16 electrons correspond to a Bond Order of 2.0.

2. $O_2^{+}$ (Dioxygenyl ion): This is an $O_2$ molecule that has lost one electron. Total = $16-1=15$ electrons. - Moving one step away from 16 towards 14, the bond order increases by 0.5. - Bond Order = 2.5.

3. $O_2^{-}$ (Superoxide ion): This is an $O_2$ molecule that has gained one electron. Total = $16+1=17$ electrons. - Moving one step away from 16 towards 18, the bond order decreases by 0.5. - Bond Order = 1.5.

4. $O_2^{2-}$ (Peroxide ion): This is an $O_2$ molecule that has gained two electrons. Total = $16+2=18$ electrons. - Moving two steps away from 16, the bond order decreases by $2\times 0.5=1.0$. - Bond Order = 1.0.

Now that we have the bond orders, arranging them in increasing order of bond strength is straightforward. We just arrange them from the lowest bond order to the highest:

- $O_2^{2-}$ (Bond Order = 1.0) - $O_2^{-}$ (Bond Order = 1.5) - $O_2$ (Bond Order = 2.0) - $O_2^{+}$ (Bond Order = 2.5)

Therefore, the increasing order of bond strength is:

This perfectly matches option (d). Always remember, if the question had asked for the increasing order of bond length, the sequence would be exactly reversed, because a stronger bond pulls the atoms closer together!