Question

Minimum bond length is of:

• A. $\mathrm{O_2}$
• B. $\mathrm{O_2^+}$
• C. $\mathrm{O_2^-}$
• D. $\mathrm{O_2^{2-}}$

Hint:

Key concepts:

• Higher bond order $\Rightarrow$ stronger, shorter bonds
• Cation formation removes antibonding electrons
• Anion formation adds antibonding electrons
• $\pi^*$ electrons significantly affect bond order

Answer 1

The Correct Option is B

Step 1: Recall bond length fundamentals
Bond length decreases with increasing bond order according to: \[ \text{Bond length} \propto \frac{1}{\text{Bond order}} \]
Step 2: Determine bond orders using MOT
Molecular orbital configuration for oxygen species: \[ \mathrm{O_2}: \sigma(1s)^2 \sigma^*(1s)^2 \sigma(2s)^2 \sigma^*(2s)^2 \sigma(2p_z)^2 \pi(2p_x)^2 = \pi(2p_y)^2 \pi^*(2p_x)^1 = \pi^*(2p_y)^1 \] Bond order calculation: \[ \text{B.O.} = \frac{\text{Bonding e}^- - \text{Antibonding e}^-}{2} \]

• $\mathrm{O_2}$: $\frac{10 - 6}{2} = 2$
• $\mathrm{O_2^+}$: $\frac{10 - 5}{2} = 2.5$ (removes antibonding electron)
• $\mathrm{O_2^-}$: $\frac{10 - 7}{2} = 1.5$ (adds antibonding electron)
• $\mathrm{O_2^{2-}}$: $\frac{10 - 8}{2} = 1$ (adds 2 antibonding electrons)

Step 3: Establish bond length order
Since bond length $\propto \frac{1}{\text{B.O.}}$: \[ \mathrm{O_2^+} (2.5)<\mathrm{O_2} (2)<\mathrm{O_2^-} (1.5)<\mathrm{O_2^{2-}} (1) \]
Step 4: Experimental validation
Measured bond lengths:

• $\mathrm{O_2^+}$: 112 pm (shortest)
• $\mathrm{O_2}$: 121 pm
• $\mathrm{O_2^-}$: 133 pm
• $\mathrm{O_2^{2-}}$: 149 pm (longest)