Question

Consider the following statements.
I. In the conversion of \( \text{O}_2 \) to \( \text{O}_2^{2+} \) bond order decreases.
II. In the conversion of \( \text{O}_2 \) to \( \text{O}_2^{+} \) magnetic property is not changed.
III. In the conversion of \( \text{O}_2 \) to \( \text{O}_2^{+} \) bond length decreases.
IV. \( \text{O}_2^{2-} \) and \( \text{B}_2 \) have same bond order.
Identify the correct statements

• A. I & III only
• B. II & III only
• C. III & IV only
• D. I & IV only

Hint:

Bond Order vs Electrons count: 14e: 3 15e: 2.5 16e: 2 17e: 1.5 18e: 1 Inverse relationship with Bond Length.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:

Using Molecular Orbital Theory (MOT), determine Bond Order (BO) and Magnetic property. BO = \( \frac{1}{2}(N_b - N_a) \). Paramagnetic if unpaired electrons exist.
Step 3: Detailed Explanation:

Analyze \( \text{O}_2 \) (16 e\(^-\)):
Config: ... \( \sigma 2p_z^2, \pi 2p_x^2 = \pi 2p_y^2, \pi^* 2p_x^1 = \pi^* 2p_y^1 \). BO = \( (10 - 6)/2 = 2 \). Paramagnetic (2 unpaired). Statement I:
\( \text{O}_2 \to \text{O}_2^{2+} \) (14 e\(^-\), like \( \text{N}_2 \)). \( \text{O}_2^{2+} \) loses 2 antibonding electrons. BO = \( (10 - 4)/2 = 3 \). BO increases from 2 to 3. Statement I is False. Statement II:
\( \text{O}_2 \to \text{O}_2^{+} \) (15 e\(^-\)). \( \text{O}_2^{+} \) loses 1 antibonding electron. One unpaired electron remains in \( \pi^* \). \( \text{O}_2 \) is paramagnetic (2 unpaired). \( \text{O}_2^{+} \) is paramagnetic (1 unpaired). Magnetic character (Paramagnetic) is preserved, but magnetic moment changes. "Property is not changed" usually implies Para \(\to\) Dia or vice versa. Since both are Para, statement might be considered True? Or False because magnetic moment decreases? Let's check other statements first. Statement III:
\( \text{O}_2 \to \text{O}_2^{+} \). BO of \( \text{O}_2 = 2 \). BO of \( \text{O}_2^{+} = (10 - 5)/2 = 2.5 \). BO increases \(\implies\) Bond strength increases \(\implies\) Bond length decreases. Statement III is True. Statement IV:
\( \text{O}_2^{2-} \) (Peroxide, 18 e\(^-\)): \( \text{F}_2 \) isoelectronic. BO = 1. \( \text{B}_2 \) (10 e\(^-\)): Config ... \( \sigma 2s^2, \sigma^* 2s^2, \pi 2p_x^1 = \pi 2p_y^1 \). BO = \( (6 - 4)/2 = 1 \). Both have BO = 1. Statement IV is True. Conclusion: III and IV are definitely True. I is False. This matches Option (C).
Step 4: Final Answer:

The correct statements are III & IV.