Question

Which amongst the following is incorrect statement?

• A. The bond orders of O₂⁺, O₂, O₂^- and O2^2- are 2.5, 2, 1.5 and 1, respectively.
• B. C₂ molecule has four electrons in its two degenerate 𝜋 molecular orbitals.
• C. H₂⁺ ion has one electron.
• D. O₂⁺ ion is diamagnetic.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Molecular Orbital (MO) Theory is used to determine the bond order and magnetic properties of molecules.
Bond order \(= \frac{1}{2}(N_b - N_a)\).
Magnetic property: Paramagnetic if unpaired electrons exist, Diamagnetic if all electrons are paired.
Step 2: Detailed Explanation:
Evaluation of Option (1):
Electronic configuration of \(O_2\) (16e):
\[ \sigma 1s^2, \sigma^* 1s^2, \sigma 2s^2, \sigma^* 2s^2, \sigma 2p_z^2, (\pi 2p_x^2 = \pi 2p_y^2), (\pi^* 2p_x^1 = \pi^* 2p_y^1) \]
Bond Order of \(O_2 = 1/2(10 - 6) = 2\).
For \(O_2^+\) (15e): Remove 1e from \(\pi^* \implies B.O. = 1/2(10 - 5) = 2.5\).
For \(O_2^-\) (17e): Add 1e to \(\pi^* \implies B.O. = 1/2(10 - 7) = 1.5\).
For \(O_2^{2-}\) (18e): Add 2e to \(\pi^* \implies B.O. = 1/2(10 - 8) = 1\).
The statement is correct.

Evaluation of Option (2):
\(C_2\) molecule (12e):
\[ \sigma 1s^2, \sigma^* 1s^2, \sigma 2s^2, \sigma^* 2s^2, (\pi 2p_x^2 = \pi 2p_y^2) \]
The last 4 electrons are indeed in the two degenerate \(\pi\) orbitals.
The statement is correct.

Evaluation of Option (3):
A hydrogen atom has 1 electron. \(H_2\) has 2. \(H_2^+\) is formed by removing 1 electron from \(H_2\).
So, \(H_2^+\) has \(2 - 1 = 1\) electron.
The statement is correct.

Evaluation of Option (4):
As seen in option (1), \(O_2^+\) has 15 electrons.
Its configuration ends in \((\pi^* 2p_x^1 = \pi^* 2p_y^0)\).
Since there is one unpaired electron, \(O_2^+\) is paramagnetic.
The statement calling it diamagnetic is incorrect.
Step 3: Final Answer:
The incorrect statement is (4).