Which of the following statements is correct?

The peroxide ion has a longer and weaker bond than the oxygen molecule.

The correct answer is option 2. The peroxide ion has a longer and weaker bond than the oxygen molecule.

Let us delve deeper into why statement (2) is correct regarding the peroxide ion and oxygen molecule:

Bond Order and Bond Strength/Length:

Bond Order: This concept reflects the average number of electron pairs involved in bonding between two atoms. A higher bond order signifies a stronger bond with shorter bond length due to the increased attraction between positively charged nuclei and the shared electrons.

Oxygen Molecule \((O_2)\) vs. Peroxide Ion \((O_2^{2-})\):

1. Oxygen Molecule \((O_2)\) - Bond Order \(2\):

Each oxygen atom contributes four valence electrons. Through molecular orbital theory, these electrons fill bonding and antibonding orbitals. The net result is 10 electrons in bonding orbitals and 6 in antibonding orbitals.

Molecular orbital configuration of \(O_2 = \) \(\sigma 1s^2,\, \ \sigma ^*1s^2,\, \ \sigma 2s^2,\, \ \sigma ^*2s^2,\, \ \sigma 2p_z ^2,\, \ \sigma ^* 2p_z^2,\, \ \pi 2p_x^2 = \pi ^*2p_x^2,\, \ \pi 2p_y^1 = \pi ^*2p_y^1 \)

\(\text{Bond order = }\frac{1}{2} \times \left(\text{number of electrons in bonding orbitals - number of electrons in antibonding orbitals}\right)\)

Bond order for \(O_2\) \(= \frac{1}{2} \times (10 - 6) = 2\)

2. Peroxide Ion \((O_2^{2-})\) - Bond Order \(1\):

Two oxygen atoms share electrons, but they also gain two extra electrons due to the negative charge. These extra electrons primarily occupy antibonding orbitals. With the additional electrons, there are still 10 electrons in bonding orbitals but now 8 in antibonding orbitals.

Molecular orbital configuration of \(O_2^{2-} = \) \(\sigma 1s^2,\, \ \sigma ^*1s^2,\, \ \sigma 2s^2,\, \ \sigma ^*2s^2,\, \ \sigma 2p_z ^2,\, \ \sigma ^* 2p_z^2,\, \ \pi 2p_x^2 = \pi ^*2p_x^2,\, \ \pi 2p_y^2 = \pi ^*2p_y^2 \)

Bond order for \(O_2^{2-}\) \(= \frac{1}{2} \times (10 - 8) = 2\)

Consequences of Bond Order Difference:

The lower bond order in the peroxide ion (1) compared to the oxygen molecule (2) indicates a weaker bond. Weaker bonds generally translate to longer bond lengths because the nuclei experience less attraction due to the decreased electron sharing.

Additional Points:

Statement (3) about paramagnetism is related to unpaired electrons. The oxygen molecule has unpaired electrons, making it paramagnetic, while the peroxide ion doesn't and is diamagnetic.

Statement (1) is incorrect because it reverses the relationship between bond order and strength.

In essence, the presence of the extra electrons in the peroxide ion disrupts the optimal electron sharing in the O-O bond, leading to a weaker and longer bond compared to the oxygen molecule.