Question

The MO clectron configuration of peroxide ion \(\left(O_{2}^{2}\right)\) is (1) \(\mathrm{KK}^{*}\left[\sigma 2 \mathrm{~s}^{2} \sigma^{*} 2 \mathrm{~s}^{2} \sigma 2 \mathrm{p}_{x}^{2} \pi 2 \mathrm{p}_{x}^{2} \pi 2 \mathrm{p}_{\mathrm{y}}^{2} \pi * 2 \mathrm{p}_{x}^{2} \pi+2 \mathrm{p}_{\mathrm{y}}^{2}\right]\) (2) \(\mathrm{KK}^{*} \mid \sigma 2 \mathrm{~s}^{2} \sigma^{*} 2 \mathrm{~s}^{2} \sigma 2 \mathrm{p}_{z}^{2} \pi 2 \mathrm{p}_{\mathrm{x}}^{2} \pi 2 \mathrm{p}_{\mathrm{y}}^{2} \pi^{*} 2 \mathrm{p}_{\mathrm{x}}^{1} \pi^{*} 2 \mathrm{p}_{\mathrm{y}}^{1} \mathrm{l}\) (3) \(\mathrm{KK}^{*}\left[\sigma 2 \mathrm{~s}^{2} \sigma^{*} 2 \mathrm{~s}^{2} \sigma 2 \mathrm{p}_{z}^{2} \pi 2 \mathrm{p}_{\mathrm{x}}^{2} \pi 2 \mathrm{p}_{y}^{2} \pi^{*} 2 \mathrm{p}_{\mathrm{x}}^{2} \pi^{*} 2 \mathrm{p}_{y}^{\prime}\right]\) (4) \(\mathrm{KK}^{*} \mid \sigma 2 \mathrm{~s}^{2} \sigma^{*} 2 \mathrm{~s}^{2} \sigma 2 \mathrm{p}_{k}^{2} \pi 2 \mathrm{p}_{x}^{2} \pi 2 \mathrm{p}_{y}^{2} \pi * 2 \mathrm{p}_{\mathrm{x}}^{2} \mathrm{l}\)

Short answer

Option (3) is correct.

Step-by-step solution

- MO Electron Configuration of Peroxide Ion

Identify the correct molecular orbital (MO) configuration for the peroxide ion, \(\text{O}_{2}^{2-}\)

- Count the Total Electrons

Each oxygen atom in \(\text{O}_{2}^{2-}\) contributes 8 electrons, and the \(-2\) charge adds 2 more electrons. Therefore, the number of electrons is \(2 \times 8 + 2 = 18\) electrons.

- Fill the Molecular Orbitals

Using the molecular orbital theory, fill in the orbitals in increasing order of energy: \(1\text{s}\), \(1\text{s}^*\), \(2\text{s}\), \(2\text{s}^*\), \(2\text{p}_{z}\), \(\text{2p}_{x}\) & \(\text{2p}_{y}\), \(2\text{p}_{z}^*\), \(\text{2p}_{x}^*\), \(\text{2p}_{y}^*\).

- Compare with Given Configurations

Compare the filled molecular orbital configuration to the options provided. Option (1) does not match the expected occupation of molecular orbitals. Option (2) wrongly states \(1 \text{p}_{x}^{1} \text{ and } 1\text{p}_{y}^{1}\) in \( \text{2p}_{x}^* \text{ and } 2\text{p}_{y}^*\) orbitals. Option (4) also uses incorrect terms. Therefore, the correct MO configuration matches with option (3).

Key concepts

Peroxide ion

The peroxide ion, \(O_{2}^{2-}\), is an interesting molecule. It consists of two oxygen atoms sharing two extra electrons. These extra electrons give the molecule a \(-2\) charge.
Each oxygen atom typically has 8 electrons. When they form the peroxide ion, another two electrons are added because of the charge. So, in total, we have 18 electrons.
This unique electron count leads to special properties and behaviors, which we can explain using Molecular Orbital Theory.

Molecular Orbital Theory helps us understand how these electrons are distributed among the different orbitals.

Understanding the peroxide ion is crucial for grasping more complex chemistry concepts. Before delving into molecular orbitals, let's recap the basics of electron configurations.

Electron configuration

Electron configuration is the arrangement of electrons around the nucleus of an atom.
For each element, electrons fill orbitals in a specific order based on increasing energy, adhering to the Aufbau principle.

First, electrons fill the lowest energy orbitals, like the 1s orbital. They then move to higher energy levels, like 2s, 2p, 3s, and so on.
In molecular systems, like \(O_{2}^{2-}\), electron configurations help predict chemical behavior and bonding.

For the peroxide ion, we first identify each oxygen atom’s electrons (8 per atom) and then add the extra two from the charge.
This gives us a total of 18 electrons to distribute.

We'll use the Molecular Orbital Theory to see how these electrons are added. This includes considering both bonding and anti-bonding molecular orbitals.

Molecular orbitals

Molecular Orbital Theory explains the behavior of electrons in molecules. Unlike atomic orbitals (which are within a single atom), molecular orbitals extend over the entire molecule.

Think of molecular orbitals as combinations of atomic orbitals. When atomic orbitals combine, they form bonding and anti-bonding molecular orbitals.
Bonding orbitals are lower in energy and help hold the molecule together. Anti-bonding orbitals are higher in energy and can destabilize the molecule if occupied.

In the peroxide ion \(O_{2}^{2-}\), the electrons fill these molecular orbitals in order of increasing energy:
* \(1\text{s}\)
* \(1\text{s}^*\)
* \(2\text{s}\)
* \(2\text{s}^*\)
* \(2\text{p}_{z}\)
* \(2\text{p}_{x}\) and \(2\text{p}_{y}\)
* \(2\text{p}_{z}^*\)
* \(2\text{p}_{x}^*\) and \(2\text{p}_{y}^*\)

To find the correct electron configuration for the peroxide ion, we count and place electrons into these orbitals.
The final configuration matches one of the given multiple choices, which, in this case, is option (3). By following these steps, we deeply understand the structure and behavior of the \(O_{2}^{2-}\) ion.