How can the paramagnetism of \(\mathrm{O}_{2}\) be explained using the molecular orbital model?

First, determine the electron configuration of an individual oxygen atom. Oxygen has 8 electrons, with 1s, 2s, and 2p atomic orbitals. The electron configuration is \(1s^{2}2s^{2}2p^{4}\).

Now, we need to form molecular orbitals from the atomic orbitals of two oxygen atoms. The molecular orbitals for oxygen are made up of combinations of the 1s, 2s, and 2p atomic orbitals. The molecular orbital diagram for 2s and 2p atomic orbitals contributes the most to the explanation of paramagnetism.

Since there are two oxygen atoms, we have a total of \(8 \times 2 = 16\) electrons to add to the molecular orbitals for the oxygen molecule (\(\mathrm{O}_{2}\)). We fill the molecular orbitals according to the following rules: 1. Aufbau Principle: Electrons are added to the lowest energy orbitals first. 2. Pauli Exclusion Principle: No more than two electrons with opposite spin can occupy a single orbital. 3. Hund's Rule: Electrons will spread among degenerate orbitals before pairing up in the same orbital. Here is the electron configuration for the molecular orbitals of oxygen: - \(2\sigma_{1s}^{2}\) (from 1s orbitals) - \(2\sigma_{2s}^{2}\) (from 2s orbitals) - \(2\sigma_{2p}^{2}\) (from 2p orbitals) - \(4\sigma_{2p}^{1}\), \(1\pi_{2p}^{3}\) (from 2p orbitals)

There are a total of four electrons occupying the \(\sigma_{2p}\) and \(\pi_{2p}\) molecular orbitals, two in the \(2p_{x}\) and two in the \(2p_{y}\) orbitals. According to Hund's rule, each orbital gets one electron with the same spin before pairing occurs. Hence, there are two unpaired electrons in the molecular orbital configuration of oxygen, one in each of the \(2p_{x}\) and \(2p_{y}\) orbitals.

Paramagnetism arises due to the presence of unpaired electrons in the molecular orbitals of the substance. In the case of oxygen, we have found two unpaired electrons in its molecular orbitals; one in the \(2p_{x}\) and another in the \(2p_{y}\) orbital. The unpaired electrons create a magnetic moment that aligns with an external magnetic field, resulting in the paramagnetic behavior of oxygen. To summarize, we have shown that the paramagnetism of the oxygen molecule (\(\mathrm{O}_{2}\)) can be explained using the molecular orbital model by identifying the presence of unpaired electrons in its molecular orbitals.