Question

The paramagnetic species among the following is: (a) \(\mathrm{KO}_{2}\) (b) \(\mathrm{SiO}_{2}\) (c) \(\mathrm{TiO}_{2}\) (d) \(\mathrm{BaO}_{2}\)

Short answer

The paramagnetic species is (a) \(\mathrm{KO}_{2}\).

Step-by-step solution

Understand Paramagnetism

A paramagnetic substance has one or more unpaired electrons in its atomic or molecular structure. These unpaired electrons contribute to a net magnetic moment.

Analyze the Electron Configurations

Examine each substance's electron configuration, considering the oxidation states of their components:1. \(\mathrm{KO}_{2}\): Contains \(\mathrm{O}_{2}^{-}\), which has an odd number of electrons, implying unpaired electrons.2. \(\mathrm{SiO}_{2}\): Silicon and oxygen are paired as \(\mathrm{Si}^{4+}\) and \(\mathrm{O}^{2-}\), leading to no unpaired electrons.3. \(\mathrm{TiO}_{2}\): Titanium is \(\mathrm{Ti}^{4+}\) and oxygen is \(\mathrm{O}^{2-}\), resulting in no unpaired electrons.4. \(\mathrm{BaO}_{2}\): Barium is \(\mathrm{Ba}^{2+}\) and oxygen is in peroxide form \(\mathrm{O}_{2}^{2-}\), balanced with paired electrons.

Identify the Paramagnetic Species

From the above analysis, \(\mathrm{KO}_{2}\) contains \(\mathrm{O}_{2}^{-}\) with an odd number of electrons and unpaired electrons, indicating paramagnetism.

Key concepts

Unpaired Electrons

Unpaired electrons are electrons that occupy orbitals singly rather than in pairs. In most atoms, electrons prefer to pair up to fill lower energy states, but sometimes, due to electronic interactions and the specifications of electron configurations, unpaired electrons can exist. These unpaired electrons contribute directly to the magnetic properties of the substance, such as paramagnetism. If an atom or molecule has one or more unpaired electrons, it can interact with a magnetic field and exhibit paramagnetic behavior.

For example, the molecular ion \(\mathrm{O}_{2}^{-}\), found in potassium superoxide (\(\mathrm{KO}_{2}\)), contains an odd number of electrons with unpaired electrons. This allows \(\mathrm{KO}_{2}\) to be attracted to magnetic fields, thus demonstrating paramagnetic properties.

Electron Configuration

Electron configuration is a method of detailing the arrangements of electrons in the orbitals of atoms or molecules. The configuration follows the rules of quantum mechanics and fills orbitals from lowest to highest energy level. Electrons tend to fill lower energy sublevels before moving to higher ones, obeying the Aufbau principle, Hund's rule, and the Pauli exclusion principle.

For the compounds in the exercise:

• \(\mathrm{KO}_{2}\), contains \(\mathrm{O}_{2}^{-}\), which because it has an unpaired electron, illustrates how electron configuration can affect magnetic properties.
• \(\mathrm{SiO}_{2}\), focuses on \(\mathrm{Si}^{4+}\) and \(\mathrm{O}^{2-}\), where all electrons are paired, indicating no paramagnetism.
• \(\mathrm{TiO}_{2}\), has \(\mathrm{Ti}^{4+}\) where the configuration results in paired states.
• \(\mathrm{BaO}_{2}\), features \(\mathrm{O}_{2}^{2-}\) and paired electrons, consistent with its non-paramagnetic nature.

Understanding these configurations helps visualize why certain substances are paramagnetic.

Magnetic Properties

The magnetic properties of elements and compounds are significantly influenced by their electron configurations and, specifically, the presence or absence of unpaired electrons. When electrons are paired, their magnetic fields cancel each other out, resulting in diamagnetism, where there is no net magnetic moment. However, unpaired electrons cause a net magnetic moment, leading to paramagnetism.

In paramagnetic materials, the unpaired electrons align themselves with an external magnetic field, making them attracted to the field. The intensity of this attraction depends on the number of unpaired electrons. \[\mathrm{KO}_{2}\], due to its unpaired electron in \(\mathrm{O}_{2}^{-}\), is an example of such a substance. In contrast, \(\mathrm{SiO}_{2}\), \(\mathrm{TiO}_{2}\), and \(\mathrm{BaO}_{2}\) have all their electrons paired, resulting in a lack of any significant magnetic properties.

Oxidation States

Oxidation states are a formalism that indicates the degree of oxidation of an atom in a compound. They can affect the electron configurations directly, which in turn influences the compound's magnetic properties. By changing an element's oxidation state, its electron count and arrangement can vary, impacting whether electrons are paired or remain unpaired.

Taking the example of \(\mathrm{KO}_{2}\), \(\mathrm{K}\) is in the \(\mathrm{K}^{+}\) oxidation state, while \(\mathrm{O}\), being \(\mathrm{O}_{2}^{-}\), has one more electron than \(\mathrm{O}_{2}\) allowing for unpaired electrons. When electron configurations are analyzed in relation to their oxidation states, one can predict the magnetic properties effectively. For other compounds like \(\mathrm{SiO}_{2}\), \(\mathrm{TiO}_{2}\), and \(\mathrm{BaO}_{2}\), the oxidation states ensure the presence of only paired electrons, confirming their lack of paramagnetism.