Problem 94 - A Complete Resource Book in Chemistry for JEE Main

Question

Which among the following paramagnetic pairs rare? (1) \(\left[\mathrm{BaO}_{2}, \mathrm{NO}_{2}\right]\) (2) \(\left[\mathrm{KO}_{2}, \mathrm{NO}\right]\) (3) \(\left[\mathrm{H}_{2} \mathrm{O}_{2}, \mathrm{NO}\right]\) (4) \(\left[\mathrm{K}_{3} \mathrm{Fe}(\mathrm{CN})_{6}, \mathrm{CuCl}_{2}\right]\) (a) 3,4 only (b) 1,3 only (c) 2,4 only (d) \(1,2,4\)

Step-by-Step Solution

Answer

The paramagnetic pairs are option (c) 2,4 only.

Step 1: Understanding Paramagnetism

Paramagnetism occurs due to the presence of unpaired electrons in the molecular or atomic orbitals. Molecules that have one or more unpaired electrons are paramagnetic in nature.

Step 2: Examine Option 1

For \([\text{BaO}_2, \text{NO}_2]\), \([\text{BaO}_2]\) is not a paramagnetic substance because both barium and oxygen are typically involved with paired electrons in their stable states. \(\text{NO}_2\), however, is paramagnetic because it has an odd number of electrons (23) which provides one unpaired electron in its molecular orbital.

Step 3: Examine Option 2

For \([\text{KO}_2, \text{NO}]\), \([\text{KO}_2]\) is paramagnetic because the superoxide ion \(\text{O}_2^-\) has an unpaired electron. \(\text{NO}\) is also paramagnetic due to having an odd number of electrons and one unpaired electron.

Step 4: Examine Option 3

For \([\text{H}_2\text{O}_2, \text{NO}]\), \(\text{H}_2\text{O}_2\) has all electrons paired up which makes it non-paramagnetic. \(\text{NO}\) is paramagnetic.

Step 5: Examine Option 4

For \([\text{K}_3\text{Fe}(\text{CN})_6, \text{CuCl}_2]\), \(\text{K}_3\text{Fe}(\text{CN})_6\) is diamagnetic because iron in this complex is in a +3 oxidation state and the complex is low-spin with all electrons paired. \(\text{CuCl}_2\) is paramagnetic because Cu(II) has an unpaired electron.

Step 6: Identify Paramagnetic Pairs

The paramagnetic pairs according to their presence in option are: \([\text{KO}_2, \text{NO}]\) and \(\text{CuCl}_2\) from option 2 and 4 respectively. Hence, the correct pairs are option (2) and option (4).

Step 7: Choose the Correct Answer

Based on the analysis of paramagnetism for each provided pair, options (2) and (4) are the paramagnetic pairs. Therefore, the answer is option (c) which corresponds to these pairs.

Key Concepts

Unpaired Electrons

Unpaired electrons play a crucial role in understanding the concept of paramagnetism. Electrons inhabit an atom or molecule's orbitals, and if an electron is alone in an orbital without a paired partner, it is considered unpaired.
Unpaired electrons contribute to magnetic behavior, where the lone electrons create a magnetic moment through their intrinsic angular momentum, or spin.
In paramagnetic substances, the presence of these unpaired electrons results in a net magnetic moment. This is because the unpaired electrons produce a magnetic field.
It is important to note that even one unpaired electron can make an entire molecule or substance exhibit paramagnetic properties.
To identify the presence of unpaired electrons, one must understand molecular or atomic orbital configurations. These configurations are crucial in determining if a substance is paramagnetic. Substances such as \[ ext{NO}\] and \[ ext{KO}_2\] have unpaired electrons, highlighting their paramagnetic nature.

Molecular Orbitals

Molecular orbitals are essential in analyzing the magnetic properties of molecules. They result from the combination of atomic orbitals when atoms form molecules, allowing us to predict the behavior of electrons in a molecule.
In the molecular orbital model, electrons fill these orbitals according to energy levels, starting from the lowest. The arrangement of electrons within these orbitals determines whether the substance will display magnetism.
In molecules like \[ ext{NO}\], the molecular orbital configuration predicts an unpaired electron, confirming its paramagnetic behavior.
Conversely, when all electrons in molecular orbitals are paired, the molecule exhibits diamagnetic properties and shows little to no magnetic response, as seen in substances like \[ ext{K}_3 ext{Fe}( ext{CN})_6\] in its low-spin form.

Oxidation State

The oxidation state of an element within a molecule greatly influences its magnetic properties. It dictates the electron configuration which can provide insight into the magnetic behavior of a compound.
The oxidation state affects whether electrons are paired or unpaired in molecular orbitals. In some transition metal complexes, different oxidation states can result in varying numbers of unpaired electrons.
For instance, in \[ ext{K}_3 ext{Fe}( ext{CN})_6\], iron is in a +3 oxidation state. Due to the strong field ligand \[ ext{CN}^-\], this results in a low-spin state where all electrons are paired, thus making it diamagnetic.
By contrast, \[ ext{CuCl}_2\] contains copper in a +2 oxidation state, leading to one unpaired electron and marking it as paramagnetic.

Magnetic Properties

Magnetic properties of substances result from their electronic structure and are broadly classified into paramagnetism and diamagnetism. Paramagnetic materials contain unpaired electrons and exhibit a strong attraction to magnetic fields.
These materials have a net magnetic moment due to the sum of individual electron spins. A common characteristic is that the strength of magnetism in paramagnets varies with temperature; they become less magnetic at higher temperatures as thermal energy overcomes the magnetic order.
Diamagnetic materials, on the other hand, have all paired electrons and are weakly repelled by magnetic fields. They lack a permanent magnetic moment.
Examples like \[ ext{BaO}_2\] and \[ ext{K}_3 ext{Fe}( ext{CN})_6\] are diamagnetic due to fully paired electrons, while \[ ext{NO}_2\] and \[ ext{CuCl}_2\] showcase paramagnetic properties due to having unpaired electrons.