Problem 50 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Among the species given below, the total number of diamagnetic species is \(\mathrm{H}\) atom, \(\mathrm{NO}_{2}\) monomer, \(\mathrm{O}_{2}^{-}\)(superoxide), dimeric sulphur in vapour phase, \(\mathrm{Mn}_{3} \mathrm{O}_{4},\left(\mathrm{NH}_{4}\right)_{2}\left[\mathrm{FeCl}_{4}\right],\left(\mathrm{NH}_{4}\right)_{2}\left[\mathrm{NiCl}_{4}\right], \mathrm{K}_{2} \mathrm{MnO}_{4}, \mathrm{~K}_{2} \mathrm{CrO}_{4}\).

Step-by-Step Solution

Answer

There are 2 diamagnetic species: dimeric sulphur (S2) and K2CrO4.

Step 1: Understanding Diamagnetism

Diamagnetic species have all their electrons paired. This means that there are no unpaired electrons present in the molecular or atomic orbitals. For an element or compound to be diamagnetic, its electronic configuration should conclude with paired electrons.

Step 2: Analyze Each Species

Identify which species are likely to be diamagnetic by evaluating their electron configurations or molecular structures: - **H atom**: Has 1 electron, so it is not paired. Not diamagnetic. - **NO2 monomer**: Typically has an unpaired electron. Not diamagnetic. - **O2^- (superoxide)**: Molecular orbital theory shows unpaired electron in the antibonding orbitals. Not diamagnetic. - **Dimeric sulphur in vapor phase (S2)**: Follows the same principle as dioxygen, usually has paired electrons. Likely diamagnetic. - **Mn3O4**: Contains manganese ions in mixed oxidation states, typically leading to unpaired electrons. Not diamagnetic. - **(NH4)2[FeCl4]**: Fe typically carries unpaired electrons in such compounds due to its oxidation states. Not diamagnetic. - **(NH4)2[NiCl4]**: Nickel typically carries unpaired electrons in tetrahedral complexes. Not diamagnetic. - **K2MnO4**: Manganese in the oxidation state within this compound typically has unpaired electrons. Not diamagnetic. - **K2CrO4**: Chromium here is typically in the +6 oxidation state, which means all d-electrons are removed and non-bonding. Diamagnetic.

Step 3: Count Diamagnetic Species

From the analysis, the diamagnetic species include dimeric sulphur in the vapor phase (S2) and K2CrO4. Thus, there are two diamagnetic species in total.

Key Concepts

Electron Configuration

Understanding electron configuration is fundamental in determining the magnetic properties of atoms or molecules. An electron configuration describes the distribution of electrons among the various atomic orbitals, such as s, p, d, and f orbitals. Each orbital can hold a maximum of two electrons and they must have opposite spins.

In the case of diamagnetism, all the electrons in the species are paired within these orbitals. This implies that there are no unpaired electrons to generate a net magnetic moment.

• An example of this is the electron configuration of the \[ ext{Cr}^{6+} \] ion in \[ ext{K}_2 ext{CrO}_4 \]. With a \[ d^0 \] configuration, it doesn’t exhibit any paramagnetic behavior and is hence diamagnetic.
• However, species like the hydrogen atom (\[ ext{H} \]), with a single electron in the 1s orbital, have a net magnetic moment due to the unpaired electron.

Molecular Orbital Theory

Molecular Orbital (MO) Theory provides a more in-depth understanding of how electrons are distributed in molecules. According to MO theory, atomic orbitals combine to form molecular orbitals that can be occupied by electrons spread over the entire molecule. These can be bonding or antibonding with differing energy states.

MO Theory helps us predict the magnetic properties of molecules based on the electronic configuration in these orbitals. For example, in the case of \[ ext{O}_2^- \] (superoxide), it belongs to the category where unpaired electrons are present in the antibonding \[ ext{2p}_ ext{*} \] orbitals. This presence of unpaired electrons within antibonding orbitals indicates a paramagnetic nature, meaning it is not diamagnetic.

• Diamagnetic species, on the other hand, have their electrons all paired, resulting in no net magnetic field.
• Molecular orbitals thus play a crucial role in determining if a molecule like dimeric sulphur, \[ ext{S}_2 \], is likely to be diamagnetic since it follows the same principle as \[ ext{O}_2 \], but all electrons are paired.

Unpaired Electrons

Unpaired electrons in atomic or molecular orbitals are a key factor in determining the magnetic properties of any species. The presence of one or more unpaired electrons tends to result in a paramagnetic property, which means the material is attracted to a magnetic field.

When considering unpaired electrons, diamagnetic materials are those where every electron has a partner, resulting in no net attraction or repulsion by a magnetic field. Meanwhile, a chemical species like \[ ext{NO}_2 \] is known to have an unpaired electron, making it paramagnetic.

• This concept is crucial in identifying which compounds can be classified as diamagnetic, such as \[ ext{K}_2 ext{CrO}_4 \], where chromium is in a state that leads to a \[ d^0 \] electron configuration, resulting in all electrons being paired.
• Manganese in compounds like \[ ext{Mn}_3 ext{O}_4 \] typically has unpaired electrons due to its mixed oxidation states, thus not diamagnetic.

Transition Metal Complexes

Transition metal complexes often exhibit varying magnetic properties based on their electron configuration and the presence of unpaired electrons. These properties can be understood through crystal field theory or ligand field theory, which describe how the surrounding ligands in a complex affect the energy of the d orbitals.

In tetrahedral transition metal complexes like \[ ( ext{NH}_4)_2[ ext{NiCl}_4] \], the energy difference is generally smaller, allowing unpaired electrons to remain, thereby indicating paramagnetism. This means such complexes are not diamagnetic.

• For example, \[ ext{FeCl}_4^{2-} \] in \[ ( ext{NH}_4)_2[ ext{FeCl}_4] \] contains unpaired electrons due to iron’s multiple oxidation states, which typically leads to a paramagnetic nature.
• Understanding the arrangement and pairing of electrons in the d orbitals of transition metal complexes is pivotal in predicting whether a complex will display diamagnetic or paramagnetic behavior.