Problem 141 - A Complete Resource Book in Chemistry for JEE Main

Question

Amongst the following, the total number of species which are diamagnetic is \(\mathrm{K}_{4}[\mathrm{Fe}(\mathrm{CN})], \mathrm{K}_{3}[\mathrm{Cr}(\mathrm{CN})], \mathrm{K}_{3}\left[\mathrm{Co}(\mathrm{CN})_{6}\right]\) \(\mathrm{K}_{2}\left[\mathrm{Ni}(\mathrm{CN})_{4}\right],\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+}, \mathrm{K}_{2} \mathrm{TiF}_{6}\left[\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}\)

Step-by-Step Solution

Answer

5 species are diamagnetic.

Step 1: Understand Diamagnetism

Diamagnetism refers to substances with all paired electrons that do not create a net magnetic moment, thus not responding to a magnetic field. We need to determine if there are any unpaired electrons in each species to identify if it is diamagnetic.

Step 2: Analysis of \(\mathrm{K}_{4}[\mathrm{Fe}(\mathrm{CN})]\)

The central metal ion here is Fe and its oxidation state can be determined as +2 (since 4 potassium ions provide +4 and the complex's total charge is 0). Since CN is a strong field ligand, it will pair all the electrons in the \(\text{Fe}^{2+}\) ion. The electron configuration is \([Ar]\,3d^6\) with all electrons paired. Hence, \(\mathrm{K}_{4}[\mathrm{Fe}(\mathrm{CN})]\) is diamagnetic.

Step 3: Evaluation of \(\mathrm{K}_{3}[\mathrm{Cr}(\mathrm{CN})_{6}]\)

Cr in this complex is in the +3 oxidation state. CN is a strong field ligand, causing pairing of electrons in \(\text{Cr}^{3+}\). The electron configuration is \([Ar]\,3d^3\), which has unpaired electrons. Therefore, \(\mathrm{K}_{3}[\mathrm{Cr}(\mathrm{CN})_{6}]\) is not diamagnetic.

Step 4: Evaluation of \(\mathrm{K}_{3}\left[\mathrm{Co}(\mathrm{CN})_{6}\right]\)

Co in this complex is in the +3 oxidation state. CN is a strong field ligand, leading to complete pairing of electrons in \(\text{Co}^{3+}\). The electron configuration is \([Ar]\,3d^6\) and all electrons are paired. Thus, \(\mathrm{K}_{3}[\mathrm{Co}(\mathrm{CN})_{6}]\) is diamagnetic.

Step 5: Analysis of \(\mathrm{K}_{2}\left[\mathrm{Ni}(\mathrm{CN})_{4}\right]\)

Ni in this complex is in the +2 oxidation state. CN, being a strong field ligand, will cause all electrons to pair in \(\text{Ni}^{2+}\). The electron configuration is \([Ar]\,3d^8\), all electrons are paired. Thus, \(\mathrm{K}_{2}[\mathrm{Ni}(\mathrm{CN})_{4}]\) is diamagnetic.

Step 6: Analysis of \([\mathrm{Co}(\mathrm{NH}_{3})_{6}]^{3+}\)

Co is the metal ion with an oxidation state of +3. \(\text{NH}_3\), although a moderate field ligand, does not pair all electrons in \(\text{Co}^{3+}\). The electron configuration is \([Ar]\,3d^6\), with one unpaired electron. Hence it is not diamagnetic.

Step 7: Analysis of \(\mathrm{K}_{2}\mathrm{TiF}_{6}\)

Ti in this complex is in the +4 oxidation state. \(\text{F}^-\) is a weak field ligand and will not pair the electrons in \(\text{Ti}^{4+}\). The electron configuration is \([Ar]\), which means there are no d-electrons left; therefore, it is diamagnetic.

Step 8: Analysis of \([\mathrm{Pt}(\mathrm{NH}_{3})_{4}]^{2+}\)

The \(\text{Pt}^{2+}\) ion with \(\text{NH}_3\) as a ligand has the electron configuration \([Xe]\,4f^{14}\,5d^8\). All electrons are paired. Therefore, \([\mathrm{Pt}(\mathrm{NH}_{3})_{4}]^{2+}\) is diamagnetic.

Step 9: Count Diamagnetic Species

After analyzing each species, we identify \(\mathrm{K}_{4}[\mathrm{Fe}(\mathrm{CN})]\), \(\mathrm{K}_{3}[\mathrm{Co}(\mathrm{CN})_{6}]\), \(\mathrm{K}_{2}[\mathrm{Ni}(\mathrm{CN})_{4}]\), \(\mathrm{K}_{2}\mathrm{TiF}_{6}\), and \([\mathrm{Pt}(\mathrm{NH}_{3})_{4}]^{2+}\) as diamagnetic. This gives a total of 5 species.

Key Concepts

Electron Configuration

Electron configuration describes the distribution of electrons in an atom's orbitals. Each electron occupies a specific energy level and orbital, following the principles outlined by quantum mechanics. Key rules include the Aufbau principle, Pauli exclusion principle, and Hund's rule.

• Aufbau Principle: Electrons fill the lowest energy orbitals first before moving to higher energy levels.
• Pauli Exclusion Principle: No two electrons can have identical sets of quantum numbers in the same atom, meaning each orbital can hold a maximum of two electrons with opposite spins.
• Hund's Rule: Electrons will fill degenerate orbitals (orbitals with the same energy) singly, with parallel spins, before pairing up.

By knowing the electron configuration, you can predict magnetic properties, such as diamagnetism or paramagnetism. For instance, species that have all their electrons paired are typically diamagnetic, exhibiting no response to magnetic fields.

Oxidation State

The oxidation state or oxidation number is a figure assigned to an element in a chemical compound, signifying the number of electrons lost or gained by an atom compared to its elemental state. It provides a way to track electron transfer in redox reactions.

• Typifying Ionic States: In ionic compounds, oxidation states reflect the charge of individual ions. For instance, in \( ext{K}_4[ ext{Fe}( ext{CN})_6]\), Fe typically has an oxidation state of +2.
• Determining Electron Count: Oxidation states help in deducing the total number of electrons around the central atom, assisting in electron configuration and magnetic property predictions.
• Versatility in Use: It’s applicable to all elements, facilitating the understanding of complexation and electron sharing or transfer.

Recognizing oxidation states is crucial for calculating electronic configuration post-electron transfer, essential for identifying if species are diamagnetic.

Ligand Field Strength

The concept of ligand field strength revolves around how ligands affect the energies of d orbitals in a transition metal complex, which is crucial for determining electron pairing. Ligands are molecules or ions that donate a pair of electrons to a metal atom or ion to form a coordination complex.

• Strong field ligands: Such as CN⁻, can pair electrons within d orbitals. This often leads to low-spin configurations, meaning fewer unpaired electrons and a tendency toward diamagnetism.
• Weak field ligands: Like F⁻, tend not to induce such pairing, often resulting in high-spin configurations with unpaired electrons, typically not diamagnetic.
• Influence on Electron Configuration: The strength of the ligand influences whether electron configurations remain paired or unpaired.

Understanding ligand field strength helps predict the magnetic behavior of complexes and elements in various coordination environments, essential for determining whether a species is paramagnetic or diamagnetic.

Unpaired Electrons

Unpaired electrons are electrons occupying orbitals singly rather than in pairs, primarily influencing a substance's magnetic properties. In transition metals, the presence and arrangement of these unpaired electrons in d-orbitals decide if a substance is paramagnetic or diamagnetic.

• Magnetic Properties: Unpaired electrons result in paramagnetism, where substances are attracted to magnetic fields. No unpaired electrons indicate diamagnetism, where a substance weakly repels magnetic fields.
• Spin Configurations: High-spin states have more unpaired electrons and hence display paramagnetism. Low-spin states have paired electrons, indicating diamagnetic properties.
• Role of Electron Pairing: The pairing of electrons, influenced by ligand field strength and the oxidation state of the central metal, determines whether unpaired electrons exist.

Understanding unpaired electrons' role is vital in predicting and explaining the magnetic properties of various chemical species, particularly transition metal complexes.