Problem 40 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

The complex showing a spin-only magnetic moment of \(2.82\) B.M. is : (a) \(\left[\mathrm{Ni}(\mathrm{CO})_{4}\right]\) (b) \(\left[\mathrm{NiCl}_{4}\right]^{2-}\) (c) \(\left[\mathrm{Ni}\left(\mathrm{PPh}_{3}\right)_{4}\right]\) (d) \(\left[\mathrm{Ni}(\mathrm{CN})_{4}\right]^{2-}\)

Step-by-Step Solution

Answer

The complex is \([\mathrm{NiCl}_{4}]^{2-}\).

Step 1: Understanding Spin-Only Magnetic Moment

The spin-only magnetic moment for a complex is given by the formula: \( \mu_{s} = \sqrt{n(n+2)} \), where \( n \) is the number of unpaired electrons in the complex's central metal ion.

Step 2: Calculate the Number of Unpaired Electrons Needed

Given the magnetic moment \( \mu = 2.82 \) B.M., use the formula \( \mu_{s} = \sqrt{n(n+2)} \). Let \( \mu = 2.82 \), solve for \( n \).\[ 2.82 = \sqrt{n(n+2)} \]Squaring both sides, we get:\[ 2.82^2 = n(n+2) \]\[ 7.95 = n(n+2) \]Trial and error show that \( n = 2 \) satisfies this equation closely (since \( n = 2 \) gives \( \mu \approx 2.83 \) B.M.). Hence, the complex has 2 unpaired electrons.

Step 3: Analyze Each Complex

(a) \( [\mathrm{Ni}(\mathrm{CO})_{4}] \): \( \mathrm{Ni}^{0} \), \([\mathrm{Ni}(\mathrm{CO})_{4}] \) is a diamagnetic complex with no unpaired electrons because \( \mathrm{CO} \) is a strong field ligand.(b) \( [\mathrm{NiCl}_{4}]^{2-} \): \( \mathrm{Ni}^{2+} \), \([\mathrm{NiCl}_{4}]^{2-}\) is a tetrahedral complex and has 2 unpaired electrons.(c) \( [\mathrm{Ni}(\mathrm{PPh}_{3})_{4}] \): \( \mathrm{Ni}^{0} \), \([\mathrm{Ni}(\mathrm{PPh}_{3})_{4}] \) is a diamagnetic complex with no unpaired electrons.(d) \( [\mathrm{Ni}(\mathrm{CN})_{4}]^{2-} \): \( \mathrm{Ni}^{2+} \), \([\mathrm{Ni}(\mathrm{CN})_{4}]^{2-} \) is a square planar complex and has no unpaired electrons, as \( \mathrm{CN}^- \) is a strong field ligand.

Step 4: Identify the Correct Complex

From Step 3, option (b) \([\mathrm{NiCl}_{4}]^{2-}\) has 2 unpaired electrons matching the calculated magnetic moment of \(2.82\) B.M. Hence, this is the correct complex among the choices given.

Key Concepts

Unpaired Electrons

Unpaired electrons play a critical role in determining the magnetic properties of a chemical complex. When electrons are paired within an orbital, their opposite spins cancel each other out, resulting in a diamagnetic behavior. However, if there are unpaired electrons, the imbalance in spin creates a net magnetic moment. This net spin generates what's known as a spin-only magnetic moment. The measure of this magnetic moment is crucial for chemists when they study the electronic structure of elements and compounds. In essence, the presence of unpaired electrons can make a complex paramagnetic, which means it can be attracted to an external magnetic field.

In our problem, the magnetic moment formula \( \mu_{s} = \sqrt{n(n+2)} \) is used. Here, \( n \) represents the number of unpaired electrons. Given a magnetic moment of \( 2.82 \) Bohr Magnetons (B.M.), solving for \( n \) using this formula shows that the complex needs to have 2 unpaired electrons. This helps identify which ligand and metal center configuration can yield the expected magnetic properties.

Tetrahedral Complexes

Tetrahedral complexes are a fascinating topic within coordination chemistry, often featuring central metal ions surrounded by four ligands in a shape that resembles a triangular pyramid. Due to their unique arrangement, they exhibit a certain degree of spatial separation, leading to specific electronic properties. The crystal field splitting in tetrahedral geometry is usually smaller than in octahedral geometries. This smaller splitting often allows unpaired electrons to occupy higher energy orbitals instead of pairing up, resulting in paramagnetism with unpaired electrons.

The tetrahedral complex \( [\mathrm{NiCl}_{4}]^{2-} \) exemplifies this structure. Nickel, in the +2 oxidation state, typically has eight d-electrons. With four chloride ligands, the weak crystal field splitting leads to the retention of two unpaired electrons, consistent with the calculated magnetic moment in this exercise. Thus, tetrahedral coordination often explains why we observe specific magnetic behaviors, as weaker field ligands do not force electron pairing.

Crystal Field Theory

Crystal Field Theory (CFT) offers insight into how metal and ligand interactions affect the electronic structure and properties of metal complexes. This theory explains that different geometries, like tetrahedral shapes, influence how subatomic orbitals are split in energy when surrounded by ligands. In CFT, electron repulsions between ligands and d-orbitals dictate the splitting pattern, which ultimately defines whether unpaired electrons will exist in a complex.

Ligands like chloride exert a weaker crystal field, meaning they cause less splitting of the d-orbitals in comparison to stronger ligands like cyanide or carbon monoxide. As a result, in tetrahedral complexes such as \([\mathrm{NiCl}_{4}]^{2-}\), the energy gap is not always sufficient to force electrons to pair up in lower energy orbitals. CFT thus explains why a metal complex with weak field ligands can maintain unpaired electrons, contributing to its paramagnetic properties. Understanding these principles helps chemists predict and explain the magnetic moments observed in various coordination complexes.