Problem 110 - A Complete Resource Book in Chemistry for JEE Main

Question

The correct order of magnetic moment (spin only values in BM) among the following is (a) \(\left[\mathrm{MnCl}_{4}\right]^{2}>\left[\mathrm{CoCl}_{4}\right]^{2-}>\mathrm{Fe}\left(\mathrm{CN}_{6}\right)^{4}\) (b) \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4}>\left[\mathrm{MnCl}_{4}\right]^{2-}>\left[\mathrm{CoCl}_{4}\right]^{2-}\) (c) \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-}>\left[\mathrm{CoCl}_{4}\right]^{2-}>\left[\mathrm{MnCl}_{4}\right]^{2-}\) (d) \(\left[\mathrm{MnCl}_{4}\right]^{2}>\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4^{-}}>\left[\mathrm{CoCl}_{4}\right]^{2}\) (Atomic number of \(\mathrm{Mn}=25, \mathrm{Fe}=26, \mathrm{Co}=27, \mathrm{Ni}=28\) )

Step-by-Step Solution

Answer

Order is (a): \([\text{MnCl}_4]^{2-} > [\text{CoCl}_4]^{2-} > [\text{Fe(CN)}_6]^{4-}\).

Step 1: Determine Electronic Configuration

Find the electronic configurations for Mn, Co, and Fe in their complex forms. \([\text{MnCl}_4]^{2-}\): Mn is +2, so configuration is \([\text{Ar}]3d^5\). \([\text{CoCl}_4]^{2-}\): Co is +2, so configuration is \([\text{Ar}]3d^7\). \([\text{Fe(CN)}_6]^{4-}\): Fe is +2, so high spin configuration is \([\text{Ar}]3d^6\) but CN is a strong field ligand leading to a low spin configuration \([\text{Ar}]3d^6\).

Step 2: Calculate the Number of Unpaired Electrons

Count unpaired electrons in each configuration: \([\text{MnCl}_4]^{2-}\) has 5 unpaired (3d^5), \([\text{CoCl}_4]^{2-}\) has 3 unpaired (3d^7), and \([\text{Fe(CN)}_6]^{4-}\) has 0 unpaired electrons due to low spin state.

Step 3: Calculate Magnetic Moment

Using the formula \(\mu = \sqrt{n(n+2)}\, \text{BM}\) where \(n\) is the number of unpaired electrons: \([\text{MnCl}_4]^{2-}\): \(\sqrt{5(5+2)} = 5.92\, \text{BM}\), \([\text{CoCl}_4]^{2-}\): \(\sqrt{3(3+2)} = 3.87\, \text{BM}\), \([\text{Fe(CN)}_6]^{4-}\): \(\sqrt{0(0+2)} = 0\, \text{BM}\).

Step 4: Determine the Correct Order

Order complexes by their magnetic moment: Highest \([\text{MnCl}_4]^{2-} > [\text{CoCl}_4]^{2-} > [\text{Fe(CN)}_6]^{4-}\) lowest. This matches option (a) in the problem.

Key Concepts

Magnetic Moment

The magnetic moment of a coordination compound is an essential aspect of its magnetic properties. It is measured in Bohr magnetons (BM) and is directly connected to the number of unpaired electrons in the compound.

Magnetic moments are calculated using the spin-only formula, \[\mu = \sqrt{n(n+2)} \text{ BM}\]where \(n\) is the number of unpaired electrons. This formula accounts for electron spin, the primary source of magnetism in an atom or molecule.

For example, compounds with more unpaired electrons typically exhibit higher magnetic moments, reflecting their strong paramagnetic nature. Conversely, if a compound has no unpaired electrons, as seen in low-spin states or diamagnetic substances, its magnetic moment will be near zero, indicating a lack of paramagnetism.

• High magnetic moment: More unpaired electrons -> Strong paramagnetism
• Low magnetic moment: Fewer/no unpaired electrons -> Weak or no paramagnetism

Understanding these fundamentals helps decipher the chemical nature and magnetic behavior of coordination complexes.

Electronic Configuration

Electronic configuration defines how electrons are distributed in an atom or compound, crucial for determining its magnetic properties and reactivity. In coordination compounds, knowing the oxidation state is necessary to sketch an accurate electronic configuration.

For instance, taking \([\text{MnCl}_4]^{2-}\), Mn in this complex has a +2 oxidation state. Its electron configuration becomes \([\text{Ar}]3d^5\), indicating five 3\(d\) electrons. Moving to Co in \([\text{CoCl}_4]^{2-}\), with Co at +2, its configuration is \([\text{Ar}]3d^7\).

• Identify oxidation state
• Distribution of electrons across orbitals
• Note differences between high-spin and low-spin (strong-field) behavior

For the \([\text{Fe(CN)}_6]^{4-}\) complex, Fe is also at +2, with a normal high spin showing \([\text{Ar}]3d^6\). However, due to the strong field CN ligand, the configuration changes to low-spin \([\text{Ar}]3d^6\), meaning electrons pair up, greatly influencing its magnetic properties.
The distribution changes significantly based on whether the ligands induce pairing (low-spin) or not (high-spin), affecting the count of unpaired electrons and, hence, the magnetic moment.

Unpaired Electrons

Unpaired electrons play a crucial role in determining the magnetic nature of coordination compounds. These unpaired electrons arise from incomplete electron pairs in an atom's or molecule's d-orbitals.

Each unpaired electron adds to a compound's magnetic moment. More unpaired electrons mean a stronger magnetic response known as paramagnetism; fewer or zero unpaired electrons result in weak or no magnetic response, characteristic of diamagnetism.

Examining the complexes:

• \([\text{MnCl}_4]^{2-}\): 5 unpaired electrons due to \(3d^5\) configuration.
• \([\text{CoCl}_4]^{2-}\): 3 unpaired electrons from \(3d^7\).
• \([\text{Fe(CN)}_6]^{4-}\): Interestingly, this configuration has no unpaired electrons due to the low-spin state induced by the strong-field CN ligand.

Unpaired electrons dictate how electron repulsion between orbitals takes place, affecting the geometry and overall magnetic characteristics of a compound. Recognizing the number and implications of these electrons is essential for grasping the principles of coordination chemistry. Understanding the alignment or pairing of electrons helps predict chemical interactions and magnetic behaviors.