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

The correct order is option (a): \(\left[\mathrm{MnCl}_{4}\right]^{2-} > \left[\mathrm{CoCl}_{4}\right]^{2-} > \mathrm{Fe}(\mathrm{CN})_{6}^{4-}\).

Step 1: Determine Electronic Configurations

Identify the electronic configurations of each central metal ion. For \(\left[\mathrm{MnCl}_{4}\right]^{2-}\), Mn is in the +2 oxidation state (\(3d^5\)). For \(\left[\mathrm{CoCl}_{4}\right]^{2-}\), Co is in the +2 oxidation state (\(3d^7\)).For \(\mathrm{Fe}\left(\mathrm{CN}_{6}\right)^{4-}\), Fe is in the +2 oxidation state (\(3d^6\)).

Step 2: Identify Spin Pairing and Determine Unpaired Electrons

Use the fact that \(\mathrm{CN}^-\) is a strong field ligand and \(\mathrm{Cl}^-\) is a weak field ligand:* \(\left[\mathrm{MnCl}_{4}\right]^{2-}\): All 5 d-electrons unpaired.* \(\left[\mathrm{CoCl}_{4}\right]^{2-}\): 3 unpaired d-electrons.* \(\mathrm{Fe}(\mathrm{CN})_{6}^{4-}\): Strong field, all d-electrons paired.

Step 3: Calculate Magnetic Moment

Use the formula for the spin-only magnetic moment \( \mu = \sqrt{n(n+2)} \), where \( n \) is the number of unpaired electrons:* \(\left[\mathrm{MnCl}_{4}\right]^{2-}\): \( \mu = \sqrt{5(5+2)} = \sqrt{35} \approx 5.92 \text{ BM} \).* \(\left[\mathrm{CoCl}_{4}\right]^{2-}\): \( \mu = \sqrt{3(3+2)} = \sqrt{15} \approx 3.87 \text{ BM} \).* \(\mathrm{Fe}(\mathrm{CN})_{6}^{4-}\): \( \mu = \sqrt{0} = 0 \text{ BM} \).

Step 4: Order Magnetic Moments

The magnetic moments in order from highest to lowest are:1. \(\left[\mathrm{MnCl}_{4}\right]^{2-}\) with 5.92 BM2. \(\left[\mathrm{CoCl}_{4}\right]^{2-}\) with 3.87 BM3. \(\mathrm{Fe}(\mathrm{CN})_{6}^{4-}\) with 0 BMThus, the correct order is \(\left[\mathrm{MnCl}_{4}\right]^{2-} > \left[\mathrm{CoCl}_{4}\right]^{2-} > \mathrm{Fe}(\mathrm{CN})_{6}^{4-}\).

Key Concepts

Spin-Only Formula

The spin-only formula is used to calculate the magnetic moment of a substance, mainly when considering compounds with unpaired electrons. This formula is particularly useful because it simplifies how we understand the magnetism in coordination compounds. The formula is given by \[ \mu = \sqrt{n(n+2)} \] where \( n \) represents the number of unpaired electrons.
The spin-only magnetic moment is measured in Bohr Magnetons (BM), which is a unit used to express magnetic moments of electrons, atoms, and molecules.

• It is important to note that the formula only accounts for spin magnetic moments, assuming no substantial contribution from orbital motion;
• The applicability is greatest in cases where orbital contribution is quened, which is often seen in transition metals.

For example, in the compound \([\mathrm{MnCl}_{4}]^{2-}\), where manganese is in a +2 oxidation state, having a \(3d^5\) configuration, all d-electron spins are unpaired.
Therefore, using the spin-only formula, the calculated magnetic moment is approximately 5.92 BM, indicating strong magnetism. Understanding this concept helps in predicting the behavior of such complexes under a magnetic field.

Electronic Configuration

Electronic configuration is the distribution of electrons of an atom or molecule in atomic or molecular orbitals. It forms the foundation for understanding the magnetic properties of metal complexes. The electronic configuration determines how magnetic a compound will be based on the number of unpaired electrons.
Consider the given compounds:

• \([\mathrm{MnCl}_{4}]^{2-}\): Manganese in a +2 oxidation state has an electronic configuration of \(3d^5\).
• \([\mathrm{CoCl}_{4}]^{2-}\): Cobalt in a +2 oxidation state has an electronic configuration of \(3d^7\).
• \(\mathrm{Fe}(\mathrm{CN})_{6}]^{4-}\): Iron in a +2 oxidation state has an electronic configuration of \(3d^6\).

In these configurations:

• \([\mathrm{MnCl}_{4}]^{2-}\), having five unpaired electrons, represents a high spin complex.
• \([\mathrm{CoCl}_{4}]^{2-}\) shows three unpaired electrons.
• \(\mathrm{Fe}(\mathrm{CN})_{6}]^{4-}\), due to the presence of strong field ligands, results in a configuration where all electrons are paired.

Understanding electronic configurations is crucial for recognizing the effect of unpaired electrons on magnetic properties.

Strong and Weak Field Ligands

Ligands play a significant role in determining the magnetic properties of coordination compounds by influencing spin states through their ability to cause electronic pairing. Ligands are generally categorized as either strong field or weak field, based on how they affect the distribution of d-electrons in metal ions.

• Strong field ligands, such as cyanide \(\mathrm{CN}^-\), are known to create a large energy gap between d-orbitals. This causes electrons to pair up in lower energy orbitals, which can lead to low-spin configurations.
• Conversely, weak field ligands like chloride \(\mathrm{Cl}^-\) create a smaller energy gap, allowing more unpaired electrons, thus leading to high-spin configurations.

In the example given:

• \([\mathrm{MnCl}_{4}]^{2-}\) utilizes weak field ligand \(\mathrm{Cl}^-\), retaining unpaired electrons, hence exhibits strong magnetism.
• \(\mathrm{Fe}(\mathrm{CN})_{6}]^{4-}\) includes the strong field ligand \(\mathrm{CN}^-\), leading to paired electrons and low magnetic moment.

Recognizing whether a ligand is strong or weak not only helps in predicting the magnetic behavior of a compound but also in deducing the compound's entire electronic characteristics.