Problem 131 - A Complete Resource Book in Chemistry for JEE Main

Question

$$ \begin{aligned} &\text { Match the following }\\\ &\begin{array}{ll} \hline \text { Column-I } & \text { Column-II } \\ \hline \text { (a) }\left[\mathrm{MnCl}_{6}\right]^{3-} & \text { (p) One unpaired electron } \\ \text { (b) }\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-} & \text { (q) } \mathrm{d}^{2} \mathrm{sp}^{3} \\ \text { (c) }\left[\mathrm{CoF}_{6}\right]^{3-} & \text { (r) } \mathrm{sp}^{3} \mathrm{~d}^{2} \\ \text { (d) }\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2-} & \text { (s) Four unpaired electrons } \\ & \text { (t) Three unpaired electrons } \\ \hline \end{array} \end{aligned} $$

Step-by-Step Solution

Answer

(a) s; (b) p; (c) r; (d) s.

Step 1: Analyze the complex \( [\mathrm{MnCl}_{6}]^{3-} \)

Manganese, \( \mathrm{Mn} \), in this complex is in the \( +3 \) oxidation state. The electron configuration of \( \mathrm{Mn}^{3+} \) is \( [\mathrm{Ar}]3d^4 \). Chloride ion \( \mathrm{Cl}^- \) is a weak field ligand, leading to high spin configuration with four unpaired electrons. Therefore, \( [\mathrm{MnCl}_{6}]^{3-} \) has a high spin with four unpaired electrons (s). This complex shows \( \text{sp}^3\text{d}^2 \) hybridization, which is option (r).

Step 2: Analyze the complex \( [\mathrm{Fe}(\mathrm{CN})_{6}]^{3-} \)

Iron, \( \mathrm{Fe} \), in this complex is in the \( +3 \) oxidation state. The electron configuration of \( \mathrm{Fe}^{3+} \) is \( [\mathrm{Ar}]3d^5 \). Cyanide \( \mathrm{CN}^- \), is a strong field ligand, causing pairing of the electrons, leading to low spin configuration. This results in one unpaired electron, which corresponds to option (p). This complex has \( d^2\text{sp}^3 \) hybridization, which aligns with option (q).

Step 3: Analyze the complex \( [\mathrm{CoF}_{6}]^{3-} \)

Cobalt, \( \mathrm{Co} \), in this complex is in the \( +3 \) oxidation state. The electron configuration of \( \mathrm{Co}^{3+} \) is \( [\mathrm{Ar}]3d^6 \). Fluoride \( \mathrm{F}^- \) is a weak field ligand, leading to a high spin complex with four unpaired electrons. Therefore, \( [\mathrm{CoF}_{6}]^{3-} \) has four unpaired electrons (s) and exhibits \( \text{sp}^3\text{d}^2 \) hybridization, which matches option (r).

Step 4: Analyze the complex \( [\mathrm{Fe}(\mathrm{H}_{2}\mathrm{O})_{6}]^{2+} \)

Iron, \( \mathrm{Fe} \), in this complex is in the \( +2 \) oxidation state. The electron configuration of \( \mathrm{Fe}^{2+} \) is \( [\mathrm{Ar}]3d^6 \). Water \( \mathrm{H}_{2}\mathrm{O} \) is a weak field ligand, so the complex is high spin, with four unpaired electrons (s). This suggests that the unpaired electron configuration corresponds to option (s). This complex has \( d^2\text{sp}^3 \) hybridization, aligning with option (q).

Key Concepts

Complex Ion Structures

In coordination chemistry, a complex ion is a structure consisting of a central atom, typically a metal, bonded to surrounding molecules or ions, termed as ligands. The central metal ion is often a transition metal, which has the ability to form multiple bonds with ligands. The structure of a complex ion is crucial in predicting the geometry and properties of the compound. Generally, these structures can adopt geometries like octahedral, tetrahedral, or square planar, depending on the number and nature of ligands.

• Types of Ligands: Ligands can be classified as monodentate, binding through a single point of attachment, or polydentate, binding through multiple points.
• Charge of Complex Ions: The charge of the complex is the sum of the metal's oxidation state and the charges contributed by the ligands.
• Examples: Consider the complex ion \([\mathrm{MnCl}_{6}]^{3-}\). Here, Mn is the central metal in an octahedral arrangement, surrounded by six \(\mathrm{Cl}^-\) ligands.

Understanding complex ion structures helps in comprehending how electron configurations and hybridization contribute to the stability and magnetic properties of these ions.

Electron Configuration

The electron configuration of a complex ion reveals how electrons are distributed among the different orbitals. For transition metals, this configuration is crucial as they typically have partially filled d-orbitals. To determine the electron configuration of the central metal ion, consider its oxidation state and the electron count. This tells us about the unpaired electrons, predicting the magnetic behavior of the complex.

• Example: In \([\mathrm{Fe}(\mathrm{CN})_{6}]^{3-}\), Fe is in a \(+3\) oxidation state, making the configuration \([\mathrm{Ar}]3d^5\), with one unpaired electron due to the strong field ligand, CN\(^{-}\).
• Impact of Ligands: Strong field ligands like CN\(^{-}\) lead to paired electrons, while weak field ligands like \(\mathrm{Cl}^-\) result in unpaired electrons, affecting the complex's magnetic properties.

Electron configuration, therefore, not only describes the electron setup but also the resulting magnetism, stability, and color of the complexes.

Hybridization

Hybridization is a concept that describes the mixing of atomic orbitals to form new hybrid orbitals. In coordination complexes, this affects the molecular structure and bonding. The type of hybridization determines the geometry of the complex.

• Types: Common hybridizations in complex ions include \(d^2sp^3\) and \(sp^3d^2\), which influence the geometry as octahedral or others based on orbital interactions.
• Example: In \([\mathrm{CoF}_{6}]^{3-}\), \(sp^3d^2\) hybridization suggests an octahedral shape, formed from one \(s\), three \(p\), and two \(d\) orbitals.

Understanding hybridization in these complexes helps predict their geometrical shapes, highlighting differences between high-spin and low-spin complexes and how they are affected by ligand strength.

Ligand Field Theory

Ligand Field Theory (LFT) is an extension of crystal field theory that explores how ligands affect the energy levels of a metal's d-orbitals. This theory provides insights into the color, magnetism, and stability of complexes.

• Splitting of d-orbitals: In an octahedral field, ligands cause the d-orbitals to split into two sets with different energies, known as \(eg\) and \(t_{2g}\) orbitals.
• High-spin vs Low-spin: The difference in energy levels can result in high-spin states (more unpaired electrons) or low-spin states (fewer unpaired electrons), impacting magnetic properties and colors.
• Example: In \([\mathrm{Fe}( \mathrm{H}_{2}\mathrm{O})_{6}]^{2+}\), a weak field ligand, water, causes a high-spin configuration as it cannot cause sufficient electron pairing.

LFT is essential for explaining the electronic transitions that result in the vibrant colors seen in many coordination compounds, as well as their magnetic behaviors.