Problem 133 - A Complete Resource Book in Chemistry for JEE Main

Question

Match the following $$ \begin{array}{ll} \hline \text { Column-I } & \text { Column-II } \\ \hline \text { (a) }\left[\mathrm{Ni}(\mathrm{CN})_{4}\right]^{2-} & \text { (p) Octahedral } \\ \text { (b) }\left[\mathrm{MnF}_{6}\right]^{4-} & \text { (q) Paramagnetic } \\\ \text { (c) }\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-} & \text { (r) Square planar } \\ \text { (d) }\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+} & \text { (s) } \mathrm{d}^{2} \mathrm{sp}^{3} \text { hybridization } \\ & \text { (t) Weak field ligand. } \end{array} $$

Step-by-Step Solution

Answer

(a) - r, (b) - q, (c) - p, (d) - t.

Step 1: Analyze [Ni(CN)4]2-

The ion \([\text{Ni}(\text{CN})_4]^{2-}\) typically forms a square planar structure because nickel primarily exhibits \([\text{Ni}^{2+}]\) with sp\(^3\) hybridization, especially when coordinated with strong field ligands like CN\(^-\). Hence, it matches with (r) Square planar.

Step 2: Analyze [MnF6]4-

The compound \([\text{MnF}_6]^{4-}\) involves manganese in a high oxidation state (Mn(II)), with weak field ligands such as \(\text{F}^-\) which allows it to be paramagnetic. Due to paramagnetic nature, this ion corresponds to option (q) Paramagnetic.

Step 3: Analyze [Fe(CN)6]3-

The complex \([\text{Fe}(\text{CN})_6]^{3-}\) contains a low-spin iron(III) ion due to the strong field ligand CN\(^-\), resulting in d\(^2\)sp\(^3\) hybridization which typically supports an octahedral geometry. Thus, it matches with (p) Octahedral.

Step 4: Analyze [Cr(H2O)6]3+

The complex \([\text{Cr}(\text{H}_2\text{O})_6]^{3+}\) includes \(\text{H}_2\text{O}\), a weak field ligand, which does not lead to electron pairing in the 3d orbitals of Cr(III). Consequently, it forms an octahedral arrangement with (t) Weak field ligand.

Key Concepts

Hybridization

Hybridization is a fundamental concept in coordination chemistry that explains the mixing of atomic orbitals to form new hybrid orbitals. This concept helps us understand the shape and geometry of coordination compounds.
Hybrid orbitals are combinations of atomic orbitals on a metal ion that are used to bond with ligands. Several types of hybridizations can occur, such as:

• **sp extsuperscript{3} hybridization**: Common in tetrahedral structures like methane, involving one s and three p orbitals mixing.
• **d extsuperscript{2}sp extsuperscript{3} hybridization**: Seen in octahedral complexes, involving two d, one s, and three p orbitals.

The choice of hybridization depends on the metal center and the types of ligands bound to it. In coordination chemistry, the geometry of the compound is often determined by this hybridization.
For example, in the complex \([ ext{Fe}( ext{CN})_6]^{3-}\), the strong field ligand \( ext{CN}^-\) causes pairing of the electrons in the 3d orbitals of iron, leading to \(d^2sp^3\) hybridization and resulting in an octahedral shape.

Crystal Field Theory

Crystal Field Theory (CFT) is a model that describes the electronic structure of coordination complexes. This theory helps in understanding how the metal ion's degenerate d orbitals are influenced by the presence of ligands.
When ligands approach a metal ion, their negative charges affect the d orbitals due to repulsion. This leads to differences in energy levels, creating a split in the d orbitals.

• In octahedral complexes, this results in a splitting into two energy levels: a higher energy \(e_g\) set and a lower energy \(t_{2g}\) set.
• In tetrahedral complexes, the splitting is reversed, with a higher energy \(t_2\) set and a lower energy \(e\) set.

CFT provides insight into the color and magnetic properties of complexes. For example, in the complex \([ ext{Cr}( ext{H}_2 ext{O})_6]^{3+}\), water is a weak field ligand that creates a smaller splitting in the d orbitals, keeping the compound paramagnetic.

Ligands

Ligands are ions or molecules that bind to a central metal atom to form coordination complexes. They are crucial because they define the structure, reactivity, and properties of these complexes. Ligands can be classified into several types based on their bonding ability:

• **Monodentate ligands**: Bind to the metal atom through a single donor atom, like \(\text{H}_2\text{O}\) or \(\text{NH}_3\).
• **Polydentate ligands**: Can bond through multiple sites, with examples including ethylenediamine and oxalate.

Another important classification is based on their field strength:

• **Strong field ligands**, like \(\text{CN}^-\), cause a large splitting of the d orbitals, often leading to low-spin configurations.
• **Weak field ligands**, such as \(\text{F}^-\), cause smaller splitting, often resulting in high-spin configurations.

The effect of ligands in complexes can be observed in their geometry and magnetism. For example, the complex \([ ext{MnF}_6]^{4-}\) involves \(\text{F}^-\), a weak field ligand, contributing to its paramagnetic nature due to less pairing of electrons.

Paramagnetism

Paramagnetism is a property of certain materials that causes them to be attracted to a magnetic field. This is usually due to the presence of unpaired electrons. In coordination chemistry, the number of unpaired electrons in the metal ion's d orbitals determines the magnetic property of the complex.
A paramagnetic compound contains one or more unpaired electrons, which align with external magnetic fields, enhancing the compound's magnetic properties. To determine paramagnetism, we analyze the electron configuration and the influence of the ligand field strength.

• Compounds with weak field ligands, such as \(\text{F}^-\), often have unpaired electrons leading to paramagnetism.
• Strong field ligands, like \(\text{CN}^-\), often cause all electrons to pair, resulting in diamagnetism.

For example, the complex \([ ext{MnF}_6]^{4-}\) is paramagnetic due to \(\text{F}^-\) being a weak field ligand, which allows unpaired electrons on the \(\text{Mn}^{2+}\) ion. Understanding these properties is crucial for predicting the behavior of coordination compounds in magnetic fields.