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

Question

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

Step-by-Step Solution

Answer

(a) r, (b) t/q, (c) s, (d) p/q

Step 1: Analyze Complex (a)

Identify the geometry of \([\mathrm{Ni}(\mathrm{CN})_4]^{2-}\). Nickel is in a +2 oxidation state, and CN is a strong field ligand, leading to dsp\(^2\) hybridization, forming a square planar geometry. Hence, \([\mathrm{Ni}(\mathrm{CN})_4]^{2-}\) matches with (r) Square planar.

Step 2: Analyze Complex (b)

Examine \([\mathrm{MnF}_{6}]^{4-}\). Manganese is in a +2 oxidation state with fluoride, a weak field ligand, leading to high spin and maintaining paramagnetic properties. The complex is likely to be octahedral. Thus, \([\mathrm{MnF}_{6}]^{4-}\) matches with (t) Weak field ligand and can also fit into (q) Paramagnetic.

Step 3: Analyze Complex (c)

Consider \([\mathrm{Fe}(\mathrm{CN})_{6}]^{3-}\). Iron in a +3 oxidation state with CN, a strong field ligand, causes low-spin d\(^2\)sp\(^3\) hybridization, forming an octahedral complex, and is diamagnetic due to full pairing. Thus, \([\mathrm{Fe}(\mathrm{CN})_{6}]^{3-}\) matches with (s) d\(^2\)sp\(^3\) hybridization.

Step 4: Analyze Complex (d)

Evaluate \([\mathrm{Cr}(\mathrm{H}_{2}\mathrm{O})_{6}]^{3+}\). Chromium in a +3 oxidation state results in d\(^3\)sp\(^3\) hybridization with water, a weak field ligand. The complex is octahedral and paramagnetic. Therefore, \([\mathrm{Cr}(\mathrm{H}_{2}\mathrm{O})_{6}]^{3+}\) matches with (p) Octahedral and (q) Paramagnetic.

Key Concepts

Hybridization

Hybridization is a fundamental concept in coordination chemistry that helps us predict the geometry of coordination compounds. It involves the mixing of atomic orbitals to form new, hybrid orbitals that are involved in bonding. For example, in the case of \([\mathrm{Ni}(\mathrm{CN})_4]^{2-}\), hybridization involves dsp\(^2\) orbitals, resulting in square planar geometry. This is because the CN ligands are strong field ligands that cause pairing of electrons, allowing a low-energy hybridization pathway.

Another complex, \([\mathrm{Fe}(\mathrm{CN})_{6}]^{3-}\), demonstrates d\(^2\)sp\(^3\) hybridization, which is a characteristic of octahedral structures. Strong field ligands like the cyanide ion lead to electron pairing, making such a hybridization favorable. Understanding these hybridization types allows predictions of complex structures and their properties.

Ligand Field Theory

Ligand Field Theory (LFT) is an explanation of how ligands influence the energy levels of a central metal atom's d-orbitals. It explains the color, magnetism, and stability of coordination compounds by considering the impact of ligands on these d-orbitals.

In our examples, \([\mathrm{MnF}_{6}]^{4-}\), involves fluoride ligands, which are considered weak field ligands. This indicates that the d-orbitals remain as unpaired electrons due to minimal splitting, maintaining the paramagnetic property. In contrast, the \([\mathrm{Fe}(\mathrm{CN})_{6}]^{3-}\) complex uses strong field ligands that cause a significant splitting of the d-orbitals, filling all available lower-energy orbitals first, leading to diamagnetic properties.

Paramagnetic and Diamagnetic Properties

The magnetic properties of coordination compounds depend heavily on the electron configuration influenced by the ligands. When we discuss whether a compound is paramagnetic or diamagnetic, we look at the presence or absence of unpaired electrons.

• Paramagnetic: Compounds with unpaired electrons. These compounds are attracted to magnetic fields. For example, \([\mathrm{MnF}_{6}]^{4-}\) is paramagnetic due to the weak field ligands that allow unpaired electrons.
• Diamagnetic: Compounds where all electrons are paired. As a result, they are slightly repelled by a magnetic field. The \([\mathrm{Fe}(\mathrm{CN})_{6}]^{3-}\) complex exhibits diamagnetism because all electrons are paired, a result of the strong field cyanide ligands.
  

Understanding these properties can elucidate the behavior of metal complexes in external magnetic fields and aid in identifying the strength of the ligand fields present in coordination compounds.