Problem 170 - A Complete Resource Book in Chemistry for JEE Main

Question

In which of the following octahedral complexes of Co (Atomic number 27 ), will the magnitude of \(\Delta\) be the highest? (a) \(\left[\mathrm{Co}(\mathrm{CN})_{6}\right]^{3}-\) (b) \(\left[\mathrm{Co}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]^{3}\) (c) \(\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}\) (d) \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+}\)

Step-by-Step Solution

Answer

The magnitude of \(\Delta\) is highest in \(\left[\mathrm{Co}( ext{CN})_6\right]^{3-}\).

Step 1: Understand Crystal Field Splitting

In octahedral complexes, the ligand field causes the splitting of the d-orbitals into two energy levels: lower energy ( 2g) and higher energy (eg) due to crystal field splitting, denoted as Dq or . The magnitude of the splitting () depends on the strength of the ligand field.

Step 2: Consider the Spectrochemical Series

Ligands are ranked by their ability to split d-orbitals, forming the spectrochemical series. Strong-field ligands, like CN\(^{-}\), result in large  and weak-field ligands, like H\(_2\)O, result in small . In our options, the ligands in increasing order of field strength: H\(_2\)O < NH\(_3\) < C\(_2\)O\(_4\)\(^{2-}\) < CN\(^{-}\).

Step 3: Assess the Complexes

For each complex, match the ligands to the spectrochemical series, determining the field strength: (a) \( [\text{Co(CN)}_6]^{3-} \) has CN\(^{-}\) (strong-field), (b) \( [\text{Co(C}_2\text{O}_4)_3]^{3-} \) has C\(^{2-}_2\)O\(^{2-}_4\) (moderate-field), (c) \( [\text{Co(H}_2\text{O})_6]^{3+} \) has H\(_2\)O (weak-field), and (d) \([\text{Co(NH}_3)_6]^{3+}\) has NH\(_3\) (weak-field).

Step 4: Determine Which Complex Has Highest \(\Delta\)

The complex with the strongest field ligand will have the highest . Among the options, CN\(^{-}\) is the strongest ligand, appearing in \([\text{Co(CN)}_6]^{3-}\), leading to the highest crystal field splitting.

Key Concepts

Crystal Field Splitting

In coordination chemistry, understanding crystal field splitting is crucial when discussing transition metal complexes. When ligands approach a metal ion, their electrons interact with the d-orbitals of the metal, causing the degenerate d-orbitals to split into different energy levels. In an octahedral complex, this interaction results in two sets: three lower-energy orbitals (2g) and two higher-energy orbitals (8g). The energy gap between these levels is known as the crystal field splitting energy, represented as 6\( \Delta \). This splitting is key to influencing various properties of a complex, such as its color, magnetism, and reactivity. A larger 6\( \Delta \) means a greater difference in potential energy for the electrons, impacting how they occupy these orbitals. Factors such as the oxidation state of the metal and the nature of the ligands affect the magnitude of this splitting.

Spectrochemical Series

The spectrochemical series ranks ligands based on their ability to split the d-orbitals of a metal ion in a coordination complex. This series provides a powerful tool for predicting the crystal field splitting in various metal-ligand combinations. The series typically orders ligands from weak field to strong field, affecting the size of the 6\( \Delta \):

• Weak-field ligands, like H\(_2\)O and Cl\(^-\), cause smaller 6\( \Delta \) values.
• Strong-field ligands, such as CN\(^-\) and CO, lead to larger 6\( \Delta \) values.

This ordering allows chemists to predict and explain the splitting in complexes, helping to determine the electronic structure and resulting characteristics. In the given example, CN\(^-\) has the highest ligand field strength in the spectrochemical series among the options provided, leading to the greatest crystal field splitting.

Ligand Field Strength

The strength of a ligand field determines the extent to which a ligand can split the d-orbitals in a complex. Ligand field strength directly correlates with the spectrochemical series, where ligands are organized based on their ability to affect the d orbital energy levels.A ligand's field strength impacts not only the crystal field splitting ( 6\( \Delta \)) but also electronic configurations and spectral properties:

• Strong-field ligands, like CN\(^-\), contribute to larger splitting, often favoring low-spin configurations.
• Weak-field ligands, such as H\(_2\)O and NH\(_3\), result in smaller splitting, generally leading to high-spin arrangements.

These differences are essential in applications like understanding magnetic properties and transition metal complex color. In the exercise example, CN\(^-\) exhibits the strongest field strength, making it the ligand that causes the highest crystal field splitting in the complexes provided.