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? \([2008]\) (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 complex \( \left[ \mathrm{Co} ( \mathrm{CN} )_{6} \right]^{3-} \) has the highest \( \Delta \).

Step 1: Understand the Crystal Field Splitting

In an octahedral complex, the difference in energy between the two sets of d orbitals is known as the crystal field splitting energy, denoted by \( \Delta \). The magnitude of \( \Delta \) depends on the ligand field strength: stronger field ligands result in larger splitting.

Step 2: Identify the Ligands and their Field Strength

The ligands involved in the complexes are CN\(^-\), C\(_2\)O\(_4\)\(^{2-}\), H\(_2\)O, and NH\(_3\). Ligands can be ordered as per the spectrochemical series based on their field strength:- Strong field ligands: CN\(^-\)- Moderate field ligands: NH\(_3\)- Weak field ligands: H\(_2\)O- Intermediate field ligands: C\(_2\)O\(_4\)\(^{2-}\)

Step 3: Compare the Given Complexes Based on the Ligand Field Strength

For each complex:- \( \left[ \mathrm{Co} ( \mathrm{CN} )_{6} \right]^{3-} \) is coordinated with CN\(^-\), a strong field ligand.- \( \left[ \mathrm{Co} \left( \mathrm{C}_{2} \mathrm{O}_{4} \right)_{3} \right]^{3-} \) is coordinated with C\(_2\)O\(_4\)\(^{2-}\), an intermediate field ligand.- \( \left[ \mathrm{Co} \left( \mathrm{H}_{2} \mathrm{O} \right)_{6} \right]^{3+} \) is coordinated with H\(_2\)O, a weak field ligand.- \( \left[ \mathrm{Co} \left( \mathrm{NH}_{3} \right)_{6} \right]^{3+} \) is coordinated with NH\(_3\), a moderate field ligand.

Step 4: Determine the Complex with the Highest \( \Delta \)

The complex with the strongest field ligands will have the highest crystal field splitting energy. Since CN\(^-\) is a strong field ligand, \( \left[ \mathrm{Co} ( \mathrm{CN} )_{6} \right]^{3-} \) will have the highest \( \Delta \).

Key Concepts

Octahedral Complexes

Octahedral complexes are a common type of coordination compound. They feature a central metal atom surrounded by six ligands, positioned at the corners of an octahedron. The choice of ligands significantly impacts the properties of the complex. - These complexes can exhibit various colors and magnetic properties, depending on the nature of the metal and the ligands attached. - The metal-ligand interactions are vital to the compound's stability and reactivity. An essential factor in octahedral complexes is the arrangement of the d orbitals within the metal. In an octahedral field, the five d orbitals split into two energy levels, where three of them (dxy, dyz, dzx) are lower in energy compared to the other two (dx²-y², dz²). This difference in energy levels plays a crucial role in determining the complex’s behavior.

Ligand Field Strength

Ligand field strength refers to the ability of ligands to split the d orbital energy levels in a metal complex. Ligands are ordered in a spectrochemical series based on their strength. - Strong field ligands, like CN⁻, result in greater splitting of d orbitals. This often leads to lower spin states and can affect the color and magnetic properties. - Weak field ligands, such as H₂O, cause less splitting, typically resulting in higher spin states. - Intermediate and moderately strong ligands like NH₃ and C₂O₄²⁻ provide varying levels of splitting. The field strength of a ligand is crucial when predicting the behavior of metal complexes. It influences not just the splitting of energy levels, but also impacts the overall stability and reactivity of the complex.

Crystal Field Splitting Energy

The crystal field splitting energy, denoted as Δ, is the difference in energy between the split d orbitals in a metal complex. - In octahedral complexes, the energy of dx²-y² and dz² orbitals is elevated compared to the other three d orbitals. - The extent of splitting, represented by Δ, varies based on the ligands present. Strong field ligands lead to a larger Δ, while weak field ligands result in smaller Δ. This splitting in energy levels is crucial for understanding the electronic configuration of the complex. It affects the distribution of electrons, which in turn dictates the magnetic and spectral properties of the compound. The magnitude of Δ significantly influences complex stability and helps predict reactions and interactions in chemical environments.

Spectrochemical Series

The spectrochemical series is an ordered list of ligands arranged by their field strength. It helps in observing and predicting the crystal field splitting pattern in metal complexes. - The series typically starts with I⁻ as a weak field ligand, gradually moving to strong field ligands like CO. - This series includes various ligands such as CN⁻, NH₃, and H₂O, each with distinct properties affecting metal complexes differently. Understanding the spectrochemical series is vital in predicting the relative field strength of ligands. In turn, this prediction assists in comprehending the electronic structures and resultant properties of coordination compounds. By considering where a ligand falls within this series, one can better anticipate the effects it will have on changes in electronic and magnetic properties, as well as compound stability.