Problem 22 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

The complex that has highest crystal field splitting energy \((\Delta)\) is: (a) \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5}\left(\mathrm{H}_{2} \mathrm{O}\right)\right] \mathrm{Cl}_{3}\) (b) \(\mathrm{K}_{2}\left[\mathrm{CoCl}_{4}\right]\) (c) \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{Cl}\right] \mathrm{Cl}_{2}\) (d) \(\mathrm{K}_{3}\left[\mathrm{Co}(\mathrm{CN})_{6}\right]\)

Step-by-Step Solution

Answer

Complex (d) \( \mathrm{K}_{3}\left[\mathrm{Co}( \mathrm{CN})_{6}\right] \) has the highest crystal field splitting energy.

Step 1: Understand Crystal Field Splitting

Crystal Field Splitting Energy (\( \Delta \)) is influenced by the ligand attached to the metal ion. Strong ligands cause a large splitting of the d-orbitals, leading to a higher \( \Delta \). Ligands like \( \mathrm{CN}^- \) produce larger split compared to \( \mathrm{H_2O} \) and \( \mathrm{Cl}^-\).

Step 2: Analyze Ligands of Each Complex

- For complex (a) \( \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5}\left(\mathrm{H}_{2}\mathrm{O}\right)\right] \mathrm{Cl}_{3} \), ammonia \( \mathrm{NH}_3 \) is a moderate field ligand and water \( \mathrm{H_2O} \) is a weaker ligand.- In complex (b) \( \mathrm{K}_{2}\left[\mathrm{CoCl}_{4}\right] \), \( \mathrm{Cl}^- \) is a weak field ligand.- For complex (c) \( \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{Cl}\right] \mathrm{Cl}_{2} \), both \( \mathrm{NH}_3 \) and \( \mathrm{Cl}^- \) are moderate and weak field ligands, respectively.- In complex (d) \( \mathrm{K}_{3}\left[\mathrm{Co}(\mathrm{CN})_{6}\right] \), \( \mathrm{CN}^- \) is a strong field ligand.

Step 3: Determine Highest Crystal Field Splitting

Among all the given complexes, \( \mathrm{K}_{3}\left[\mathrm{Co}(\mathrm{CN})_{6}\right] \) contains the strongest ligand \( \mathrm{CN}^- \). This makes the crystal field splitting energy \( \Delta \) the highest for complex (d) as compared to other complexes with weaker ligands.

Key Concepts

Crystal Field Splitting Energy

Crystal Field Splitting Energy, often represented by the symbol \( \Delta \), is a crucial concept in coordination chemistry. It explains how the presence of ligands surrounding a metal ion can affect the energy levels of the d-orbitals.
When ligands approach a metal ion, the electrostatic interactions cause the d-orbitals to split into higher and lower energy levels. The difference in energy between these levels is what we call the Crystal Field Splitting Energy.

• Stronger ligands create a larger energy gap, resulting in a high value of \( \Delta \).
• Weaker ligands cause a smaller energy gap, giving a lower \( \Delta \).

Understanding \( \Delta \) is key to predicting properties like color or magnetic behavior of complexes.
Next time you see a coordination complex, try identifying its ligands to estimate its Crystal Field Splitting Energy.

Strong field ligands

Strong field ligands are ligands that cause significant splitting in the d-orbitals of a metal ion. The strength of a ligand field depends on its electronic properties and can have a dramatic effect on the properties of a coordination complex.
Common strong field ligands include:

• Cyanide (\( \mathrm{CN}^- \))
• Ammonia (\( \mathrm{NH}_3 \))
• Carbon monoxide (\( \mathrm{CO} \))

These ligands typically form low-spin complexes where electrons favor lower energy orbitals first, even if it means pairing up. This electron configuration minimizes electron repulsion and leads to higher stability for the complex.
For instance, in our original problem, the ligand \( \mathrm{CN}^- \) in \( \mathrm{K}_3\left[\mathrm{Co}(olinebreak\mathrm{CN})_6\right] \) creates a stronger field than \( \mathrm{H}_2\mathrm{O} \) or \( \mathrm{Cl}^- \), resulting in a higher collapse of the d-orbitals.

Coordination complexes

Coordination complexes are fascinating entities where a central metal atom or ion is surrounded by a set of molecules or ions known as ligands. These can form intricate structures with a wide variety of properties.
The key characteristics of coordination complexes include:

• The central metal, typically a transition metal, acts as a Lewis acid, accepting electron pairs from the ligands.
• Ligands, like \( \mathrm{NH}_3 \) or \( \mathrm{H_2O} \), function as Lewis bases, donating electron pairs to the metal.
• The number of coordinated ligands is called the coordination number, and it influences the geometry of the complex.

Understanding these structures helps us predict their reactivity, magnetic properties, and color. For example, the color of a complex is often related to the value of \( \Delta \) - complexes with larger crystal field splitting absorb at different wavelengths compared to those with smaller splitting.
Coordination complexes play an essential role in numerous areas such as material science, catalysis, and biological systems.