Problem 127 - A Complete Resource Book in Chemistry for JEE Main

Question

When degenerate d-orbitals of an isolated atom/ion are brought under the impact of magnetic field of ligands, the degeneracy is lost. The two newly formed sets of d-orbitals, depending upon nature and magnetic field of ligands are either stabilized or destabilized. The energy difference between the two sets whenever lies in the visible region of the electromagnetic spectrum, then the electronic transition \(\mathrm{t}_{2 \mathrm{~g}} \rightleftharpoons \mathrm{e}_{\mathrm{g}}\) are responsible for colours of the co-ordination compounds Which of following complex ions will be coloured in aqueous state? (a) \(\left[\mathrm{Ni}(\mathrm{CN})_{4}\right]^{2-}\) (b) \(\left[\mathrm{Ni}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) (c) \(\left[\mathrm{Sc}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}\) (d) Both (b) and (c)

Step-by-Step Solution

Answer

(b) \([\mathrm{Ni}(\mathrm{H}_2 \mathrm{O})_6]^{2+}\) is colored.

Step 1: Understanding the Color Origin in Coordination Compounds

In coordination compounds, the d-orbitals of transition metal ions are split into two groups in the presence of ligands. This splitting is known as crystal field splitting. The transition of electrons between these orbitals causes absorption of specific wavelengths of light, leading to the appearance of color in compounds.

Step 2: Crystal Field Explanation for \([\mathrm{Ni}({\mathrm{CN}})_{4}]^{2-}\)

\([\mathrm{Ni}({\mathrm{CN}})_{4}]^{2-}\) is a square planar complex of Nickel(II). Cyanide \((\mathrm{CN}^-\)) is a strong field ligand, leading to a significant increase in crystal field splitting energy, which may fall outside the visible range, potentially leading to a colorless appearance. Additionally, square planar complexes often have their energy levels completely filled, especially for \(d^8\) systems, limiting color generation due to lack of available electron transitions.

Step 3: Crystal Field Explanation for \([\mathrm{Ni}(\mathrm{H}_2 \mathrm{O})_6]^{2+}\)

\([\mathrm{Ni}(\mathrm{H}_2 \mathrm{O})_6]^{2+}\) is an octahedral complex. Water is a weaker field ligand compared to cyanide, resulting in smaller splitting of d-orbitals. This splitting in the visible range allows for \(t_{2g} \to e_g\) transitions, causing the complex to be colored because the transition can absorb visible light.

Step 4: Crystal Field Explanation for \([\mathrm{Sc}(\mathrm{H}_2 \mathrm{O})_6]^{3+}\)

Scandium in \([\mathrm{Sc}(\mathrm{H}_2 \mathrm{O})_6]^{3+}\) has an electronic configuration of \([\mathrm{Ar}]3d^0\). This means it lacks any electrons in the d-orbitals to undergo transitions, hence cannot absorb visible light to exhibit color. Consequently, the complex is colorless.

Step 5: Determining the Colored Complexes

From the analysis, \([\mathrm{Ni}({\mathrm{H}_2 \mathrm{O})_6}]^{2+}\) will appear colored due to its ability to absorb visible light, while \([\mathrm{Ni}({\mathrm{CN})_4}]^{2-}\) and \([\mathrm{Sc}({\mathrm{H}_2 \mathrm{O})_6}]^{3+}\) will appear colorless due to reasons explained above.

Key Concepts

Crystal Field Splitting

In coordination chemistry, crystal field splitting describes how the presence of ligands affects the energy of d-orbitals in transition metals. When ligands approach a transition metal ion, the d-orbitals experience a change in energy due to the electrostatic field created by the ligands. This interaction results in a specific pattern of energy levels being created, splitting the otherwise degenerate (equal-energy) d-orbitals into multiple levels.The pattern of splitting depends on the arrangement and type of ligands surrounding the metal ion. For example:

• Octahedral complexes result in a splitting into two sets: \(t_{2g}\) and \(e_g\), with \(t_{2g}\) being lower in energy.
• In a square planar geometry, further splitting occurs, often leading to a large energy gap.

The amount of energy difference due to this splitting is termed the "crystal field splitting energy," denoted \(\Delta\). Whether this energy difference falls within the visible spectrum determines if the complex will appear colored.

d-Orbital Splitting

The split in d-orbitals is essential for understanding why transition metal complexes can be colorful. The specific distributions in splitting, influenced by geometric arrangements and ligand types, create a unique energy difference between the higher and lower sets of d-orbitals. When electrons transition between these orbitals, it requires an absorption of energy that corresponds to light within a specific range of the electromagnetic spectrum. If this energy falls in the visible range, the compound will exhibit color. For instance:

• In octahedral complexes, water as a ligand leads to a smaller splitting energy, typically within the visible range, making these complexes often appear colored.
• Strong field ligands like cyanide cause larger splitting, which might fall outside the visible range, potentially resulting in a colorless appearance.

This understanding can help predict and explain the colors of various transition metal complexes.

Transition Metal Complexes

Transition metal complexes are compounds consisting of a central metal atom bonded to surrounding molecules or ions, known as ligands. These metals commonly have partially filled d-orbitals, which are essential for a variety of chemical behaviors, including the potential for exhibiting vivid colors.The ligands influence the metal's d-orbitals, causing splitting of energies as explained by crystal field theory. This interaction is crucial in understanding why transition metal complexes can be colorful or colorless.In addition:

• The type and strength of the ligand's field strongly dictate the extent and type of splitting.
• Transition metals are not only known for their colors but also for their diverse catalytic properties.

For example, a complex like \( \left[ \text{Ni(CN)}_4 \right]^{2-}\) can be clear due to the complete filling of d-orbitals, leaving no room for electronic transitions in the visible spectrum.

Coordination Chemistry

Coordination chemistry focuses on the study of complex structures formed between metal ions and ligands. These coordination complexes are fundamental for numerous chemical processes and technologies. They are characterized by the coordination number, which is the total number of bonds formed between the metal and ligands.This field studies:

• How ligands impact the electronic structure and energy levels of the metal center.
• How the geometry of these complexes, such as tetrahedral, square planar, or octahedral arrangements, influences properties like magnetism and color.
• The kinetics and thermodynamics of substitution reactions involving ligands.

A practical understanding of coordination chemistry is vital for industries ranging from catalysis to material science. Specific cases, like \(\left[ \text{Ni}(\text{H}_2\text{O})_6 \right]^{2+}\), demonstrate how ligand-induced energetics can lead to beautiful colored solutions due to visible light absorption.