Problem 81 - A Complete Resource Book in Chemistry for JEE Main

Question

An aqueous solution of \(\left[\mathrm{Ti}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}\) ion has a mild violet colour of low intensity. Which of the following statements is incorrect? (a) The colour results from an electronic transition of one electron from the \(t_{2}\) to an \(\mathrm{e}_{e}\) orbital (b) The ion absorbs visible light in the region of \(\sim 5000 \AA\) (c) The transition is the result of metal-ligand back bonding (d) The low colour intensity is because of a low probability of transition

Step-by-Step Solution

Answer

Statement (c) is incorrect.

Step 1: Understanding the problem

We need to identify the incorrect statement about the origin of the color of the aqueous solution of \([\mathrm{Ti}(\mathrm{H}_{2}\mathrm{O})_{6}]^{3+}\). The color originates from electronic transitions within the d-orbitals of the metal ion.

Step 1: Analyze Statement (a)

Statement (a) suggests that the color is due to an electronic transition from a \(t_{2g}\) to an \(e_{g}\) orbital. This is typical for transition metal complexes where d-d transitions occur, which can cause color. Therefore, statement (a) appears correct.

Step 2: Evaluate Statement (b)

Statement (b) claims the ion absorbs light around \(5000 \ \text{Å}\) (500 nm). Light of this wavelength is indeed in the visible spectrum, and absorption in this region would contribute to a color (like violet), so statement (b) appears to be correct.

Step 3: Assess Statement (c)

Statement (c) states that the transition is due to metal-ligand back bonding. Typically, color in transition metal complexes like \([\mathrm{Ti}(\mathrm{H}_{2}\mathrm{O})_{6}]^{3+}\) is due to d-d transitions, not back bonding, which usually applies to systems where ligands possess lone pairs that can donate to metal vacant d orbitals. Hence, statement (c) seems incorrect.

Step 4: Check Statement (d)

Statement (d) suggests that the low color intensity is due to a low probability of transition. This is generally true for d-d transitions in centrosymmetric complexes, which have low allowedness. Therefore, statement (d) is correct.

Key Concepts

d-d electronic transitions

In transition metal complexes, d-d electronic transitions refer to the movement of electrons between d-orbitals, which are degenerate in the absence of a ligand but split in the presence of a ligand due to the crystal field effect. When these electrons move from a lower-energy d-orbital (t2g) to a higher-energy d-orbital (eg), energy is absorbed. This energy absorption occurs in the visible region, and the specific wavelength absorbed determines the color we perceive.

• The most common d-d transitions involve shifts between t2g and eg orbitals.
• Electronic transitions in metal complexes can be detected using techniques such as UV-Vis spectroscopy, which measures the absorption of light.
• d-d transitions are typically weak due to their dependence on parity conservation leading to low absorptivity.

Understanding d-d transitions is crucial for predicting and interpreting the colors of metal complexes in various contexts.

color of metal complexes

The color of metal complexes arises from the electronic transitions that occur within the metal center, particularly within its d-orbitals. When these complexes absorb light, electrons are promoted to higher energy levels; the light absorbed corresponds to specific wavelengths, and the color perceived is the complementary color of the absorbed light.

For example, a solution of \([\text{Ti}(\text{H}_{2}\text{O})_{6}]^{3+}\) appears violet because it absorbs light in the yellow-green region of the spectrum (about 500 nm). The absorbed light is subtracted from the full spectrum seen by the human eye, resulting in the complementary color: violet.

• Each metal complex has a unique absorption spectrum based on its ligand field and d-orbital separation.
• Factors influencing color include oxidation state of the metal, nature of ligands, and the geometric arrangement of ligands.
• Color intensity is affected by the probability of electronic transitions, often moderated by the symmetry of the complex.

The study of colors in metal complexes overlaps with fields like chemistry, materials science, and art, showcasing the intersection of aesthetics and science.

ligand field theory

Ligand Field Theory (LFT) extends Crystal Field Theory by taking into account orbital overlap between metal d-orbitals and ligand orbitals. It provides a framework for understanding the electronic structure, color, magnetism, and reactivity of metal complexes.

LFT suggests that ligands around a metal ion influence the energy levels of the d-orbitals, causing them to split into different energy sublevels. This splitting creates the phenomenon known as "crystal field splitting".

• The magnitude of the splitting, denoted as \(\Delta\), depends on the strength of the field created by the ligands.
• Strong field ligands will result in a large \(\Delta\), potentially leading to low-spin complexes where electrons pair in the lower energy orbitals.
• Weak field ligands cause a smaller \(\Delta\), which may lead to high-spin complexes, where electrons occupy higher energy orbitals to minimize electron pairing.

Understanding ligand field theory helps chemists design complexes with desirable properties for various applications, including catalysis, biological systems, and material science.