Problem 125 - A Complete Resource Book in Chemistry for JEE Main

Question

\(\mathrm{Ti}^{3+}(\mathrm{aq})\) is purple while \(\mathrm{Ti}^{4+}(\mathrm{aq})\) is colourless because (a) The difference between \(\mathrm{t}_{2 \mathrm{x}}\) and \(\mathrm{e}_{\mathrm{g}}\) of \(\mathrm{Ti}^{4+}\) is quite high and does not fall in visible region. (b) There is no crystal field effect in \(\mathrm{Ti}^{4+}\) (c) \(\mathrm{Ti}^{4+}\) has \(\mathrm{d}^{0}\) configuration. (d) \(\mathrm{Ti}^{4+}\) is very small ion than \(\mathrm{Ti}^{3+}\) and does not adsorb any radiation.

Step-by-Step Solution

Answer

Option (c): \(\mathrm{Ti}^{4+}\) has \(\mathrm{d}^0\) configuration.

Step 1: Understanding the Properties of Ions

The question concerns the properties of two ions: \(\mathrm{Ti}^{3+}\) and \(\mathrm{Ti}^{4+}\). In aqueous solutions, \(\mathrm{Ti}^{3+}\) appears purple, while \(\mathrm{Ti}^{4+}\) is colorless. This difference in color suggests differences in their electronic configurations or interactions with light.

Step 2: Examining the Electronic Configurations

\(\mathrm{Ti}^{3+}\) has a \(\mathrm{d}^1\) electronic configuration because it has one fewer electron than neutral titanium (with configuration \([\mathrm{Ar}] 3\mathrm{d}^2 4\mathrm{s}^2\)). \(\mathrm{Ti}^{4+}\), on the other hand, has a \(\mathrm{d}^0\) configuration, as it has lost four electrons from the neutral titanium's electron configuration.

Step 3: Color and Electronic Transition

The color observed in transition metal ions is due to electronic transitions between \(\mathrm{d}\)-orbitals of different energies, which falls within the visible region of electromagnetic spectrum. \(\mathrm{Ti}^{3+}\)'s \(\mathrm{d}^1\) configuration allows such transitions. In contrast, \(\mathrm{Ti}^{4+}\) with no electrons in the \(\mathrm{d}\)-orbitals (\(\mathrm{d}^0\) configuration) cannot exhibit these transitions.

Step 4: Evaluating the Answer Options

(a) relates to the crystal field splitting but is not directly connected to the absence of electrons in \(\mathrm{Ti}^{4+}\). (b) explains the lack of crystal field splitting due to \(\mathrm{d}^0\) configuration; this is consistent. (c) correctly identifies that \(\mathrm{Ti}^{4+}\) has a \(\mathrm{d}^0\) configuration, explaining its colorlessness. (d) mentions size and radiation absorption, but doesn't directly address the absence of \(\mathrm{d}\)-electrons.

Key Concepts

Crystal Field Theory

Crystal Field Theory is a vital concept to understand when dealing with transition metals, like titanium ions, as it helps explain the color properties observed in these compounds. This theory describes how the distribution of electrons in the vicinity of a transition metal ion is influenced by the surrounding electrons, particularly in ligands which are the molecules surrounding a central metal ion.

In simple terms, as ligands approach the central metal ion, they create an electric field (or a crystal field) which influences the energy of the metal's d-orbitals. These d-orbitals, which are normally degenerate (meaning they all have the same energy level), will split into higher and lower energy levels when under the influence of the field created by the ligands. This splitting results in what's known as crystal field splitting.

The degree of splitting varies with the nature of the ligands and the central metal ion. It is this split in d-orbitals that allows for the color seen in many transition metal complexes, as electrons can absorb visible light to move between these orbitals, forming what's known as a d-d transition.

Electron Configuration

Understanding electron configuration is key to explaining why some transition metal ions appear colored while others do not. Titanium, for instance, has the ground-state electron configuration of \( \text{[Ar]} 3d^2 4s^2 \), where all the electrons are distributed among the orbitals starting from the most inner core outwards.

When it comes to ions, electrons are removed according to the energy levels, starting with the outermost shell. For \( \text{Ti}^{3+} \), one electron has been removed, resulting in a \( d^1 \) configuration. This lone electron in the d-orbital allows for electronic transitions which interact with visible light, producing the purple color associated with \( \text{Ti}^{3+} \).

On the other hand, \( \text{Ti}^{4+} \) has lost a total of four electrons resulting in a \( d^0 \) configuration. With no electrons in the d-orbitals, there are no electrons available to transition, and thus, no color is produced, making the solution appear colorless.

d-Orbital Splitting

d-Orbital splitting is a crucial component to understanding the color properties of transition metal complexes under the framework of Crystal Field Theory. This phenomenon occurs when ligands approach and interact with the transition metal ion's d-orbitals, causing them to break apart energetically into subsets of differing energies.

Generally, these d-orbitals split into two sets: the \( t_{2g} \) (lower energy) and \( e_g \) (higher energy) orbitals. The splitting pattern and magnitude, known as the crystal field splitting parameter (Δ), depend on several factors:

• The type of ligands surrounding the metal ion; strong-field ligands cause greater splitting compared to weak-field ligands.
• The central metal’s oxidation state; higher oxidation states often lead to increased splitting.
• The geometry of the complex; for instance, octahedral and tetrahedral geometries lead to different splitting patterns.

For \( \text{Ti}^{3+} \), with its \( d^1 \) configuration, the presence of a single electron in the d-orbitals allows it to transition between these differing energy levels by absorbing visible light, bestowing color. \( \text{Ti}^{4+} \), lacking d-electrons, cannot support such transitions, resulting in no observable color.