Problem 125 - 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 \(\mathrm{t}_{2 \mathrm{~g}} \rightleftharpoons \mathrm{e}_{8}\) are responsible for colours of the co- ordination compounds \(\mathrm{Ti}^{3+}(\mathrm{aq})\) is purple while \(\mathrm{Ti}^{4+}(\mathrm{aq})\) is colourless because (a) The difference between \(\mathrm{t}_{2 \mathrm{~g}}\) and \(\mathrm{e}_{\mathrm{g}}\) of \(\mathrm{T} \mathrm{i}^{4+}\) 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

The answer is (c): Ti⁴⁺ has a d⁰ configuration.

Step 1: Understanding d-orbital splitting

In an octahedral complex, the d-orbitals split into two energy levels: the lower energy level, called t2g, and the higher energy level, called eg. This splitting occurs due to the interaction of the d-orbitals with the electric field created by surrounding ligands.

Step 2: Determine the Electronic Configurations

Titanium exists in two common oxidation states: Ti³⁺ and Ti⁴⁺. For Ti³⁺, which is d¹, a single electron occupies one of the t2g orbitals. For Ti⁴⁺, which is d⁰, there are no d-electrons present.

Step 3: Analyze Color Based on Electron Transition

Ti³⁺, having an electron in t2g, can absorb visible light causing an electron to be excited to the higher eg level which results in colored compounds. Ti⁴⁺, with no d-electrons, cannot experience any d-d electron transition that leads to color formation, and thus appears colorless.

Step 4: Evaluate the Correct Explanation

Review the options provided. The correct reason for the colorlessness of Ti⁴⁺ is that it has a d⁰ configuration (option (c)), meaning there are no d-electrons available for d-d transitions that result in color.

Key Concepts

d-orbital Splitting

When transition metals form complexes, their d-orbitals split into distinct energy levels. In an octahedral complex, this splitting results in two sets of orbitals:

• Lower energy orbitals (t_2g): These are comprised of the d_xy, d_yz, and d_zx orbitals.
• Higher energy orbitals (e_g): These include the d_x²-y² and d_z² orbitals.

This energy difference, known as the crystal field splitting, affects the color and stability of coordination compounds. The magnitude of this splitting is influenced by the type and arrangement of ligands around the metal ion.
Whenever this energy difference falls within the visible region of the electromagnetic spectrum, it can result in electronic transitions that cause the compound to exhibit color.

Ligand Field Theory

Ligand Field Theory (LFT) is an extension of Crystal Field Theory (CFT), offering a more nuanced understanding of bonding in coordination compounds. It considers the effect of ligands as impacted by the metal's electrons and their molecular orbitals.

• LFT uses the concept of molecular orbitals to explain the splitting of the d-orbitals.
• It accounts for both the repulsive and attractive forces that occur between the metal ion and the ligands.

This theory helps explain why different ligands result in different magnitudes of d-orbital splitting. Strong field ligands, like CN⁻ and NH₃, cause greater splitting, whereas weak field ligands like I⁻ and Br⁻ induce lesser splitting.
LFT is crucial for explaining why similar transition metal ions exhibit different colors and properties depending on the ligands attached.

Electronic Transitions

Electronic transitions refer to the movement of electrons between different energy levels within the d-orbitals. In coordination chemistry, this primarily involves transitions between the t_2g and e_g orbitals. When light hits a coordination compound, an electron may absorb energy to move from a lower-energy t_2g orbital to a higher-energy e_g orbital. This process results in absorption of certain wavelengths of light, and the complementary color is observed in the compound. In the case of Ti³⁺, the d¹ configuration allows for such d-d transitions. The electron in the t_2g orbital can absorb visible light and jump to the e_g orbital, resulting in a colored appearance, often purple. Ti⁴⁺, being d⁰, lacks electrons for such transitions and thus appears colorless.

Octahedral Complex

An octahedral complex is a type of coordination compound where a central metal ion is surrounded by six ligands positioned at the corners of an imaginary octahedron. This is a common geometric arrangement for coordination compounds.

• In octahedral geometry, ligands approach the metal along the x, y, and z axes, causing a particular d-orbital splitting pattern.
• This arrangement plays a significant role in determining the magnetic and spectral properties of the complex.

The interaction between metal d-electrons and the ligands' field results in a specific energy level pattern, splitting the d-orbitals into t_2g and e_g sets.
Understanding octahedral complexes is fundamental for studying transition metal chemistry, as it dictates both the color and reactivity of many coordination compounds.

Oxidation States

Oxidation states describe the degree of oxidation of an atom in a chemical compound. For transition metals, different oxidation states can dramatically alter their physical and chemical properties.

• Titanium commonly presents in oxidation states of +3 and +4.
• The oxidation state impacts the electron configuration, affecting whether there are d-electrons available for transitions.
• In Ti³⁺, d¹, an electron is available for d-d transitions, resulting in visible color.
• Conversely, Ti⁴⁺ has a d⁰ configuration, lacking electrons for d-d transitions, thus appears colorless.

Recognizing oxidation states is crucial for predicting the behavior of metal ions in complexes and their potential electronic transitions.

Coordination Compounds

Coordination compounds consist of a central metal atom or ion bonded to surrounding molecules or ions, termed ligands. These compounds are pivotal in inorganic chemistry due to their diverse structures and chemical reactivity.

• Nature of the metal center and ligands significantly influence the chemical properties of the complex.
• Coordination complexes can serve various functions, such as catalysts, pigments, and in biological systems.

The metal-ligand bonding and the resulting geometric arrangements determine the compound's physical attributes, including color, magnetism, and reactivity.
Studying coordination compounds reveals the intricate balance between ligands' effects and metal ion behavior, providing insight into the broader field of chemistry.