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 \(\mathrm{t}_{2 \mathrm{R}}\) to an \(\mathrm{e}_{\mathrm{g}}\) 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 are given a transition metal complex \([\mathrm{Ti}(\mathrm{H}_{2}\mathrm{O})_{6}]^{3+}\) that has a violet color of low intensity and need to find out which statement about it is incorrect.

Step 2: Evaluating Statement (a)

Statement (a) suggests that the violet color results from an electronic transition of one electron from the \(\mathrm{t}_{2\mathrm{g}}\) to an \(\mathrm{e}_{\mathrm{g}}\) orbital. This is typical for transition metal complexes due to \(d-d\) transitions, which is correct.

Step 3: Evaluating Statement (b)

Statement (b) mentions the ion absorbs visible light around \(~ 5000 \AA\), or 500 nm, which corresponds to the green region of the visible spectrum. Absorbing green light means the observed color would be violet, which aligns with the information given, so this statement is correct.

Step 4: Evaluating Statement (c)

Statement (c) claims the transition is due to metal-ligand back bonding. Metal-ligand back bonding is not commonly associated with \(d-d\) transitions that cause the color in aqueous transition metal complexes. Therefore, this statement is incorrect.

Step 5: Evaluating Statement (d)

Statement (d) asserts that the low color intensity is due to a low probability of transition. \(d-d\) transitions in octahedral complexes have low transition probabilities (Laporte forbidden), making this statement correct.

Key Concepts

Electronic Transition

In transition metal complexes, the term "electronic transition" refers to the movement of an electron between different d-orbitals, such as from a lower energy t2g orbital to a higher energy eg orbital. This process is responsible for the distinct colors observed in many coordination compounds. The transition involves a change in the spatial distribution of electrons, which can affect both the electronic and geometric properties of the complex.

• Electronic transitions are usually caused by the absorption of visible light.
• The energy needed for this transition corresponds to the difference in energy between the involved orbitals.
• The specific wavelengths absorbed determine the color observed, which is the complementary color of the light absorbed.

Understanding how electronic transitions contribute to observed colors helps in identifying the specific chemistry of the transition metal complex and its potential applications in pigments and dyes.

Visible Light Absorption

Visible light absorption is a fundamental concept explaining why transition metal complexes often exhibit vivid colors. In the context of these complexes, when light falls upon them, electrons can absorb certain parts of the light spectrum to jump to higher energy orbitals.

• The wavelength of light absorbed determines the color we perceive.
• A complex that absorbs light in the green region (500 nm) appears violet, as violet is the complementary color of green.
• This absorption of visible light is closely related to the electronic configuration of the metal center and its ligands.

The exact nature of the light absorbed provides insight into the energy differences between d-orbitals, allowing chemists to understand the electronic nature of the complex.

d-d Transitions

d-d transitions are a type of electronic transition that occur within the d-orbitals of transition metal ions. These transitions are unique to transition metals due to their partially filled d-orbitals.

• These transitions involve an electron moving from one d-orbital to another, typically involving a small change in energy.
• Not all d-d transitions are equally probable; those violating selection rules are less intense.
• The Laporte rule, which states that d-d transitions are forbidden, contributes to their low intensity, leading to the pale colors of many transition metal solutions.

Despite these restrictions, d-d transitions remain a powerful tool for understanding the properties and behaviors of transition metal complexes in various environments.

Metal-Ligand Back Bonding

Metal-ligand back bonding refers to a situation where there is a donation of electron density from a filled metal orbital back into an empty ligand orbital. This concept is crucial in the chemistry of metal complexes but is not typically responsible for the colors seen in these complexes, especially in aqueous solutions.

• Back bonding can stabilize certain metal-ligand combinations, especially where ligands have empty \(\pi\) orbitals.
• It's mostly observed in complexes with ligands such as CO or PR3, which can accept electron density.
• In the context of an aqueous solution like \([\text{Ti}( ext{H}_2 ext{O})_6]^{3+}\), back bonding does not play a significant role in the electronic transitions causing color.

Understanding when metal-ligand back bonding is involved helps in predicting the properties of different complexes and their reactivity in various chemical environments.