Problem 20 - A Complete Resource Book in Chemistry for JEE Main

Question

Which one of the following ionic species will impart colour to an aqueous solution? (a) \(\mathrm{Cr}^{3+}\) (b) \(\mathrm{Cu}^{+}\) (c) \(\mathrm{Ti}^{4+}\) (d) \(\mathrm{Zn}^{2+}\)

Step-by-Step Solution

Answer

\( \mathrm{Cr}^{3+} \) imparts color to an aqueous solution.

Step 1: Understand the Question

Identify which ion among the given options will impart color to an aqueous solution. Color arises due to the presence of unpaired electrons in the d-orbitals of transition metals.

Step 2: Examine Ion \( \mathrm{Cr}^{3+} \)

Chromium(III) ion, \( \mathrm{Cr}^{3+} \), has an electronic configuration of \([\mathrm{Ar}] 3d^3\). This means it has unpaired electrons in the d-orbitals, which can absorb light and result in colored solutions.

Step 3: Examine Ion \( \mathrm{Cu}^{+} \)

Copper(I) ion, \( \mathrm{Cu}^{+} \), has an electronic configuration of \([\mathrm{Ar}] 3d^{10}\). With fully filled d-orbitals, there are no unpaired electrons, so it won't impart any color to the solution.

Step 4: Examine Ion \( \mathrm{Ti}^{4+} \)

Titanium(IV) ion, \( \mathrm{Ti}^{4+} \), has an electronic configuration of \([\mathrm{Ar}]\). It lacks d-electrons entirely, resulting in no unpaired electrons to absorb light and impart color.

Step 5: Examine Ion \( \mathrm{Zn}^{2+} \)

Zinc(II) ion, \( \mathrm{Zn}^{2+} \), has an electronic configuration of \([\mathrm{Ar}] 3d^{10}\). Similar to \( \mathrm{Cu}^{+} \), it has fully filled d-orbitals, meaning no unpaired electrons, and thus it will not impart color to the solution.

Step 6: Determine the Answer

Based on the analysis, \( \mathrm{Cr}^{3+} \) has unpaired electrons in its d-orbitals, allowing it to impart color to the solution through light absorption and d-d transitions.

Key Concepts

Unpaired Electrons

Unpaired electrons in transition metal ions play a crucial role in the chemistry of color. When electrons in the d-orbitals are not paired, they can transition between different energy levels when absorbing specific wavelengths of light. This absorption results in the complementary color being displayed, causing the solution to appear colored.
For example:

• A ion like \( \mathrm{Cr}^{3+} \) with a configuration of \( [\mathrm{Ar}] 3d^3 \) has three unpaired electrons, making it capable of absorbing visible light.
• Conversely, \( \mathrm{Cu}^{+} \) and \( \mathrm{Zn}^{2+} \) ions do not exhibit any unpaired electrons, as they have fully filled d-orbitals \( 3d^{10} \), thus being colorless.

In essence, the presence of unpaired electrons is essential for light absorption, which is a primary aspect of why some solutions appear colored while others remain clear.

d-Orbitals

The d-orbitals in transition metals are fundamental to understanding why these elements and their compounds can have diverse colors. Transition metals have d-orbitals that vary in energy, which allows electrons to move between these levels. This movement is called electronic transition.

• When light hits the ions, the photons can excite the unpaired d-electrons to higher energy levels.
• The energy difference between these levels determines the wavelength of light absorbed, which in turn impacts the color perceived.
• An even distribution of electrons across all the d-orbitals, as in \( \mathrm{Cu}^{+} \) or \( \mathrm{Zn}^{2+} \), implies no net absorption of visible light, hence no color.

Thus, the layout and occupancy of d-orbitals are central to color production in transition metal ions.

Color of Aqueous Solutions

Transition metal ions are often colorful in solutions due to their electron configuration. Solutions containing these ions absorb certain wavelengths of light corresponding to electronic transitions within the d-orbitals.
For instance:

• In an ion like \( \mathrm{Cr}^{3+} \), the absorption of certain wavelengths due to transitions of unpaired electrons in the d-orbitals respectively results in a complementary color being reflected and seen.
• On the contrary, ions such as \( \mathrm{Ti}^{4+} \), which have no d-electrons, absorption does not occur at visible wavelengths, leading to clear solutions.

This process explains why some solutions appear blue, red, green, etc., based on the specific wavelengths of visible light absorbed. Understanding the behavior of d-orbitals in transition metal ions allows us to predict and explain the color of different aqueous solutions.