Problem 10 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following pairs of ions is colourless? (a) \(\mathrm{Ti}^{3+}, \mathrm{Cu}^{2+}\) (b) \(\mathrm{Sc}^{3+}, \mathrm{Zn}^{2+}\) (c) \(\mathrm{Co}^{2+}, \mathrm{Fe}^{3+}\) (d) \(\mathrm{Ni}^{2+}, \mathrm{V}^{3+}\)

Step-by-Step Solution

Answer

The colorless pair is \(\mathrm{Sc}^{3+}, \mathrm{Zn}^{2+}\).

Step 1: Understanding the Criteria for Color

Transition metal ions are colored due to d-d transitions. If an ion has no unpaired d electrons, it is typically colorless. Therefore, we need to find ions that have no d electrons or complete d orbitals.

Step 2: Analyzing Ion a: \(\mathrm{Ti}^{3+}, \mathrm{Cu}^{2+}\)

\(\mathrm{Ti}^{3+}\) has the electronic configuration \([\mathrm{Ar}] \, 3d^1\), so it has one unpaired d electron, making it colored. \(\mathrm{Cu}^{2+}\) has \([\mathrm{Ar}] \, 3d^9\), also resulting in color due to unpaired electrons.

Step 3: Analyzing Ion b: \(\mathrm{Sc}^{3+}, \mathrm{Zn}^{2+}\)

\(\mathrm{Sc}^{3+}\) has the electronic configuration \([\mathrm{Ar}]\), which means it has no d electrons, making it colorless. \(\mathrm{Zn}^{2+}\) has \([\mathrm{Ar}] \, 3d^{10}\), a complete d orbital with no unpaired electrons, also colorless.

Step 4: Analyzing Ion c: \(\mathrm{Co}^{2+}, \mathrm{Fe}^{3+}\)

\(\mathrm{Co}^{2+}\) with configuration \([\mathrm{Ar}] \, 3d^7\), has unpaired electrons and is colored. \(\mathrm{Fe}^{3+}\) has \([\mathrm{Ar}] \, 3d^5\), which also results in color due to d-d transitions.

Step 5: Analyzing Ion d: \(\mathrm{Ni}^{2+}, \mathrm{V}^{3+}\)

\(\mathrm{Ni}^{2+}\) has the electronic configuration \([\mathrm{Ar}] \, 3d^8\), leaving unpaired electrons making it colored. \(\mathrm{V}^{3+}\) has \([\mathrm{Ar}] \, 3d^2\), and is also colored.

Step 6: Conclusion

Based on the electron configurations, the pair \(\mathrm{Sc}^{3+}, \mathrm{Zn}^{2+}\) is colorless.

Key Concepts

d-d transitions

When discussing transition metal colors, the concept of d-d transitions is crucial. These transitions occur when electrons in d orbitals absorb light of specific wavelengths to move between different d orbitals. This absorption creates the vibrant colors we see. Transition metals have part-filled d orbitals, which allow these electronic jumps. Each transition metal exhibits unique absorption patterns based on its electronic configuration, giving rise to a variety of observable colors.

Essentially, the d-d transitions involve:

• Movement of electrons between split d orbitals.
• Absorption of light corresponding to those energy differences.
• The resulting perception of complementary colors as some light wavelengths are absorbed.

This fascinating process is foundational to the aesthetics of many compounds and a key point in understanding the colorful nature of transition metal ions.

unpaired d electrons

The presence of unpaired d electrons heavily influences the color of transition metal ions. Unpaired electrons allow for d-d transitions to happen, as these electrons can move if there are available empty d orbitals. This movement underlies the absorption of visible light.

When a transition metal ion has:

• Unpaired electrons: Results in colored ions due to light absorption in the d-d transitions.
• Paired or no d electrons: Potentially colorless, as no electron transitions occur.

Thus, by checking for unpaired d electrons, we can predict if an ion is likely to be colored or colorless.

electron configuration

Knowing the electron configuration of an ion helps to determine its color and properties. Electron configuration describes how electrons are distributed in an atom or ion's orbitals. For transition metals, the d orbital occupancy is particularly significant.

The basics of electron configuration in transition metals:

• The d subshell can hold up to 10 electrons.
• High-energy electrons absorb visible light, causing transitions.
• Each element's electron configuration provides information regarding possible d-d transitions.

By examining an ion's electron configuration, we can deduce the potential presence of unpaired d electrons, which informs us about its colors.

transition metal ions

Transition metal ions form when transition metals lose electrons to achieve a stable configuration. These ions are often colored due to the intricate nature of their d orbitals. Transition metals are characterized by their ability to form multiple oxidation states, which significantly impacts their color.

Important aspects include:

• Flexible d orbitals capable of various electron configurations.
• Presence of unpaired or paired d electrons affecting coloration.
• Variable oxidation states leading to different colors.

Transition metal ions are a captivating field of study due to this variability and their widespread real-world applications.

colorless ions

Some transition metal ions are colorless, primarily due to their electron configurations. If an ion has no d electrons or a completely filled d subshell, no d-d transitions can occur, rendering the ion colorless.

Characteristics of colorless ions:

• Lack of unpaired d electrons.
• Either empty or fully filled d orbitals.
• No absorptive d-d transitions possible.

A classic example is \(\mathrm{Sc}^{3+}\), which is colorless due to having no d electrons at all, and \(\mathrm{Zn}^{2+}\) with its full \(3d^{10}\) configuration, indicating complete d orbital filling. Exploring these instances helps illustrate why certain transition metal ions lack any visible color.