Problem 55 - A Complete Resource Book in Chemistry for JEE Main

Question

Cuprous ion is colourless, while cupric ion is coloured, because (a) cuprous ion has incomplete d orbital and cupric ion has a complete \(\mathrm{d}\) orbital (b) cuprous ion has a complete d orbital and cupric ion has incomplete d orbital (c) cuprous ion has half filled d orbital (d) cupric ion has unpaired electrons in d orbital

Step-by-Step Solution

Answer

(b) Cuprous ion has a complete d orbital and cupric ion has an incomplete d orbital.

Step 1: Understand the Electron Configuration

Cuprous ion is denoted as \( ext{Cu}^+ \) and cupric ion as \( ext{Cu}^{2+} \). Copper's atomic number is 29, so the electron configuration of neutral copper is \( [ ext{Ar}] ext{4s}^1 ext{3d}^{10} \). For \( ext{Cu}^+ \), an electron is removed from the \( 4s \) orbital, resulting in \( [ ext{Ar}] ext{3d}^{10} \). For \( ext{Cu}^{2+} \), an additional electron is removed from the \( 3d \) orbital, leading to \( [ ext{Ar}] ext{3d}^9 \).

Step 2: Analyze Cuprous Ion

The \( ext{Cu}^+ \) ion has a fully filled \( 3d \) orbital with the electron configuration \( ext{3d}^{10} \). Fully filled \( d \)-orbitals are generally more stable and do not absorb visible light significantly, hence making the ion colorless.

Step 3: Analyze Cupric Ion

The \( ext{Cu}^{2+} \) ion has an electron configuration of \( ext{3d}^9 \), which means it has an incomplete \( d \) orbital. This incomplete \( d \)-orbital leads to the presence of unpaired electrons. Unpaired electrons can undergo electronic transitions that absorb certain wavelengths of visible light, making the ion appear colored.

Step 4: Evaluate the Statements

(a) is incorrect because it's the opposite of the correct configuration. (b) is correct: \( ext{Cu}^+ \) has a complete \( d \) orbital, and \( ext{Cu}^{2+} \) has an incomplete one. (c) is incorrect since \( ext{Cu}^+ \) has a fully filled \( d \) orbital. (d) supports \( ext{Cu}^{2+} \)'s color but does not address \( ext{Cu}^+ \).

Step 5: Conclusion

Based on the analysis, the correct choice is (b): Cuprous ion has a complete \( d \) orbital, and cupric ion has an incomplete \( d \) orbital.

Key Concepts

Cuprous Ion

Cuprous ion, represented as \( \text{Cu}^+ \), plays a key role in the color properties of copper compounds. To understand its characteristics, we begin with the electron configuration of neutral copper, which is \([\text{Ar}] 4s^1 3d^{10}\). When copper loses one electron to form the cuprous ion, the electron is removed from the \( 4s \) orbital. Hence, the electron configuration for the cuprous ion becomes \([\text{Ar}] 3d^{10}\).

This configuration corresponds to a fully filled \( d \)-orbital, known for its stability. A filled \( d \)-orbital minimizes the interaction with visible light, which is why cuprous ions usually do not exhibit color. As they do not absorb visible light, they appear colorless to our eyes.

Cupric Ion

The cupric ion, denoted as \( \text{Cu}^{2+} \), is another significant copper ion revealing the link between electron configuration and color. For forming a cupric ion, copper loses two electrons: one from the \( 4s \) orbital and another from the \( 3d \) orbital. Therefore, the electron configuration of cupric ion becomes \([\text{Ar}] 3d^9\).

Having a partially filled \( 3d \) orbital means there are unpaired electrons present. These unpaired electrons can transition between different energy levels within the \( 3d \) orbital, absorbing certain wavelengths of visible light. As these specific wavelengths are absorbed, the light that is transmitted or reflected gives the cupric ion its characteristic color. This ability of unpaired electrons to absorb and react to light makes \( \text{Cu}^{2+} \) ions visually detectable as colored.

d-Orbital Transitions

The concept of \( d \)-orbital transitions is fundamental to understanding the color of transition metal ions. In transition metals like copper, \( d \)-orbitals are not completely filled, allowing electrons to move or "jump" between different energy levels within the \( d \)-orbitals. This movement is termed as \( d \)-d transitions.

When light hits these electrons, they absorb energy and transition to higher energy \( d \)-orbitals. The most interesting aspect is that these transitions absorb light from specific parts of the visible spectrum. The wavelength of light absorbed determines the color that will be observable to us. The light energy not absorbed is what is reflected or transmitted, giving the metal ion its color.

Color of Ions

The color exhibited by ions, especially those of transition metals, is directly linked to the arrangement and transitions of electrons in their \( d \)-orbitals. The absorption of light due to these transitions often results in a vibrant display of colors. For instance, \( \text{Cu}^+ \) ions appear colorless as they do not have \( d \)-orbital transitions. In contrast, \( \text{Cu}^{2+} \) ions exhibit a blue-green color because their incomplete \( d \)-orbitals lead to such transitions.

Several factors affect the exact hue including:

• Oxidation state of the ion: Determines electron arrangement.
• Ligand field surrounding the ion: Changes the energy gap between \( d \)-orbitals.
• Nature of the metal ion itself: Defines the possible energy levels.

Understanding the origin of these colors helps in various scientific applications, such as in the creation of pigments and in analytical chemistry to infer the presence of specific ions.