Problem 56 - General Chemistry: Principles and Modern Applications

Question

Explain why aqueous solutions of \(\left[\operatorname{Sc}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right] \mathrm{Cl}_{3}\) and \(\left.\mathrm{Zn}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}\right] \mathrm{Cl}_{2}\) are colorless, but an aqueous solution of \(\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right] \mathrm{Cl}_{3}\) is not.

Step-by-Step Solution

Answer

Scandium and Zinc complexes are colorless because there are no unpaired d electrons in their complexes, so 'd-d' transitions are not possible. However, the Iron complex has unpaired d electrons, so these transitions can occur, and the complex can absorb wavelengths within the visible light range, which gives it a color.

Step 1: Understanding Scandium Complex

For the Scandium complex, Sc\[ \left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\] Cl_{3}, consider the atomic number of scandium, which is 21. Its electron configuration ends in 3d1 4s2. When the Scandium ion is formed (Sc^3+), the 3d and 4s electrons are lost, leaving no unpaired d electrons. Therefore, there cannot be any 'd-d' transition. As a result, the Scandium complex is colorless.

Step 2: Understanding Zinc Complex

For the Zinc complex, Zn\[ \left(\mathrm{H}_{2} \mathrm{O}\right)_{4}\] Cl_{2}, the atomic number of zinc is 30, and its electron configuration ends in 3d10 4s2. When the Zinc ion is formed (Zn^2+), the 4s electrons are lost, with the 3d10 orbital completely filled. Again, as there are no unpaired d electrons, there can't be any 'd-d' transitions. Therefore, the Zinc complex is also colorless.

Step 3: Understanding Iron Complex

In the case of the Iron complex, Fe\[ \left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\] Cl_{3}, Iron has an atomic number of 26, with electron configuration ending in 3d6 4s2. When the Iron ion (Fe^3+) is formed, it loses the 3d and 4s electrons, leaving five in the 3d orbital. This means there are unpaired electrons, and as a result, 'd-d' transitions are possible. Therefore, the Iron complex can absorb certain wavelengths within the visible light range, giving it color.

Key Concepts

d-d transitions

When discussing the colors of transition metal complexes, 'd-d transitions' are often key players. These transitions involve the movement of electrons between the d orbitals of a metal ion. In a complex, such as those surrounding a transition metal, the d orbitals do not all have the same energy.
The incoming ligands, such as water molecules, cause an energy split among these d orbitals.
Whenever a complex absorbs light, if it has unpaired d electrons, these electrons can jump from a lower energy d orbital to a higher energy d orbital.

• This movement creates what's known as a 'd-d transition'.
• During this process, specific colors from white light are absorbed.
• The color you see is the remaining light that is reflected or transmitted after absorption.

A lack of unpaired d electrons, as seen in complexes like Scandium and Zinc, means no 'd-d transitions' can occur, leaving the solutions colorless.

Unpaired d electrons

Unpaired d electrons are crucial for imparting color to transition metal complexes. These electrons refer to those in the d orbital that do not have a pair.
In transition metal ions, if any unpaired d electrons exist, they increase the chance of those 'd-d transitions' we talked about.
When examining complexes:

• Complexes with only paired d electrons can't undergo 'd-d transitions'.
• This is because all available d electrons are already paired, leaving no room for movement.
• Without these transitions, the metal complex won't absorb visible light effectively and thus won't show color.

Thus, the presence or absence of these unpaired electrons plays a pivotal role in why some metal complexes are vividly colored while others remain colorless.

Electron configuration

Electron configuration is the arrangement of electrons in an atom's orbitals, playing a significant role in determining the color of a metal complex.
By learning the electron configuration of a metal ion, we can predict the number of unpaired electrons and the likelihood of 'd-d transitions'.
Here’s how it works for some common ions:

• Scandium loses all its outer electrons becoming Sc³⁺. This leaves it with no d electrons at all, hence no 'd-d transitions'.
• Zinc forms the Zn²⁺ ion by losing its 4s electrons. It has a fully filled 3d10 configuration, with no unpaired electrons.
• Iron, when in Fe³⁺ form, loses some 3d and 4s electrons, leaving unpaired electrons in the d orbitals.

These examples illustrate how the specific electron configuration of each ion decides the visible properties like color.