Question

Compounds containing the \(\mathrm{Sc}^{3+}\) ion are colorless, whereas those containing the \(\mathrm{Ti}^{3+}\) ion are colored. Explain.

Short answer

Compounds with \\(\mathrm{Sc}^{3+}\\) are colorless due to an empty \\(3d\\) orbital, while \\(\mathrm{Ti}^{3+}\\) compounds are colored due to electron transitions in the \\(3d\\) orbital.

Step-by-step solution

Understanding Ion Electron Configuration

Begin by determining the electronic configurations of the ions involved. Scandium (Sc) has an atomic number of 21, meaning it has 21 electrons. A neutral Scandium has the electron configuration of \([Ar] 3d^1 4s^2\). When Sc forms a \(\mathrm{Sc}^{3+}\) ion, it loses three electrons, resulting in \(\mathrm{Sc}^{3+}\) with the configuration of \([Ar]\), where the \(3d\) shell is empty.

Analyzing Scandium Compounds' Colorlessness

Compounds with \(\mathrm{Sc}^{3+}\) are colorless because the Sc ion, when in the \(\mathrm{Sc}^{3+}\) oxidation state, has an electron configuration of \([Ar]\). With no electrons in the \(3d\) orbital, there is no possibility of electron transitions that absorb visible light, which typically creates a colored compound. Thus the compound remains colorless.

Examining Titanium Ion Electron Configuration

Titanium (Ti) has an atomic number of 22, leading to an electron configuration of \([Ar] 3d^2 4s^2\). When forming a \(\mathrm{Ti}^{3+}\) ion, it loses three electrons, reducing its configuration to \([Ar] 3d^1\). This leaves one electron in the \(3d\) orbital.

Explaining Ti Compounds' Color

In a \(\mathrm{Ti}^{3+}\) ion, having an unpaired electron in the \(3d\) orbital allows for electronic transitions between \(3d\) sub-levels when exposed to visible light. These electron transitions absorb specific wavelengths of light, which is why compounds containing \(\mathrm{Ti}^{3+}\) ions appear colored.

Key concepts

Electronic Configuration

Atoms are structured with electrons arranged in various energy levels around the nucleus. The specific arrangement of these electrons is called electronic configuration. Every element has its unique configuration.
For Scandium (Sc), which has an atomic number of 21, the electronic configuration is written as \[ [Ar] 3d^1 4s^2 \]. However, its ion \( ext{Sc}^{3+}\) loses three electrons and simplifies to \[ [Ar] \].
This means that in its ion state, Scandium lacks electrons in the 3d orbital, making certain electron transitions impossible.
Similarly, Titanium (Ti), with the atomic number 22, starts with the configuration \[ [Ar] 3d^2 4s^2 \]. When forming \( ext{Ti}^{3+}\), it loses three electrons, resulting in \[ [Ar] 3d^1 \].
This single electron in the 3d orbital is key for its color properties. Understanding the electronic configuration gives insights into why specific ion forms appear colored or colorless.

d-orbital Transitions

The d-orbitals play a significant role in color formation for transition metals. In a neutral atom or a less oxidized ion, these orbitals can be partially filled with electrons.
When light hits these ions, electrons may "jump" between different d-orbitals. These jumps are called d-orbital transitions.
In the case of \( ext{Sc}^{3+}\), since it has an electron configuration \[ [Ar] \], it has no electrons in the 3d orbitals.
Thus, it lacks d-orbital transitions, leading to its compounds being colorless.
Meanwhile, \( ext{Ti}^{3+}\) has a configuration of \[ [Ar] 3d^1 \], containing one electron in the 3d orbital.
This arrangement permits d-orbital transitions, where the electron can move between d sublevels, absorbing light and contributing to the color observed in compounds containing \( ext{Ti}^{3+}\).

Electron Transitions

Electron transitions describe the movement of electrons between different energy levels. This movement is crucial for the appearance of color in transition metal compounds.
When electrons in an ion's orbitals absorb energy from light, they can jump to a higher energy orbital. When they fall back to their original orbitals, light is emitted, often in the visible spectrum.
For colorless compounds like those of \( ext{Sc}^{3+}\), no such transitions occur because the 3d orbitals are empty, resulting in no absorption of visible light.
In contrast, for \( ext{Ti}^{3+}\), the single electron in the 3d orbital can transition between d sub-levels.
These transitions absorb specific wavelengths from visible light, making these compounds appear colored. Each transition corresponds to a specific color, based on the energy difference between orbitals.

Oxidation States

The oxidation state of an ion impacts its electronic configuration, and thus, its ability to display color. The oxidation state is the charge of the ion, resulting from the loss or gain of electrons.
For Scandium, the \( ext{Sc}^{3+}\) oxidation state means it has lost three electrons, resulting in the electron configuration \[ [Ar] \]. Without electrons in its d-orbitals, no light absorption occurs, keeping the compound colorless.
Titanium, in the \( ext{Ti}^{3+}\) oxidation state, has also lost three electrons but retains one in the 3d orbital, allowing transitions that lead to color.
The oxidation state effectively determines how full the d-orbitals are, influencing whether electron transitions that create color are possible.
Understand that different oxidation states can dramatically change a metal's color properties, depending on how d-orbitals are filled or emptied.