Question

The \(f^{1}\) ion \(\mathrm{Ce}^{\mathrm{III}}\) is colourless in aqueous solution, whereas the \(\mathrm{d}^{1}\) ion \(\mathrm{Ti}^{\text {ill }}\) is purple. Outline the reason for this difference.

Short answer

The difference in color between the \(f^{1}\) ion \(\mathrm{Ce}^{\mathrm{III}}\) and the \(\mathrm{d}^{1}\) ion \(\mathrm{Ti}^{\text {ill }}\) arises from the energy required for the electronic transitions. The \(\mathrm{d}^{1}\) ion \(\mathrm{Ti}^{\text {ill }}\) absorbs light energy in the visible range causing a transition in the loosely bound d-electrons, resulting in the purple color. The \(f^{1}\) ion \(\mathrm{Ce}^{\mathrm{III}}\), however, requires a much larger energy for f-electrons' transition which is beyond the visible range, hence it is colorless in aqueous solution.

Step-by-step solution

Understand the Electronic Transitions

Electronic transitions are movements of electrons from one energy level to another. These transitions absorb energy in the form of light. If the energy absorbed falls within the visible region of the electromagnetic spectrum, the ion shows color. Otherwise, if the transition does not fall in the visible region, the ion will be colorless.

Discuss about d-block Elements

D-block elements possess loosely bound electrons in their outermost orbitals, which are generally empty in the ground state. These are known as valence electrons. The absorption of light facilitates the transition of these valence electrons to higher energy levels. The energy gaps for these transitions in the visible region are usually relatively small, hence creating color.

Discuss about f-block Elements

F-block elements have electrons in their inner f-orbitals. For the electron transition to occur in these elements, a higher amount of energy is required. This transition energy tends to be beyond the visible range in the electromagnetic spectrum, which results in no color being observed.

Connect the Facts with Ions

The \(\mathrm{d}^{1}\) ion \(\mathrm{Ti}^{\text {ill }}\) is a d-block element, and it has loosely bound electrons in its d-orbital which, upon absorbing light, can transition to a higher energy level. This energy corresponds to the visible portions of electromagnetic spectrum, hence we see it as colored, specifically purple. In contrast, the \(f^{1}\) ion \(\mathrm{Ce}^{\mathrm{III}}\) is a f-block element. The transition of electrons in this ion by any excuse falls outside of the visible range, so it appears colorless in aqueous solution.

Key concepts

D-block Elements

D-block elements, also known as transition metals, include elements from groups 3 to 12 on the periodic table. These elements are characterized by the presence of electrons in the outermost d orbitals.

The electronic structure of d-block elements is typically represented by the configuration \((n-1)d^{1-10}ns^{0-2}\), where the \((n-1)d\) orbitals are being filled with electrons. One of the fascinating aspects of transition metals is their ability to display a variety of oxidation states, mainly because the energy difference between the \(ns\) and \((n-1)d\) orbitals is quite small. This flexibility in oxidation states facilitates the formation of colorful compounds.

Due to the comparable energy levels of the d orbitals, electrons can be excited by absorbing light in the visible spectrum. This absorption and the subsequent electronic transition is responsible for the vibrant colors exhibited by compounds of d-block elements. This is particularly relevant for ions like \(\mathrm{Ti}^{\mathrm{III}}\), which has a \(\mathrm{d}^{1}\) configuration, showing a distinct purple color as electrons jump to higher energy levels within the d orbitals.

F-block Elements

The f-block elements, located at the bottom of the periodic table, are composed of the lanthanides and actinides. These elements have electrons occupying the f orbitals, which are more complex and have a higher capacity for electrons compared to the d orbitals.

The typical electron configuration for f-block elements is \((n-2)f^{1-14}(n-1)d^{0-1}ns^{2}\), illustrating that they have electrons in the \((n-2)f\) shell. A unique feature of f-block elements is the shielding provided by the outer orbitals, which makes the f electrons less interactive with the surroundings, hence transitions involving f electrons require a lot of energy.

Because of the high energy required to excite these f electrons, the electronic transitions often do not occur in the visible range of light. This is why ions like \(\mathrm{Ce}^{\mathrm{III}}\), with an \(f^{1}\) configuration, are often colorless in aqueous solutions, as the light absorbed does not correspond to the visible spectrum.

Energy Levels in Atoms

Atoms consist of a nucleus surrounded by electrons that occupy specific energy levels or shells. These energy levels are like the rungs of a ladder, where each rung represents a certain energy level that an electron can inhabit.

The energy levels closer to the nucleus are lower in energy, and as we move further away, the energy levels become higher. When an electron jumps from a lower to a higher energy level, it must absorb the right amount of energy to make the jump. This energy often comes from light. The converse is also true; when an electron falls back to a lower energy level, it releases energy often in the form of light.

In coordination chemistry, the focus is often on the transition of electrons between these defined energy levels within the d or f orbitals. The specific wavelength of light absorbed during these transitions can dictate the color of the substance, based on the difference in energy between the two levels.

Color in Coordination Compounds

Coordination compounds can show a wide array of colors due to the electronic transitions that occur within their metal complexes. The metal ion at the center of the complex has a specific number of coordination sites where ligands, molecules or ions that donate pairs of electrons, can attach. These ligands affect the energy levels of the d or f orbitals in the metal ion.

The nature of the ligands and the geometry of the complex can cause a splitting of the d orbital energy levels into two groups, resulting in an energy gap. When visible light shines on these complexes, the electrons may absorb a photon and jump from the lower to the higher energy level d orbitals. This absorbed energy corresponds to a specific color of light, and the compound appears as the complementary color of the light absorbed. For instance, if a compound absorbs green light, it will appear red. This phenomenon is known as ligand field theory, and it helps to explain the vivid colors of many coordination compounds, a trait often exploited in materials science and art.