Question

Consider the tetrahedral anions \(\mathrm{VO}_{4}^{3-}\) (orthovanadate ion), \(\mathrm{CrO}_{4}^{2-}\) (chromate ion), and \(\mathrm{MnO}_{4}^{-}\)(permanganate ion). (a) These anions are isoelectronic. What does this statement mean? (b) Would you expect these anions to exhibit \(d-d\) transitions? Explain. (c) As mentioned in "A Closer Look" on charge- transfer color, the violet color of \(\mathrm{MnO}_{4}^{-}\)is due to a ligand- to-metal charge transfer (LMCT) transition. What is meant by this term? (d) The LMCT transition in \(\mathrm{MnO}_{4}^{-}\)occurs at a wavelength of \(565 \mathrm{~nm}\). The \(\mathrm{CrO}_{4}^{2}\) ion is yellow. Is the wavelength of the LMCT transition for chromate larger or smaller than that for \(\mathrm{MnO}_{4}^{-}\)? Explain. (e) The \(\mathrm{VO}_{4}^{3-}\) ion is colorless. Do you expect the light absorbed by the LMCT to fall in the UV or the IR region of the electromagnetic spectrum? Explain your reasoning.

Short answer

These tetrahedral anions, VO4^3-, CrO4^2-, and MnO4^-, are isoelectronic which means they have the same number of electrons, in this case, 34 electrons. They don't exhibit d-d transitions because they lack a center of symmetry. LMCT (ligand-to-metal charge transfer) transition refers to an electron transfer from a ligand's molecular orbital to a metal's empty molecular orbital. The LMCT for MnO4^- occurs at 565 nm (violet color), while the CrO4^2- ion absorbs light at lower wavelengths (yellow color). The VO4^3- ion is colorless, and the LMCT absorbed light falls in the UV region of the electromagnetic spectrum.

Step-by-step solution

Understanding Isoelectronic Ions

Isoelectronic ions are those that have the same number of electrons. VO4^3-, CrO4^2-, and MnO4^- all have 34 electrons. Therefore, these anions are isoelectronic.

Discussing d-d Transitions

d-d transitions are electronic transitions between d-orbitals in a metal complex. Since VO4^3-, CrO4^2-, and MnO4^- are tetrahedral anions, they do not exhibit d-d transitions. This is because these anions possess no center of symmetry, which leads to the absence of a degenerate set of d-orbitals in the complexes.

Defining Ligand-to-Metal Charge Transfer (LMCT) Transition

A ligand-to-metal charge transfer (LMCT) transition is an electronic transition where an electron is transferred from the ligand's molecular orbital to a metal's empty molecular orbital. In the case of MnO4^-, the violet color is due to an LMCT transition.

Comparing LMCT Wavelengths

The LMCT transition in MnO4^- occurs at a wavelength of 565 nm. Since the CrO4^2- ion is yellow, its LMCT transition will have a lower wavelength than that of MnO4^-. This is because yellow color results from the absorption of light at a lower wavelength compared to violet.

Determining the Absorption Region of VO4^3-

The VO4^3- ion is colorless, which means that it doesn't absorb light in the visible region of the electromagnetic spectrum. To determine whether the absorbed light falls in the UV or IR regions, we can consider the energy levels of the ion. The energy required for LMCT transitions is in the UV region, while IR absorption is associated with lower energy transitions. Therefore, the LMCT absorbed light in VO4^3- falls in the UV region of the electromagnetic spectrum.

Key concepts

d-d Transitions

d-d transitions occur within a metal complex when an electron jumps between d-orbitals. These are known as electronic transitions. Imagine electrons moving from one d-orbital to another; these movements cause changes in energy levels, which can be observed as changes in color.
For d-d transitions to take place, a reduced or broken symmetry is essential. This allows degenerate d-orbitals (orbitals that share the same energy level) to be present. Tetrahedral anions like ext{VO}_4^{3-}, ext{CrO}_4^{2-}, and ext{MnO}_4^- do not display these transitions because they lack any center of symmetry. Without this symmetry, degenerate d-orbitals are absent, resulting in no d-d transitions being observed. The presence or absence of these transitions greatly affects how a compound absorbs light and can influence its observable color in solution.

Ligand-to-Metal Charge Transfer (LMCT)

Ligand-to-Metal Charge Transfer (LMCT) is an intriguing type of transition in coordination compounds. During an LMCT transition, an electron is moved from a ligand, which is the molecule or ion around the metal, to the metal itself.
This process changes the electronic structure of the complex significantly, often leading to noticeable color changes. Take the ext{MnO}_4^- anion, for example; its distinct violet color arises from an LMCT transition. The electron moves from the oxygen ligands to the manganese metal, imparting this striking color. During this transition, energy is absorbed, typically from the visible region of the spectrum, and this absorption is what mostly determines the perceived color of the compound. LMCT transitions are integral to understanding the brilliant colors often present in transition metal compounds.

Electromagnetic Spectrum

The electromagnetic spectrum is a wide range of wavelengths over which electromagnetic radiation extends. It encompasses everything from very short wavelengths, like gamma rays and X-rays, to long wavelengths, such as radio waves.
Visible light falls within a narrow band of this spectrum from approximately 400 nm to 700 nm. When speaking of color in chemistry, we typically focus on this portion.
In our example with ext{CrO}_4^{2-}, its yellow hue is due to LMCT occurring at wavelengths shorter than those of the violet colored ext{MnO}_4^- at 565 nm. Moving beyond the visible, the colorless ext{VO}_4^{3-} absorbs light not visible to the human eye, likely in the UV region. This high-energy absorption in the UV range shows that simple color observations can provide a deeper understanding of where absorption occurs in the electromagnetic spectrum. Thus, by analyzing these interactions at various wavelengths, chemists piece together complex information about a compound's electronic structure.