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.

Step by step solution

01

Part (a): Understanding Isoelectronic

Isoelectronic species have the same number of electrons and are usually the same in the electron configuration. In this case, all three anions have the same total number of electrons, but different numbers of protons and charges.

02

Part (b): d-d Transitions

The d-d transition occurs when an electron in a metal ion gets excited from a lower energy d-orbital to a higher energy d-orbital. For \(\mathrm{VO}_{4}^{3-}\), \(\mathrm{CrO}_{4}^{2-}\), and \(\mathrm{MnO}_{4}^{-}\), their central metal ions are V, Cr, and Mn, respectively. For d-d transition to occur, the central metal ions must have unpaired d-electrons. In these anions, however: - V in \(\mathrm{VO}_{4}^{3-}\) has an oxidation state of +5, which results in an electron configuration devoid of unpaired d-electrons. - Cr in \(\mathrm{CrO}_{4}^{2-}\) has an oxidation state of +6, which also results in an electron configuration devoid of unpaired d-electrons. - Mn in \(\mathrm{MnO}_{4}^{-}\) has an oxidation state of +7, which results in an electron configuration devoid of unpaired d-electrons. Therefore, none of these anions would exhibit d-d transitions because all have a central metal ion with no unpaired d-electrons.

03

Part (c): Ligand-to-Metal Charge-Transfer (LMCT) Transition

A ligand-to-metal charge transfer (LMCT) transition occurs when an electron from a ligand (such as oxygen in these cases) moves to an empty orbital of the central metal ion. This process usually involves a significant change in energy, which is often observed as the absorption of light of a specific wavelength corresponding to the said energy change. In the case of \(\mathrm{MnO}_{4}^{-}\), the violet color is due to such a ligand-to-metal charge transfer transition.

04

Part (d): Wavelength of LMCT Transition for Chromate

As the chromate ion (\(\mathrm{CrO}_{4}^{2-}\)) is yellow, it absorbs light in the complementary region of the electromagnetic spectrum, which is blue/violet light. Since violet light has a shorter wavelength than yellow light, the wavelength of the LMCT transition for chromate is smaller (shorter) than that for \(\mathrm{MnO}_{4}^{-}\).

05

Part (e): Absorption of UV or IR Light by \(\mathrm{VO}_{4}^{3-}\)

Since the \(\mathrm{VO}_{4}^{3-}\) ion is colorless, it does not absorb any visible light. The LMCT transition for the \(\mathrm{VO}_{4}^{3-}\) must have a much higher energy change than that of \(\mathrm{MnO}_{4}^{-}\) and \(\mathrm{CrO}_{4}^{2-}\), resulting in a significantly different absorption wavelength. Ultraviolet (UV) light has shorter wavelengths and higher energy than visible light, while infrared (IR) light has longer wavelengths and lower energy than visible light. Given that the energy is being absorbed in \(\mathrm{VO}_{4}^{3-}\), it suggests that the corresponding wavelengths of the absorbed light are in the UV region of the electromagnetic spectrum.

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