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 \(\mathrm{Cr} \mathrm{O}_{4}^{2-}\) 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. Is this observation consistent with the wavelengths of the LMCT transitions in \(\mathrm{MnO}_{4}^{-}\) and \(\mathrm{CrO}_{4}^{2-}\) ?

Short answer

(a) The statement that the anions \(VO_{4}^{3-}\), \(CrO_{4}^{2-}\), and \(MnO_{4}^{-}\) are isoelectronic means that they have the same number of electrons (50 electrons each in this case). (b) None of these anions will exhibit d-d transitions, as their central metal ions are in high oxidation states with empty d-orbitals. (c) A ligand-to-metal charge transfer (LMCT) transition occurs when an electron in the ligand (oxygen) is excited and transferred to an empty or partially occupied d-orbital of the metal ion (Mn, Cr, or V). (d) The wavelength of the LMCT transition for chromate (\(CrO_{4}^{2-}\), yellow) would be larger than that for permanganate (\(MnO_{4}^{-}\), violet - 565 nm). (e) The colorless nature of the orthovanadate ion (\(VO_{4}^{3-}\)) is consistent with the trends observed for the anions \(MnO_{4}^{-}\) and \(CrO_{4}^{2-}\), as it does not absorb light in the visible spectrum.

Step-by-step solution

(a) Understanding Isoelectronic Anions

To say that the anions \(VO_{4}^{3-}\), \(CrO_{4}^{2-}\), and \(MnO_{4}^{-}\) are isoelectronic means that they have the same number of electrons. To verify this, we can find the total number of electrons in each anion: 1. For \(VO_{4}^{3-}\): \(23 (V) + 4 \times 8 (O) + 3 (extra\, electrons) = 50\, electrons\) 2. For \(CrO_{4}^{2-}\): \(24 (Cr) + 4 \times 8 (O) + 2 (extra\, electrons) = 50\, electrons\) 3. For \(MnO_{4}^{-}\): \(25 (Mn) + 4 \times 8 (O) + 1 (extra\, electron) = 50\, electrons\) In all cases, each anion has 50 electrons, so it's correct to say that they are isoelectronic.

(b) Expectation of d-d Transitions

To determine whether the anions would exhibit d-d transitions, consider the central metal ions in each anion: V, Cr, and Mn. They are all transition metals and form tetrahedral complexes with oxygen. However, in all these anions, the central metals are in high oxidation states: +5 for V, +6 for Cr, and +7 for Mn. In such high oxidation states, the d-orbitals are empty. Since d-d transitions require at least one electron in the d-orbitals, none of these anions will exhibit d-d transitions.

(c) Understanding Ligand-to-Metal Charge Transfer (LMCT) Transition

A ligand-to-metal charge transfer (LMCT) transition occurs when an electron in the ligand (in this case, oxygen) is excited and transferred to an empty or partially occupied d-orbital of the metal ion (in this case, Mn, Cr, or V). In the context of MnO\(_4^{-}\), the transition is responsible for the violet color of permanganate ion, as the LMCT transition absorbs certain wavelengths of light, causing the complementary wavelength to be reflected or transmitted.

(d) Comparing LMCT Wavelengths of Permanganate and Chromate

The colors of the anions are given, permanganate being violet and chromate being yellow. The wavelength responsible for the violet color of permanganate is 565 nm. According to the visible light spectrum: - Violet: approximately 380 - 450 nm - Yellow: approximately 570 - 590 nm Since we know that the color of the permanganate \(MnO_4^-\) is violet, and the color of the chromate \(CrO_{4}^{2-}\) is yellow, it means that the wavelength of the LMCT transition for chromate would be larger than that for permanganate.

(e) Assessing Consistency with LMCT Wavelengths of Permanganate, Chromate, and Orthovanadate

The orthovanadate ion (\(VO_{4}^{3-}\)) is colorless, meaning that it does not absorb light in the visible spectrum. Absorption in the visible spectrum would require energy differences corresponding to the energy absorbed by the LMCT transition, and a color change would occur. Since the LMCT wavelengths of \(MnO_{4}^{-}\) and \(CrO_{4}^{2-}\) are in the visible spectrum, causing them to be violet and yellow respectively, and the \(VO_{4}^{3-}\) ion is colorless, the color (or lack thereof) of the orthovanadate ion is consistent with the trends observed for the other anions in this exercise.

Key concepts

Isoelectronic Anions

Isoelectronic anions are ions that share the same number of electrons but may have different elemental compositions or charge states. This concept becomes particularly interesting in inorganic chemistry when analyzing the electronic structure of transition metal complexes. For instance, the tetrahedral anions orthovanadate (\(VO_{4}^{3-}\)), chromate (\(CrO_{4}^{2-}\)), and permanganate (\(MnO_{4}^{-}\)) are isoelectronic, each containing a total of 50 electrons.

Understanding the isoelectronic nature of these anions is crucial in predicting their chemical and physical properties. Despite their similar electron count, each ion's differing charge and central metal atom influence how they interact with light. This concept is foundational to understanding why these ions may exhibit diverse colors and behaviors, leading us to explore other related phenomena like LMCT transition wavelengths and complex colors.

d-d Transitions

The phenomenon of d-d transitions plays a central role in the coloration of transition metal complexes. It involves the electron transition between different d-orbitals of a metal ion within a compound. These transitions are allowed when there are unpaired electrons present in the d-orbitals.

In the case of the anions mentioned, the high oxidation states of V(+5), Cr(+6), and Mn(+7) result in the d-orbitals being empty, implying that d-d transitions will not occur. This is significant when considering the colors of these compounds, as the absence of d-d transitions means that any observed colors must arise from other types of electronic transitions, such as LMCT.

LMCT Transition Wavelengths

Ligand-to-metal charge transfer (LMCT) transitions involve an electron moving from a ligand to a metal's d-orbital. The wavelength at which an LMCT transition occurs can influence the color of a complex. Light of a particular wavelength is absorbed during this electron transfer, which often leads to a complementary color being observed. In the case of the permanganate ion, LMCT occurs at a wavelength of 565 nm, producing its characteristic violet color.

Knowing the wavelength for permanganate allows us to predict that chromate ions, which appear yellow, have a larger wavelength for their LMCT transitions. This is due to the fact that yellow color is observed at around 570 - 590 nm on the visible spectrum, which is higher than the violet range.

Transition Metal Complex Colors

The vivid colors we observe in transition metal complexes are not just aesthetically pleasing but are a manifestation of light interaction with the electrons in these complexes. The specific color is a direct result of which wavelengths are absorbed and which are transmitted or reflected. For instance, the permanganate ion is violet because it absorbs light in the yellow-green region, around 565 nm.

The orthovanadate ion being colorless suggests that its LMCT transition wavelengths do not fall within the visible spectrum, unlike the chromate and permanganate ions. This colorless nature aligns with the observation that complexes with LMCT transitions outside of the visible spectrum do not absorb visible light and, thus, do not exhibit colors perceptible by the human eye.