Problem 82 - Chemistry The Central Science

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 \(\mathrm{VO}_{4}{\underline{\phantom{xx}}}^{3-}\) 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

Answer

The anions \(\mathrm{VO}_{4}^{3-}\), \(\mathrm{CrO}_{4}^{2-}\), and \(\mathrm{MnO}_{4}^{-}\) are isoelectronic, meaning they have the same number of electrons and similar electronic configurations. They do not exhibit \(d-d\) transitions due to empty \(3d\) orbitals in their central metal ions. Ligand-to-metal charge transfer (LMCT) transitions involve electron transfer from a ligand to a metal center, affecting the color of the complex. The wavelength of the LMCT transition for \(\mathrm{CrO}_{4}^{2-}\) (yellow) is larger than that for \(\mathrm{MnO}_{4}^{-}\) (violet). The colorless \(\mathrm{VO}_{4}{\underline{\phantom{xx}}}^{3-}\) ion likely absorbs light in the UV region of the electromagnetic spectrum due to the nature of LMCT transitions.

Step 1: (a) Meaning of Isoelectronic

Isoelectronic means that the species have the same number of electrons and the same electronic structure. In the case of the mentioned anions: \(\mathrm{VO}_{4}^{3-}\), \(\mathrm{CrO}_{4}^{2-}\), and \(\mathrm{MnO}_{4}^{-}\), they all have 34 electrons and similar electronic configurations. This is because they are formed by metal ions from the same period of the periodic table and have the same number of oxygen atoms in their structure.

Step 2: (b) Expectation for d-d Transitions

We would not expect these anions to exhibit \(d-d\) transitions because their central metal ions (\(\mathrm{V}^{5+}\), \(\mathrm{Cr}^{6+}\), and \(\mathrm{Mn}^{7+}\)) have a completely empty \(3d\) orbital due to their high oxidation states. \(d-d\) transitions require an electron to be promoted from one \(d\) orbital to another within the same energy shell, which is not possible when there are no electrons in the \(d\) orbitals.

Step 3: (c) Definition of LMCT Transition

A Ligand-to-Metal Charge Transfer (LMCT) transition refers to an electronic transition where an electron is promoted from a ligand's occupied orbital to an empty metal orbital. It is a type of charge transfer process where electron density is transferred from the ligand to the metal center, which can result in changes in the color or other spectroscopic properties of the complex.

Step 4: (d) Wavelength Comparison of LMCT Transitions for \(\mathrm{MnO}_{4}^{-}\) and \(\mathrm{CrO}_{4}^{2-}\)

The wavelength of the LMCT transition for \(\mathrm{MnO}_{4}^{-}\) is given as 565 nm, which corresponds to violet color. The \(\mathrm{CrO}_{4}^{2-}\) ion is yellow. According to the visible light spectrum, yellow light has a longer wavelength than violet light. Therefore, the wavelength of the LMCT transition for chromate would be larger than that for permanganate.

Step 5: (e) UV or IR Region for \(\mathrm{VO}_{4}{ }^{3-}\)'s Absorbed Light

The \(\mathrm{VO}_{4}{\underline{\phantom{xx}}}^{3-}\) ion is colorless, which means that the light absorbed by the LMCT transition in this ion must not be in the visible region of the electromagnetic spectrum. As LMCT transitions typically involve promoting an electron from the ligand's occupied orbital to an empty metal orbital, it is reasonable to expect that this absorption would occur in the ultraviolet (UV) region, since UV light has higher energy than infrared (IR) light. Therefore, the absorbed light would likely fall in the UV region of the electromagnetic spectrum.

Key Concepts

Isoelectronic Species

In coordination chemistry, isoelectronic species are compounds or ions that have the same number of electrons and a similar electronic structure. This is an interesting concept because, despite having the same number of electrons, these species can feature different central atoms or ions and differ significantly in their chemical and physical properties.
For example, consider the anions \(\mathrm{VO}_{4}^{3-}, \, \mathrm{CrO}_{4}^{2-},\) and \(\mathrm{MnO}_{4}^{-}.\)

• All three species have 34 electrons.
• They are made with transition metals from the same period in the periodic table.
• The number of oxygen atoms surrounding each metal ion remains constant.

Consequently, these anions are considered isoelectronic. Understanding isoelectronic species helps in predicting and contrasting the reactivity and behavior of different compounds in various chemical environments.

d-d Transitions

d-d transitions occur when an electron moves between d-orbitals within the same transition metal ion. These transitions are responsible for the colorful appearance of many coordination compounds. However, not all compounds can exhibit this property.
For the anions in question, \(\mathrm{VO}_{4}^{3-}, \, \mathrm{CrO}_{4}^{2-},\) and \(\mathrm{MnO}_{4}^{-},\) d-d transitions do not occur. Here's why:

• The ions involved have \(3d\) orbitals completely devoid of electrons.
• The central metal ions, \(\mathrm{V}^{5+}, \, \mathrm{Cr}^{6+}, \, \text{and} \, \mathrm{Mn}^{7+},\) are in high oxidation states.

Since d-d transitions require an electron to move within the d-orbitals, but these anions have no electrons in those orbitals, the transition is impossible. Hence, the colors observed in these anions are due to other types of transitions, like charge-transfer transitions.

Ligand-to-Metal Charge Transfer

Ligand-to-Metal Charge Transfer (LMCT) is a fascinating concept in coordination chemistry where an electron is transferred from a filled orbital of a ligand to an empty orbital on a metal. This transfer can significantly affect the spectral features of the compound.
In the case of \(\mathrm{MnO}_{4}^{-},\) the violet color observed is due to such a transition.

• The transition occurs when an electron from an oxygen ligand's orbital is excited to a manganese-centered orbital.
• This transfer highlights why high-energy light absorption leads to visible coloration.

Different LMCT transitions absorb different wavelengths, influencing the color we perceive. For example, the LMCT transition for \(\mathrm{CrO}_{4}^{2-}\) occurs at a longer wavelength than that for \(\mathrm{MnO}_{4}^{-},\) resulting in the chromate ion appearing yellow. Understanding LMCT can aid in controlling color and light-absorption properties in materials.