Problem 84 - Chemistry The Central Science In Si Units

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.

Step-by-Step Solution

Answer

(a) Isoelectronic means they have the same number of electrons. (b) No, they do not exhibit d-d transitions. (c) LMCT is electron transfer from ligand to metal. (d) Larger; CrO4 absorbs a different color. (e) VO4 absorbs in the UV region.

Step 1: Understanding Isoelectronic Species

Isoelectronic species have the same number of electrons in total. For \(\mathrm{VO}_{4}^{3-}\), \(\mathrm{V}^{5+}\) contributes 18 electrons, and each oxygen contributes 8 electrons, totaling 50 electrons. For \(\mathrm{CrO}_{4}^{2-}\), \(\mathrm{Cr}^{6+}\) contributes 18 electrons, and each oxygen again contributes 8, for a total of 50 electrons. \(\mathrm{MnO}_{4}^{-}\) follows similarly with \(\mathrm{Mn}^{7+}\) having 25 electrons and oxygen 32 (4x8=32), totaling 50. All these ions have the same number of total electrons.

Step 2: Evaluating d-d Transitions

d-d transitions generally occur in transition metal complexes where d orbitals are split in energy. However, for tetrahedral ions like \(\mathrm{VO}_{4}^{3-}\), \(\mathrm{CrO}_{4}^{2-}\), and \(\mathrm{MnO}_{4}^{-}\), the highest occupied orbitals are primarily \(\pi^*\) or antibonding p orbitals, not d orbitals. Therefore, while they do involve transition metals, traditional d-d transitions are not expected.

Step 3: Defining Ligand-to-Metal Charge Transfer (LMCT)

LMCT involves the transfer of electrons from ligand orbitals to empty metal orbitals. This occurs when the energy of the transition from a ligand orbital to a metal orbital is within the visible range, resulting in the characteristic color of the compound. In \(\mathrm{MnO}_{4}^{-}\), its violet color is due to such a LMCT.

Step 4: Comparing LMCT in Permanganate and Chromate

\(\mathrm{MnO}_{4}^{-}\) absorbs light at 565 nm (violet), corresponding to a high-energy transition in the visible region. The \(\mathrm{CrO}_{4}^{2-}\) anion is yellow, suggesting it absorbs purple or blue light, which is lower in energy than violet. Therefore, the LMCT transition wavelength for chromate is larger than 565 nm.

Step 5: Analyzing Colorless VO4 Ion

Since \(\mathrm{VO}_{4}^{3-}\) is colorless, the LMCT transition does not occur in the visible spectrum. A colorless compound can still absorb electromagnetic radiation outside the visible range, absoring in the ultraviolet which would not be visible to the human eye. This suggests \(\mathrm{VO}_{4}^{3-}\) absorbs UV light.

Key Concepts

d-d Transitions

In the realm of chemistry, particularly in transition metal complexes, d-d transitions play a pivotal role in the absorption of light.
These transitions involve the movement of an electron between d orbitals of different energy levels within the same metal ion.
In a more technical sense, when a transition metal complex absorbs light, an electron can be excited from one d orbital to another of a higher energy.Many factors can affect the likelihood of d-d transitions, including:

• The arrangement of ligands around the metal ion
• The type of metal
• The oxidation state of the metal

In tetrahedral ions like \(\mathrm{VO}_{4}^{3-}\), \(\mathrm{CrO}_{4}^{2-}\), and \(\mathrm{MnO}_{4}^{-}\), these d orbitals are not the highest in energy.
Instead, we see that they involve antibonding \(\pi^*\) orbitals or p orbitals rather than d orbitals.Thus, traditional d-d transitions are not expected.This is why these ions, despite being associated with transition metals, do not exhibit the usual d-d transitions seen in other complexes.

Ligand-to-Metal Charge Transfer (LMCT)

Ligand-to-Metal Charge Transfer (LMCT) is a fascinating concept where electrons are transferred from a ligand to the metal ion within a complex.
This can result in the absorption of light, providing color to the compound.
Typically, this occurs when the energy needed for an electron to jump from a ligand's orbital to a metal's empty orbital matches the energy of visible light.Here's a simplified breakdown of the process:

• Ligands contain non-bonding or antibonding orbitals filled with electrons.
• Metal ions have empty orbitals ready to accept electrons.
• When light is absorbed, an electron from the ligand jumps to an empty metal orbital, causing a change in electron distribution and energy absorption.

For instance, the violet color in \(\mathrm{MnO}_{4}^{-}\) is directly related to LMCT.
This transition occurs at a wavelength of \(565\ nm\), which falls in the visible spectrum.Understanding LMCT helps us appreciate how the energies involved contribute to the perceived colors of various compounds, highlighting the intricate dance between molecules and light.

Tetrahedral Anions

Tetrahedral anions are a class of compounds where a central metal atom is surrounded by four atoms or groups, forming a shape similar to a pyramid.
This configuration, due to its symmetry and spatial arrangement, impacts the electronic properties and the way these compounds interact with light.Characteristics of tetrahedral anions include:

• Four ligands symmetrically arranged around a central metal atom.
• Absence of d-d transitions due to the involvement of other energy orbitals, like \(\pi^*\) orbitals.
• Potential for LMCT, leading to vibrant colors based on the ligand and metal pairing.

For the ions \(\mathrm{VO}_{4}^{3-}\), \(\mathrm{CrO}_{4}^{2-}\), and \(\mathrm{MnO}_{4}^{-}\), their arrangement not only defines their chemical reactivity but also how they absorb light.
In some cases, like \(\mathrm{VO}_{4}^{3-}\), the lack of color implies electronic transitions occur outside the visible range, typically in the ultraviolet spectrum.This shape and electronic structure strongly affect the properties and applications of these ions across scientific and industrial fields.