Explain why Cr^2+ forms high-spin and low-spin octahedral complexes, but Cr^3+ does not.

Name: Problem 53, Chapter 25: Chemistry
Uploaded: 2021-12-02T07:03:02-08:00
Duration: 1 min 13 s
Channel: Adriano Chikande
Description: Explain why Cr^2+ forms high-spin and low-spin octahedral complexes, but Cr^3+ does not.

step 1 In this question we're going to be comparing CR2 plus and CR3 plus. So what we have here is the

Explain why Cr^2+ forms high-spin and low-spin octahedral...

Key Concepts

Electron Configuration and Spin States

The d electron count of the metal ion determines the possible arrangements of electrons in the split d-orbitals. For a d? configuration, as in Cr²?, two arrangements are possible depending on the ligand field strength: a high-spin configuration where electrons occupy both t?g and e_g orbitals with minimal pairing, or a low-spin configuration where electrons pair in the t?g orbitals. In contrast, a d³ configuration, as found in Cr³?, naturally fills the t?g orbitals with one electron each, yielding the same electronic arrangement regardless of ligand strength, and thus only a high-spin-like state is observed.

Oxidation State Effects

The oxidation state of the metal ion affects the extent of d-orbital splitting. A higher oxidation state, like Cr³?, increases the effective nuclear charge, which in turn enhances the ligand field splitting. However, for a d³ system (Cr³?), this increase doesn’t lead to alternative electron arrangements since the electrons already occupy the lower-energy t?g orbitals. For lower oxidation states such as Cr²? (d?), the smaller splitting allows for the possibility of both high-spin and low-spin configurations depending on the strength of the ligand field.

Crystal Field Theory

This theory explains how the degenerate d-orbitals of a transition metal ion split into different energy levels when surrounded by a field of ligands. In an octahedral geometry, the d-orbitals split into a lower-energy t?g set and a higher-energy e_g set. The relative stabilization of these orbitals, quantified by the ligand field splitting energy (??), influences how electrons are arranged among them.

Ligand Field Splitting Energy versus Pairing Energy

The decision between high-spin and low-spin configurations hinges on the competition between the ligand field splitting energy (??) and the electron pairing energy. When ?? is small relative to the pairing energy, electrons occupy higher-energy orbitals rather than pair up in lower ones, leading to a high-spin complex. Conversely, when ?? is large, electrons pair in the lower orbitals, resulting in a low-spin complex.

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