For each of the following octahedral complexes, give the...

For each of the following octahedral complexes, give the number of unpaired electrons expected. (a) $\left[\mathrm{CrCl}_{6}\right]^{3-}$ (b) $\left[\mathrm{Co}(\mathrm{CN})_{5}\left(\mathrm{H}_{2} \mathrm{O}\right)\right]^{2-}$ (c) $\left[\mathrm{Mn}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}$ (d) $\left[\mathrm{Rh}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}$ (e) $\left[\mathrm{V}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}$

For each of the following octahedral complexes, give the number of unpaired electrons expected.
(a) $\left[\mathrm{CrCl}_{6}\right]^{3-}$
(b) $\left[\mathrm{Co}(\mathrm{CN})_{5}\left(\mathrm{H}_{2} \mathrm{O}\right)\right]^{2-}$
(c) $\left[\mathrm{Mn}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}$
(d) $\left[\mathrm{Rh}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}$
(e) $\left[\mathrm{V}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}$

Key Concepts

Octahedral Crystal Field Theory

This concept explains how the five degenerate d orbitals of a transition metal ion split into two groups (t2g and eg sets) in an octahedral coordination environment. The energy difference between these levels, known as the crystal field splitting energy (?o), plays a critical role in determining the electron configuration within the metal complex.

d-Electron Count and Oxidation State Determination

Determining the number of d electrons is essential, and it is obtained by considering the oxidation state of the central metal ion. Once the oxidation state is established, the corresponding electron configuration in the d orbitals is assigned, which is crucial for predicting magnetic properties and the number of unpaired electrons.

High Spin vs Low Spin Configurations

The arrangement of electrons in the split d orbitals can follow either a high spin or low spin configuration. This decision is influenced by the balance between the crystal field splitting energy (?o) and the electron pairing energy. A small ?o relative to the pairing energy favors high spin (more unpaired electrons), while a large ?o favors low spin (fewer unpaired electrons).

Ligand Field Strength and the Spectrochemical Series

Ligands influence the magnitude of the crystal field splitting energy. The spectrochemical series ranks ligands from weak field, which produce a small ?o and typically high spin complexes, to strong field, which produce a large ?o and often low spin complexes. Understanding the nature of the ligands in a complex helps predict its electronic configuration and magnetic behavior.

Electron Pairing and Unpaired Electrons Counting

After determining the electron configuration within the split d orbitals, counting the unpaired electrons involves considering both the electron filling order and whether the complex is high spin or low spin. This count of unpaired electrons is crucial as it directly relates to the magnetic properties of the metal complex.

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