Question

(a) The value of \(\mu_{\mathrm{eff}}\) for \(\left[\mathrm{CoF}_{6}\right]^{3-}\) is \(5.63 \mu_{\mathrm{B}} .\) Explain why this value does not agree with the value for \(\mu\) calculated from the spin-only formula. (b) By using a simple \(\mathrm{M} \mathrm{O}\) approach, rationalize why oneelectron oxidation of the bridging ligand in \(\left[(\mathrm{CN})_{5} \mathrm{CoOOCo}(\mathrm{CN})_{5}\right]^{6-}\) leads to a shortening of the \(\mathrm{O}-\mathrm{O}\) bond (c) Salts of which of the following complex ions might be expected to be formed as racemates: \(\left[\mathrm{Ni}(\operatorname{acac})_{3}\right]^{-}\) \(\left[\mathrm{CoCl}_{3}(\mathrm{NCMe})\right]^{-},\) cis-\(\left[\mathrm{Co}(\mathrm{en})_{2} \mathrm{Cl}_{2}\right]^{+},\) trans- \(\left[\mathrm{Cr}(\mathrm{en})_{2} \mathrm{Cl}_{2}\right]^{+} ?\)

Short answer

(a) Ligand field effects cause the discrepancy. (b) Oxidation fills an antibonding orbital, shortening the \(O-O\) bond. (c) The cis-\([\text{Co(en)}_2\text{Cl}_2]^+\) complex can form racemates.

Step-by-step solution

Understanding Spin-Only Magnetic Moment

The spin-only formula for calculating magnetic moment is given by \( \mu = \sqrt{n(n+2)}\), where \(n\) is the number of unpaired electrons. For \([\text{CoF}_{6}]^{3-}\), we assume that the Co ion has a \(d^5\) configuration. According to the spin-only formula, the expected magnetic moment would be \(\mu = \sqrt{5(5+2)} = \sqrt{35} \approx 5.92 \mu_{B} \). However, the given value is \(5.63 \mu_{B}\).

Consider Ligand Field Effects

The discrepancy between experimental and spin-only values indicates the presence of ligand field effects, possibly due to spin-orbit coupling in \(\text{Co}^{3+}\) or contributions from orbital angular momentum. In other words, the actual arrangement of electrons can cause variations in expected magnetic moments.

MO Approach for One-Electron Oxidation of \([\text{(CN)}_{5} \text{CoOOCo(CN)}_{5}]^{6-}\)

In the given complex, the \(\mathrm{O}-\mathrm{O}\) bond is a peroxo bridge. Upon one-electron oxidation, the added electron would fill an antibonding molecular orbital associated with the O-O bond, causing a weakening of this bond and hence leading to its shortening.

Analyze Chirality in Complex Ions

A complex that can have non-superimposable mirror images, or chiral molecules, can form racemates. Among the given complexes, cis-\([\text{Co(\text{en})}_2\text{Cl}_2]^+\) is capable of existing as two enantiomers. The others, \([\text{Ni(acac)}_3]^-\), \([\text{CoCl}_3(\text{NCMe})]^-\), and trans-\([\text{Cr(\text{en})}_2\text{Cl}_2]^+\), do not exhibit chirality.

Key concepts

Spin-only magnetic moment

The spin-only magnetic moment is an important concept in inorganic chemistry that provides insight into the magnetic properties of a complex. The formula used to calculate this moment is \( \mu = \sqrt{n(n+2)} \), where \( n \) represents the number of unpaired electrons in the d orbitals of the transition metal ion. This formula specifically considers the spin angular momentum without taking other effects into account.

For the complex \([\text{CoF}_{6}]^{3-}\), cobalt is in a +3 oxidation state, typically leading us to assume a \(d^5\) electron configuration. Thus, one might predict a magnetic moment of \( \sqrt{5(5+2)} \approx 5.92 \mu_B \). However, the experimental observation is \(5.63 \mu_B \).

This discrepancy often arises because the spin-only formula does not take into account other phenomena such as orbital contribution or spin-orbit coupling, which can affect the actual distribution of electron spins and result in a different magnetic moment.

Ligand field effects

Ligand field effects refer to changes in the electronic structure of metal ions due to the presence of surrounding ligands. These effects can significantly influence the magnetic and optical properties of coordination complexes. In the context of \([\text{CoF}_{6}]^{3-}\), fluoride ligands create a specific type of field around the cobalt ion.

In more detail, ligand field theory helps us understand how ligands alter the degenerate energy levels of the d orbitals on the central metal ion by splitting these levels. Depending on the nature of the ligands and the geometry of the complex, this resultant splitting can lead to differences in the arrangement of electrons and thus affect the magnetic properties.

• For \([\text{CoF}_{6}]^{3-}\), the observed magnetic moment being lower than the spin-only value suggests additional contributions from factors like spin-orbit coupling.
• Spin-orbit coupling results from the interaction between electrons' spin and their motion around the nucleus, further altering the magnetic behavior.

Overall, ligand field effects highlight why it's crucial to consider more than just electron spin when predicting and understanding the magnetic properties of coordination complexes.

Chirality in coordination complexes

Chirality in coordination complexes refers to the ability of complexes to have non-superimposable mirror images, similar to how left and right hands are chiral. This characteristic is crucial in coordination chemistry as it impacts how these complexes interact with other chiral entities, such as biological molecules.

Among the complexes given, cis-\([\text{Co}( ext{en})_{2} ext{Cl}_{2}]^{+}\) is chiral because it can exist as two enantiomers - mirror image isomers that can't be superimposed. Each enantiomer can potentially rotate plane-polarized light differently, a property exploitable in various applications.

On the other hand:

• \([\text{Ni}( ext{acac})_{3}]^{-}\)
• \([\text{CoCl}_{3}( ext{NCMe})]^{-}\)
• trans-\([\text{Cr}( ext{en})_{2} ext{Cl}_{2}]^{+}\)

are not chiral because they lack the geometrical complexity needed for chirality or possess a center of symmetry, making them and their mirror images superimposable. Understanding which complexes can form racemates (mixtures of enantiomers) is vital for fields like pharmaceuticals, where chirality can significantly affect drug activity.

Molecular orbital theory

Molecular orbital (MO) theory provides a powerful way to rationalize the bonding within a molecule by considering how atomic orbitals combine to form molecular orbitals. This theory helps explain the behavior of molecules by analyzing the distribution and energy of electrons.

In the case of the complex \([\text{(CN)}_{5} \text{CoOOCo(CN)}_{5}]^{6-}\), the MO approach offers insights into the oxidation process and bonding changes. When the complex undergoes one-electron oxidation:

• The electron enters an antibonding orbital associated with the \(\text{O}-\text{O}\) bond.
• This additional electron occupancy in an antibonding orbital weakens the bond, leading to a shortening of the \(\text{O}-\text{O}\) bond's length."

MO theory thus aids in explaining the structural changes observed upon oxidation, by highlighting the effect of electron distribution across different orbitals.