Question

Give explanations for the following observations. (a) The complex \(\left[\mathrm{Co}(\mathrm{en})_{2} \mathrm{Cl}_{2}\right]_{2}\left[\mathrm{CoCl}_{4}\right]\) has a room temperature magnetic moment of \(3.71 \mu_{\mathrm{eff}}\) (b) The room temperature magnetic moment of \(\left[\mathrm{CoI}_{4}\right]^{2-}\) (e.g. \(5.01 \mu_{\mathrm{B}}\) for the \(\left[\mathrm{Et}_{4} \mathrm{N}\right]^{+}\) salt) is larger than that of salts of \(\left[\mathrm{CoCl}_{4}\right]^{2-}\)

Short answer

The mixed oxidation states and geometries of cobalt complexes lead to the observed magnetic moments.

Step-by-step solution

Understanding the Magnetic Moment

The magnetic moment (3.71 1_{6} 1_{0}") provided for the complex 3[6o(6n)_2 1_{1}_2]4[6o1_{1}]1 is essentially a measure of the unpaired electrons present in the system. Typically, the number of unpaired electrons can be related to the observed magnetic moment using the formula: \( \mu_{\text{eff}} = \sqrt{n(n+2)} \) where \(n\) is the number of unpaired electrons.

Analyzing the Cobalt Complex Structures

The complex 3[6o(6n)_2 1_{1}_2]4[6o1_{1}]1 likely shows that cobalt exists in different oxidation states or geometries, leading to differing numbers of unpaired electrons. The 1ion frequently has a tetrahedral configuration while the other parts could have square planar or distorted coordination leading to mixed spin states responsible for the net magnetic moment.

Assessing the Geometry of [CoI4]2-

The complex 3[6o1_{0}]^{2-}1, having a larger magnetic moment than 3[6o1_{0}]^{2-}1 with electrolytes, indicates a higher number of unpaired electrons. Comparing salts, the larger sized iodide ions in 1 introduces more delocalization of d-electrons and potentially causes a geometry that maximizes the separation between orbitals, thereby encouraging more unpaired electrons which contribute to the magnetic moment.

Key concepts

Cobalt Complex Structures

Cobalt complexes are fascinating because their structures determine their magnetic properties and electronic behavior. Cobalt can exist in various oxidation states and adopt different geometries in its coordination complexes. Here are some key points to consider:

• In the complex \([\mathrm{Co} (\mathrm{en})_2 \mathrm{Cl}_2]_2[\mathrm{CoCl}_4]\), there are likely different environments for cobalt ions which affect their electronic configurations.
• The "en" ligand, short for ethylenediamine, is a bidentate ligand. It chelates the metal center and influences the electronic environment by altering the oxidation state and d-electron configuration.
• Cobalt commonly exhibits two oxidation states in complexes—the +2 and +3 states. These result in low-spin or high-spin configurations, impacting the number of unpaired electrons.

These variations in oxidation states and geometries of cobalt within complexes lead to differences in magnetic properties, which are observed through techniques like Magnetic Moment Calculation.

Magnetic Moment Calculation

The magnetic moment is an insightful property of coordination compounds, reflecting the electronic dynamics within them. It is a dipole moment that provides valuable information about the unpaired electrons around the central atom. Here's how it connects to cobalt complexes:

• The formula for calculating the magnetic moment \( \mu_{\text{eff}} = \sqrt{n(n+2)} \) is based on the number of unpaired electrons \(n\).
• For the complex \([\mathrm{Co} (\mathrm{en})_2 \mathrm{Cl}_2]_2[\mathrm{CoCl}_4]\), the magnetic moment at room temperature was observed to be 3.71 \(\mu_{\mathrm{eff}}\), suggesting a specific configuration of electrons. This translates to approximately three unpaired electrons.
• Differences in the observed magnetic moments of related complexes like \([\mathrm{CoI}_4]^{2-}\) relate to how geometrical changes impact electron pairing and distribution.

This information allows chemists to infer the electronic structure of the metal center, and therefore, the behavior of the compound under various conditions.

Geometry of Coordination Complexes

The geometry of coordination complexes significantly influences their magnetic properties. The arrangement of ligands around a central metal atom determines the energy splitting of d-orbitals, directly affecting the number of unpaired electrons. Here's how it applies to cobalt complexes:

• Coordination geometries such as tetrahedral, square planar, or octahedral are common in cobalt complexes. Each geometry results in a different electronic configuration and, consequently, magnetic moment.
• For instance, in tetrahedral geometry as in \([\mathrm{CoI}_4]^{2-}\), iodide ions create a field that leads to a higher magnetic moment due to the greater number of unpaired electrons.
• Contrast this with a square planar geometry, which often results in low-spin configurations that possess fewer unpaired electrons, impacting the strength of the magnetic moment.

The choice of ligand, its size, and electronegativity can either stabilize high-spin states or induce low-spin formations, altering the magnetic properties of coordination compounds.