Problem 25 - Chemistry and Chemical Reactivity

Question

Determine the number of unpaired electrons in the following tetrahedral complexes. All tetrahedral complexes are high spin. (a) \(\left[\mathrm{FeCl}_{4}\right]^{2-}\) (c) \(\left[\mathrm{MnCl}_{4}\right]^{2-}\) (b) \(\mathrm{Na}_{2}\left[\mathrm{CoCl}_{4}\right]\) (d) \(\left(\mathrm{NH}_{4}\right)_{2}\left[\mathrm{ZnCl}_{4}\right]\)

Step-by-Step Solution

Answer

(a) 4 unpaired, (b) 3 unpaired, (c) 5 unpaired, (d) 0 unpaired.

Step 1: Determine the oxidation state of the metal

For each complex, count the charge contributed by the ligands and calculate the charge on the metal atom. (a) In \( \left[\mathrm{FeCl}_{4}\right]^{2-} \), each Cl contributes \(-1\), total \(-4\). Therefore, \( \text{Oxidation state of Fe} = +2 \). (b) In \( \mathrm{Na}_{2}\left[\mathrm{CoCl}_{4}\right] \), each Cl contributes \(-1\), total \(-4\), and there's \( \text{charge of 0} \). Therefore, \( \text{Oxidation state of Co} = +2 \). (c) In \( \left[\mathrm{MnCl}_{4}\right]^{2-} \), each Cl contributes \(-1\), total \(-4\). Therefore, \( \text{Oxidation state of Mn} = +2 \). (d) In \( \left(\mathrm{NH}_{4}\right)_{2}\left[\mathrm{ZnCl}_{4}\right] \), each Cl contributes \(-1\), total \(-4\), net \(0\). Therefore, \( \text{Oxidation state of Zn} = +2 \).

Step 2: Determine the electron configuration of the metal ion

Calculate the number of d-electrons based on the oxidation state derived in Step 1.(a) \( \text{Fe}^{2+} \): Has 6 d-electrons (from \([\text{Ar}]3d^6\)).(b) \( \text{Co}^{2+} \): Has 7 d-electrons (from \([\text{Ar}]3d^7\)).(c) \( \text{Mn}^{2+} \): Has 5 d-electrons (from \([\text{Ar}]3d^5\)).(d) \( \text{Zn}^{2+} \): Has 10 d-electrons (from \([\text{Ar}]3d^{10}\)).

Step 3: Determine the number of unpaired electrons

Tetrahedral complexes are high spin, meaning they don't pair electrons that could remain unpaired. (a) \( \text{Fe}^{2+} \): With 6 electrons, \([\uparrow\downarrow,\, \uparrow\downarrow,\, \uparrow,\, \uparrow]\), resulting in 4 unpaired.(b) \( \text{Co}^{2+} \): With 7 electrons, \([\uparrow\downarrow,\, \uparrow\downarrow,\, \uparrow,\, \uparrow,\, \uparrow]\), resulting in 3 unpaired.(c) \( \text{Mn}^{2+} \): With 5 electrons, \([\uparrow,\, \uparrow,\, \uparrow,\, \uparrow,\, \uparrow]\), resulting in 5 unpaired.(d) \( \text{Zn}^{2+} \): With 10 electrons, \([\uparrow\downarrow,\, \uparrow\downarrow,\, \uparrow\downarrow,\, \uparrow\downarrow,\, \uparrow\downarrow]\), resulting in 0 unpaired.

Key Concepts

Tetrahedral Complex

Tetrahedral complexes feature a specific geometric arrangement where four ligands surround a central metal ion. Unlike octahedral complexes, tetrahedral complexes typically have ligands positioned at the four corners of a tetrahedron.
This means the angles between the ligands are approximately 109.5 degrees. Because of their shape, tetrahedral complexes often do not form strong crystal fields, meaning that electron pairing energy and crystal field splitting are less significant compared to octahedral arrangements.

• This often leads to high spin configurations.
• Electrons prefer to remain unpaired if possible in these complexes.

This property greatly influences the magnetic and spectral characteristics of the compounds.

Unpaired Electrons

Unpaired electrons are simply electrons in the d-orbitals that do not find a pair. These unpaired electrons can lead to magnetic properties, such as paramagnetism, in a compound. The more unpaired electrons a compound has, the stronger its magnetic properties will be.
In high spin tetrahedral complexes, like those mentioned, electrons resist pairing.

• This results in the maximum number of unpaired electrons for that configuration.
• For example, as seen with \([\text{MnCl}_4]^{2-}\), there are 5 unpaired electrons due to its high spin nature.

Unpaired electrons heavily influence the color and behavior of the metal complexes.

Oxidation State

Oxidation state describes the degree of oxidation of an atom within a complex. It represents the hypothetical charge the atom would have if all bonds were completely ionic.
In coordination chemistry, determining the oxidation state is crucial for understanding the electron configuration and the number of d-electrons.

• For instance, chlorine generally contributes -1 to the overall charge.
• Each metal has a resulting oxidation state, such as +2 for \(\text{Fe}\) in \([\text{FeCl}_4]^{2-}\).

Correctly identifying the oxidation state helps predict magnetic properties and reactivity.

Electron Configuration

Electron configuration provides the distribution of electrons in an atom or molecule across different orbitals. It follows specific rules and aids in predicting the chemical properties of elements and compounds.
For transition metals in tetrahedral complexes, the configuration especially emphasizes the d-orbitals.

• For example, \(\text{Fe}^{2+}\) has the configuration \[\text{[Ar]}3d^6\] indicating 6 electrons in the d-orbitals.
• This becomes significant when predicting unpaired electrons.

Understanding these configurations is essential for grasping the metal's reactivity, coloration, and magnetic behavior, especially in high spin scenarios.