Problem 44 - Chemistry and Chemical Reactivity

Question

For the low-spin coordination compound \(\left[\mathrm{Fe}(\mathrm{en})_{2} \mathrm{Cl}_{2}\right] \mathrm{Cl}\) identify the following. (a) the oxidation number of iron (b) the coordination number for iron (c) the coordination geometry for iron (d) the number of unpaired electrons per metal atom (e) whether the complex is diamagnetic or paramagnetic (f) the number of geometric isomers

Step-by-Step Solution

Answer

(a) +3 (b) 6 (c) octahedral (d) 1 unpaired electron (e) paramagnetic (f) 2 geometric isomers.

Step 1: Determine the Oxidation Number of Iron

In the compound \([ ext{Fe}( ext{en})_2 ext{Cl}_2] ext{Cl}\), the ligands "en" (ethylenediamine) are neutral, and each chlorine ion has a charge of \(-1\). Given an overall neutral compound, let's find the oxidation state of iron. Let the oxidation state of iron be \(x\). The equation will be: \[x + 2(0) + 2(-1) = +1.\] Solving for \(x\), \[x = +3.\] Therefore, the oxidation number of iron is \(+3\).

Step 2: Determine the Coordination Number of Iron

In our complex, there are two ethylenediamine ligands and two chlorides attached to the iron. Ethylenediamine is a bidentate ligand, meaning it coordinates through two atoms. So, the coordination number is given by: 2 (from two chlorides) + 4 (from two ethylenediamine ligands) = 6. Therefore, the coordination number is 6.

Step 3: Identify the Coordination Geometry of Iron

With a coordination number of 6, the most common geometry is octahedral. Therefore, the coordination geometry for iron in this compound is octahedral.

Step 4: Determine the Number of Unpaired Electrons

For \( ext{Fe}^{3+}\), the electron configuration after losing 3 electrons is \([Ar] 3d^5\). In a low-spin complex with strong field ligands like ethylenediamine, all d-orbitals are filled as low energy as possible before any are singly occupied, resulting in 1 unpaired electron. Therefore, the number of unpaired electrons is 1.

Step 5: Determine if the Complex is Diamagnetic or Paramagnetic

Since there is one unpaired electron, the complex is paramagnetic as opposed to diamagnetic, which would be the case if there were zero unpaired electrons.

Step 6: Determine the Number of Geometric Isomers

In the octahedral complex \([ ext{Fe}( ext{en})_2 ext{Cl}_2]\), there can be cis(identical ligands adjacent) and trans(identical ligands opposite) forms. Hence, there are 2 geometric isomers possible for this complex.

Key Concepts

Oxidation Number

The oxidation number represents the charge of a metal in a coordination compound, assuming all bonds are ionic. In the compound \([\mathrm{Fe}(\mathrm{en})_{2}\mathrm{Cl}_{2}]\mathrm{Cl}\), we are solving for the oxidation state of iron (Fe).
Ethylenediamine (en) is a neutral ligand and each chloride ion (Cl) has a charge of -1. To maintain overall neutrality, we calculate the oxidation state of Fe using:

• \(x + 2(0) + 2(-1) = +1\)

Solving for \(x\), we find that iron's oxidation number is \(+3\). This means that Fe effectively has lost three electrons in its interactions within the compound.

Coordination Number

The coordination number of a metal ion in a coordination compound is the total number of ligand-to-metal coordinate bonds. In \([\mathrm{Fe}(\mathrm{en})_{2}\mathrm{Cl}_{2}]\), the iron ion is bound to ligands as follows:

• Ethylenediamine (en) acts as a bidentate ligand, meaning it uses two donor atoms to bind to the metal ion. There are two en ligands contributing a total of four coordinates.
• There are also two monodentate chloride ions contributing one coordinate each.

Thus, the coordination number for iron in this complex is 6. This count tells us how many atoms are directly bonded to the central iron atom.

Coordination Geometry

Coordination geometry describes the shape formed by the ligands attached to a central metal ion. The geometry depends on the coordination number. For the iron complex in question, it has a coordination number of 6.

• The most common geometry associated with a coordination number of 6 is octahedral.

This shape features six ligands arranged symmetrically around the central metal, creating a roughly octahedron-like structure. This gives the compound stability and has implications for its chemical properties.

Unpaired Electrons

The number of unpaired electrons in a coordination compound affects its magnetic properties. Here, we determine the number of unpaired electrons in the low-spin complex \([\mathrm{Fe}^{3+}(\mathrm{en})_{2}\mathrm{Cl}_{2}]\).

• The electron configuration for \(\mathrm{Fe}^{3+}\) is \([\mathrm{Ar}] 3d^5\), showing five d-electrons.
• In low-spin complexes, strong field ligands like ethylenediamine cause electrons to pair up in lower energy orbitals before occupying higher ones.

This results in one unpaired electron in the d-orbital, leading to paramagnetism, as single unpaired electron contributes to magnetic behavior.

Geometric Isomers

Geometric isomerism occurs when different spatial arrangements of ligands occur around a central metal atom. In octahedral complexes like \([\mathrm{Fe}(\mathrm{en})_{2}\mathrm{Cl}_{2}]\), ligands can be positioned in different locations leading to isomers.

• The cis isomer has identical ligands (e.g., the chloride ions) adjacent to each other.
• The trans isomer features identical ligands opposite each other.

Thus, this compound can form two geometric isomers: cis and trans. This variety influences characteristics like solubility and stability.