Problem 42 - Chemistry and Chemical Reactivity

Question

For the low-spin complex [Fe(en) \(\left._{2} \mathrm{Cl}_{2}\right]\) 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) +2 (b) 6 (c) Octahedral (d) 0 (e) Diamagnetic (f) 2 isomers.

Step 1: Determine Oxidation Number of Iron

In this complex, ethylenediamine (en) is a neutral ligand and chloride (Cl) is a monodentate ligand. The outer chloride also contributes a -1 charge. Assuming the oxidation state of Fe as x, the overall charge of the complex ion is zero. The equation is: \( x + 2(0) + 2(-1) = 0 \) leading to \( x = +2 \). Therefore, the oxidation number of iron is +2.

Step 2: Find Coordination Number of Iron

The coordination number is determined by the number of ligand atoms directly attached to the metal center. Ethylenediamine (en) is a bidentate ligand, so 2 en ligands contribute 4 coordination sites. Additionally, there are 2 chloride ions making a total coordination number of 6.

Step 3: Identify Coordination Geometry

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

Step 4: Determine Number of Unpaired Electrons

Fe is in the +2 oxidation state which means it is a d^6 system. In a low-spin octahedral complex, electrons fill t2g orbitals first, resulting in a low spin state configuration of t2g^6 eg^0 with no unpaired electrons.

Step 5: Determine Magnetic Property

Since there are no unpaired electrons in this low-spin complex configuration, the complex is diamagnetic.

Step 6: Count Geometric Isomers

The complex [Fe(en)2Cl2]+ can have geometric isomers because en is a bidentate ligand. Due to the possibility of 'cis' and 'trans' arrangements of chlorine ligands in the octahedral structure, there are 2 geometric isomers.

Key Concepts

Oxidation Number

The oxidation number of an element in a chemical compound tells us how many electrons it has gained or lost compared to its elemental form. For the complex \([\text{Fe(en)}_{2}\text{Cl}_{2}]\)Cl, we start by understanding that ethylenediamine (en) is a neutral ligand, providing no charge, while chloride (Cl) bears a single negative charge. In this compound, the oxidation state of iron (Fe) can be calculated by setting up an equation based on the charge contributions:

• Ethylenediamine (en) contributes nothing to the charge as it is neutral.
• Each chloride ion contributes a -1 charge.
• The entire complex has a neutral charge externally, meaning it sums to zero.

Thus, if we let \( x \) be the oxidation state of iron, the equation becomes \( x + 2(0) + 2(-1) = 0 \). Therefore, solving for \( x \), we find that the iron in this complex is in the +2 oxidation state.

Coordination Number

The coordination number in a coordination complex refers to the number of ligand atoms that are directly bonded to the central metal atom. In \([\text{Fe(en)}_{2}\text{Cl}_{2}]\)Cl, ethylenediamine (en) acts as a bidentate ligand. Bidentate means each en molecule can form two bonds with the metal center. Since there are two ethylenediamine molecules, they contribute four coordination sites in total. The two chloride ions each contribute one coordination site, making for a total sum of six coordination sites around iron.

Simply put, the coordination number of iron in this complex is six, indicating that there are six atoms bound directly to the central iron atom.

Low-Spin Complex

Low-spin complexes arise in coordination chemistry when the splitting of energy levels (due to the crystal field splitting) within the d orbitals is significant enough that electrons pair in the lower-energy orbitals (t\(_{2g}\)) before occupying higher-energy ones (e\(_g\)). This phenomenon typically occurs in the presence of strong field ligands and can affect the magnetic properties of the compound.

For the iron (II) complex \([\text{Fe(en)}_{2}\text{Cl}_{2}]\)Cl, the d electrons of the Fe\(^{2+}\) are arranged as t\(_{2g}^6\). This means all six electrons fill the lower-energy t\(_{2g}\) orbitals completely, and the higher-energy e\(_g\) orbitals remain empty, resulting in a low-spin configuration with no unpaired electrons. Consequently, this low-spin state makes the complex diamagnetic, as there are no unpaired electrons to contribute to magnetic behavior.

Geometric Isomers

Geometric isomerism in coordination compounds occurs due to different spatial arrangements of ligands around the central metal atom, leading to isomers with unique properties. In octahedral complexes, such as \([\text{Fe(en)}_{2}\text{Cl}_{2}]^+\), geometric isomers can emerge based on how bidentate ligands like ethylenediamine (en) and monodentate ligands like chloride (Cl) are positioned.

• Cis Isomer: The chloride ligands are adjacent to each other, paired on the same side of the octahedron.
• Trans Isomer: The chloride ligands are situated opposite one another, across the octahedron.

In our specific complex, these spatial arrangements of ligands form two unique geometric isomers: cis and trans, each with distinct properties. Understanding these configurations is crucial in predicting and explaining the physical and chemical behavior of the complex.