Problem 27 - Chemistry and Chemical Reactivity

Question

For the high-spin complex \(\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right] \mathrm{SO}_{4},\) identify the following. (a) the coordination number of iron (b) the coordination geometry for iron (c) the oxidation number of iron (d) the number of unpaired electrons (e) whether the complex is diamagnetic or paramagnetic

Step-by-Step Solution

Answer

(a) 6, (b) octahedral, (c) +2, (d) 4, (e) paramagnetic.

Step 1: Determine the Coordination Number

The coordination number is the number of ligands attached to the central metal ion. In \(\left[\mathrm{Fe}\left(\mathrm{H}_{2}\mathrm{O}\right)_{6}\right]^ {2+}\), there are 6 water molecules, thus the coordination number is 6.

Step 2: Identify the Coordination Geometry

Common geometries for coordination numbers are determined by the number of ligands. For a coordination number of 6, the geometry is typically octahedral. Therefore, the coordination geometry is octahedral.

Step 3: Find the Oxidation Number of Iron

The complex has a neutral sulfate ion \(\mathrm{SO}_4^ {2-}\), leading to the formula of the complex ion being \(\left[\mathrm{Fe}\left(\mathrm{H}_{2}\mathrm{O}\right)_{6}\right]^ {2+}\). The oxidation number of iron can be found by balancing the charges: water is neutral, so the oxidation number is +2.

Step 4: Count the Number of Unpaired Electrons

Iron in the +2 oxidation state is \(\mathrm{Fe}^{2+}\). The electron configuration of \(\mathrm{Fe}\) is \([\mathrm{Ar}]\,3d^6\,4s^2\). Fe loses 2 electrons from the 4s orbital, leaving \([\mathrm{Ar}]\,3d^6\). As it is a high-spin complex, all 5 d-orbitals participate equally according to Hund's rule, resulting in 4 unpaired electrons.

Step 5: Determine Magnetic Properties

A complex is diamagnetic if all electrons are paired and paramagnetic if there are unpaired electrons. Since \(\left[\mathrm{Fe}\left(\mathrm{H}_{2}\mathrm{O}\right)_{6}\right]^{2+}\) has 4 unpaired electrons, it is paramagnetic.

Key Concepts

Coordination Number

In coordination chemistry, the coordination number refers to the number of ligand atoms bonded to the central metal ion. For the complex \[ ext{[Fe(H}_2 ext{O})}_6 ext{]}^{2+} \], the iron ions are surrounded by six water molecules. Therefore, the coordination number of iron in this complex is 6. It is a straightforward calculation where each ligand, in this case, water, acts as a single point of attachment. The number of ligands directly attached indicates the coordination number, a vital concept as it influences the overall structure and stability of the complex.

Coordination Geometry

Coordination geometry describes the spatial arrangement of the ligands that are attached to the central metal ion. When a coordination number is given, typical geometries are easily predicted. For a coordination number of 6, as seen in \[ ext{[Fe(H}_2 ext{O})}_6 ext{]}^{2+} \], the most common geometry is octahedral. This arrangement optimally spaces out the six ligands to minimize repulsion and maximize stability. Think of it like placing the ligands at the vertices of an octahedron, which, in three-dimensional space, allows for equal positioning around the metal center. This tendency highlights the natural three-dimensional symmetry taken by atoms in coordination complexes.

Oxidation Number

The oxidation number is crucial in understanding the charge distribution within the complex. It represents the hypothetical charge that the central atom would have if all ligands were removed, along with the pairs of electrons shared with them. For \[ ext{[Fe(H}_2 ext{O})}_6 ext{]}^{2+} \], we need to determine the oxidation state of iron. Since water is a neutral ligand, it does not affect the oxidation state. The sulfate ion \[ ext{SO}_4^{2-} \] balances the \[ ext{[Fe(H}_2 ext{O})}_6 ext{]}^{2+} \] complex, computing to an oxidation number of +2 for iron. This charge is inferred from the overall charge of the complex and helps infer other properties like reactivity and interaction with external agents.

Unpaired Electrons

Unpaired electrons are electrons in an atom's orbital that remain unpaired. In coordination complexes, unpaired electrons can directly influence the magnetic properties. For iron in the \[ ext{[Fe(H}_2 ext{O})}_6 ext{]}^{2+} \] complex, in its +2 oxidation state, its electron configuration becomes \[ [ ext{Ar}]3d^6 \]. In high-spin complexes like this, following Hund's rule, we place electrons in each of the five 3d orbitals before any pairing occurs. This leads to 4 unpaired electrons. Detecting the number of unpaired electrons involves examining the electron configuration while considering the spin state of the complex, which can indicate if the complex behaves as a high or low-spin system.

Magnetic Properties

The magnetic properties of coordination complexes are directly linked to the presence of unpaired electrons. A compound is diamagnetic if all its electrons are paired, resulting in no net magnetic field. In contrast, it's paramagnetic if there are one or more unpaired electrons, which create a magnetic moment. For the \[ ext{[Fe(H}_2 ext{O})}_6 ext{]}^{2+} \] complex, having 4 unpaired electrons means it is paramagnetic. This property explains why such complexes get attracted by external magnetic fields. Understanding whether a substance is paramagnetic or diamagnetic helps predict its behavior in magnetic fields, which can have significant practical applications, especially in chemical and material science fields.