Problem 3 - Chemistry An Atoms First Approach

Question

Which is more likely to be paramagnetic, \(\mathrm{Fe}(\mathrm{CN})_{6}^{4-}\) or \(\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{2+} ?\) Explain.

Step-by-Step Solution

Answer

The \(\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{2+}\) complex is more likely to be paramagnetic, as it has four unpaired electrons in its 3d orbitals, while \(\mathrm{Fe}(\mathrm{CN})_{6}^{4-}\) has only one unpaired electron in the 4s orbital. This is due to the weak-field ligand (H2O) bonding in the \(\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{2+}\) complex not resulting in the pairing of electrons in its d-orbitals, while strong-field ligand (CN-) bonding in the \(\mathrm{Fe}(\mathrm{CN})_{6}^{4-}\) complex does.

Step 1: Finding the oxidation state of iron in each complex

Let's find the oxidation state of iron (Fe) in each complex. In the complex \(\mathrm{Fe}(\mathrm{CN})_{6}^{4-}\): Each CN ligand has a charge of -1, so the overall charge due to the 6 CN ligands is -6. Since the net charge of the complex is -4, the charge on iron must be: \[+2\ (\text{for balancing the overall charge})\] In the complex \(\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{2+}\): Each H2O ligand has a charge of 0. Since the net charge of the complex is +2, the charge on iron must be: \[+2\ (\text{as given by the complex})\]

Step 2: Analyzing the electron configurations of iron in each complex

Now, let's analyze the electron configurations of iron. In both complexes, the oxidation state of iron is +2, which means it has lost 2 electrons from its neutral state of Fe (\(\text{atomic number}=26\)). The electron configuration of neutral iron is: \[[\text{Ar}] 3d^6 4s^2\] After losing 2 electrons, the electron configuration of Fe(II) will be: \[[\text{Ar}] 3d^6\]

Step 3: Determine unpaired electrons in the d-orbitals

Now we need to determine the number of unpaired electrons in the d-orbitals of both complexes. For \(\mathrm{Fe}(\mathrm{CN})_{6}^{4-}\): The Fe(II) ion in this complex undergoes strong-field ligand (CN-) bonding, which results in the pairing of electrons in its d-orbitals. Its electron configuration becomes: \[[\text{Ar}] 3d^5 4s^1\] (Note that there is only one unpaired electron in the 4s orbital) For \(\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{2+}\): The Fe(II) ion in this complex undergoes weak-field ligand (H2O) bonding, which does not result in the pairing of electrons in its d-orbitals. Its electron configuration remains: \[[\text{Ar}] 3d^6\] (Note that there are four unpaired electrons in the 3d orbitals)

Step 4: Comparing the unpaired electrons in both complexes

We have determined the number of unpaired electrons in both complexes: - In \(\mathrm{Fe}(\mathrm{CN})_{6}^{4-}\), there is only one unpaired electron in the 4s orbital. - In \(\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{2+}\), there are four unpaired electrons in the 3d orbitals. Since the \(\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{2+}\) complex has more unpaired electrons, it is more likely to be paramagnetic.

Key Concepts

Electron Configuration

Electron configuration is a representation of the distribution of electrons in an atom or ion across various energy levels and orbitals. Electrons occupy orbitals of increasing energy, following the Pauli Exclusion Principle and Hund's Rule. For a neutral iron atom with an atomic number of 26, the electron configuration is

• n i.e., \([ ext{Ar}] 3d^6 4s^2\). When iron loses two electrons to form the Fe(II) oxidation state, it becomes \([ ext{Ar}] 3d^6\).

The configuration helps determine an atom's chemical behavior, including its reactivity and bonding properties. Iron in both complexes starts with 6 d-electrons in its configuration after losing the two 4s electrons, essential for understanding its paramagnetism.

Oxidation State

In chemistry, the oxidation state of an element within a compound indicates the degree of oxidation or reduction of that element. Essentially, it describes the number of electrons an atom gains, loses, or shares when bonding with other atoms. For the iron complexes, determining the oxidation state is key to understanding their electronic arrangement.

• In \( \mathrm{Fe}( \mathrm{CN})_{6}^{4-} \), iron is in the +2 oxidation state because the 6 CN- ligands contribute a negative charge of -6, and the complex itself carries a -4 charge, resulting in iron having a +2 charge.
• In \( \mathrm{Fe}\left( \mathrm{H}_{2} \mathrm{O}\right)_{6}^{2+} \), iron is also in the +2 oxidation state since water is a neutral ligand and the complex exhibits a +2 charge as a whole.

These charges influence the electrons' arrangement, dictating the magnetic properties of the compounds.

Unpaired Electrons

The presence of unpaired electrons in an atom or ion is a central factor in determining its paramagnetic properties. An unpaired electron is one that does not have a partner electron with an opposite spin in its orbital, contributing to the magnetic moment.

• For the complex \( \mathrm{Fe}( \mathrm{CN})_{6}^{4-} \), the strong-field ligand CN- leads to a pairing of electrons within the d-orbitals, resulting in a single unpaired electron.
• In contrast, \( \mathrm{Fe}\left( \mathrm{H}_{2} \mathrm{O}\right)_{6}^{2+} \) has weak-field ligands (water), leaving four unpaired d-electrons.

This difference in unpaired electrons makes \( \mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{2+}\) paramagnetic, as the more unpaired electrons there are, the stronger the magnetic effect.

Ligand Field Theory

Ligand field theory (LFT) provides a framework for understanding the splitting of d-orbitals in transition metal complexes involving ligands. By examining how ligands affect the distribution of electrons, LFT can predict the magnetic and optical properties of a complex.

• Ligands like CN- are considered strong-field ligands. They cause significant splitting of d-orbitals, pairing electrons, and often leading to a low-spin configuration, as seen in \( \mathrm{Fe}( \mathrm{CN})_{6}^{4-} \).
• Ligands such as water are weak-field, which results in a smaller d-orbital splitting and a high-spin configuration, where electrons remain unpaired, as observed in \( \mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{2+}\).

The nature of the ligands surrounding a metal center plays a crucial role in determining the properties and reactivity of the metal complex, including its paramagnetic behavior.