Question

The complexes (a) \(\left[\mathrm{FeF}_{6}\right]^{3-}\) and (b) \(\left[\mathrm{Co}(\mathrm{ox})_{3}\right]^{4-}\) have highspin electron configurations. How many unpaired electrons are there in each complex?

Short answer

The \(\left[\mathrm{FeF}_{6}\right]^{3-}\) complex has 5 unpaired electrons. The \(\left[\mathrm{Co}(\mathrm{ox})_{3}\right]^{4-}\) complex has 4 unpaired electrons.

Step-by-step solution

Determine the electron configuration of the metal ion

Find the number of electrons for the metal ion after considering its charge. Iron (Fe) normally has 26 electrons, but in the \(\left[\mathrm{FeF}_{6}\right]^{3-}\) complex, it has a charge of +3, which means it has lost 3 electrons (26 - 3 = 23). Cobalt (Co) normally has 27 electrons, but in the \(\left[\mathrm{Co}(\mathrm{ox})_{3}\right]^{4-}\) complex, it has a charge of +3 (assuming oxalate is -2 and there are 3 oxalates, Co is left with a charge of +3 after donating 1 electron to each oxalate), which means it has lost 3 electrons (27 - 3 = 24).

Determine the crystal field splitting

Identify the geometry of the complexes and the effect of the ligands on the crystal field splitting. The complex \(\left[\mathrm{FeF}_{6}\right]^{3-}\) is presumably octahedral, meaning it has six ligands arranged symmetrically around the metal ion. High-spin configurations occur when ligands cause weak crystal field splitting, leading to more unpaired electrons. Fluoride is a weak field ligand, therefore \(\left[\mathrm{FeF}_{6}\right]^{3-}\) is high spin with unpaired electrons. The complex \(\left[\mathrm{Co}(\mathrm{ox})_{3}\right]^{4-}\) is also octahedral and oxalate is a weak field ligand, so the \(\left[\mathrm{Co}(\mathrm{ox})_{3}\right]^{4-}\) complex is high spin and has unpaired electrons.

Count the unpaired electrons

Fill the d-orbitals with electrons according to the 'Aufbau' principle, Hund's Rule, and Pauli's Exclusion Principle. For the \(\mathrm{Fe}^{3+}\) ion, there are 5 d-electrons, which will all be unpaired in a high-spin octahedral environment. For the \(\mathrm{Co}^{3+}\) ion, there are 6 d-electrons, which will result in 4 unpaired electrons in a high-spin octahedral environment.

Key concepts

Electron Configuration

Understanding electron configuration is essential for predicting the chemical properties and bonding behavior of an atom or ion. In the context of transition metal complexes, such as electron configuration refers to the distribution of electrons in an atom's orbitals after considering the number of electrons lost or gained due to ionization or bonding respectively.

Take for example, an iron ion e (symbolized as e). In its neutral state, iron has 26 electrons. With a +3 charge, as in the e complex, we subtract three electrons resulting in 23 electrons to configure. Cobalt(III) in complex case demonstrates a similar scenario, needing an electron configuration for 24 electrons.

Applying Hund's Rule, electrons fill orbitals singly before doubling up, and follow Pauli's Exclusion Principle, each orbital can hold a maximum of two electrons with opposite spins. As such, configurations for transition metals are not as straightforward as other elements due to the presence of d orbitals, which adds a layer of complexity.

Crystal Field Splitting

In transition metal complexes, ligands can interact with the d-orbitals of the central metal ion, leading to 'crystal field splitting.' This term describes how these d-orbitals, which are degenerate (of equal energy) in an isolated ion, become split into groups of higher and lower energy levels in the presence of an electric field created by approaching ligands.

The arrangement of ligands around the metal ion determines the pattern of this splitting. In octahedral complexes, like those given in the exercise (e and e), we typically see the five d-orbitals splitting into two sets: high-energy e orbitals and lower-energy e orbitals. Weak field ligands such as fluoride or oxalate do not cause a large difference between these energy sets, influencing electron distribution, and leading to high-spin configurations with maximum unpaired electrons.

High-Spin Complexes

The term 'high-spin' refers to the type of electron configuration in a metal complex, which results from crystal field splitting induced by ligands. In high-spin complexes, the energy gap between the split d-orbitals (istal field splitting energy) is small enough that electrons can occupy higher energy states rather than pairing up in lower ones.

This phenomenon occurs because electrons repel each other due to like charges and, as such, will fill up all available orbitals singly (according to Hund's Rule) before pairing up. This condition leads to a maximum number of unpaired electrons. For instance, in the e complex, iron has five d electrons, all of which remain unpaired in a weak field such as that created by fluoride ligands. The same principle applies to the cobalt ion in e with weak field oxalate ligands, resulting in four unpaired electrons. High-spin complexes are more likely to exhibit magnetic properties due to these unpaired electrons, a feature often exploited in spectroscopic analysis.