Question

The CrF_ $4-$ ion is known to have four unpaired electrons. Does the ${\mathrm{F}}^{-}$ ligand produce a strong or weak field?

Short answer

The CrF₄⁻ ion has a tetrahedral geometry with a Chromium (Cr) atom at the center in the 0 oxidation state. The electronic configuration of Cr in this complex leads to the presence of four unpaired electrons distributed across the higher and lower energy d orbitals after crystal field splitting occurs. Since more unpaired electrons occupy the higher energy orbitals, this indicates that the F⁻ ligand produces a weak field.

Step-by-step solution

Determine the central metal ion and its oxidation state

We need to first identify the central metal ion in the given complex ion. In this case, it's Chromium (Cr). Then, we should determine the oxidation state of the central metal ion in the complex. Since the fluorine ligands have a charge of -1 each, and the overall charge of the complex ion is -1, the oxidation state of Cr is: $$C{r}^{(4-4)}=C{r}^0$$

Identify the electronic configuration of the central metal ion

Now, we look at the electronic configuration of Cr. The atomic number of Cr is 24, and its electronic configuration is: $$1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{5}4s^1$$ Since the oxidation state of Cr in the complex is 0, the electronic configuration remains the same. The electrons in the 3d and 4s orbitals are the most relevant to the problem at hand.

Determine the coordination number and geometry of the complex

The CrF₄⁻ ion is a tetrahedral complex, as it has four F⁻ ligands surrounding the central Cr atom. Therefore, its coordination number is 4.

Analyze the crystal field splitting in the complex

For tetrahedral complexes, the crystal field splitting separates the d orbitals into a higher energy set of three orbitals (d(xy), d(xz), and d(yz)) and a lower energy set of two orbitals (d(z^2) and d(x^2-y^2)). In CrF₄⁻, the four unpaired electrons can be arranged in the d orbitals as follows: - Three electrons in the higher energy set (d(xy), d(xz), d(yz)) - One electron in the lower energy set (d(z^2) or d(x^2-y^2)) As there are more unpaired electrons in the higher energy orbitals than in the lower energy orbitals, this indicates that the crystal field splitting is relatively small and that the F⁻ ligand results in a weak field.

Conclude whether the F⁻ ligand produces a strong or weak field

The presence of four unpaired electrons in the CrF₄⁻ ion, which mainly occupy the higher energy 3d orbitals after crystal field splitting, indicates a weak field created by the F⁻ ligands.

Key concepts

Coordination Chemistry

Coordination chemistry explores how central metal ions bind with molecules called ligands, forming complex structures. These complexes are formed when ligands donate electrons to the metal, creating coordinate covalent bonds. In the case of the CrF₄⁻ ion, chromium (Cr) acts as the central metal ion.
The number of ligands attached to the central metal determines the coordination number, which influences the geometry of the complex. Here, with four fluoride ions ($F^{-}$), the coordination number is 4, resulting in a tetrahedral geometry.
This tetrahedral geometry affects how the d-orbitals of the metal ion split into different energy levels when ligands are present. Understanding these concepts is essential for predicting the behavior and properties of coordination compounds.

Electronic Configuration

The electronic configuration of an atom describes the distribution of electrons among the atomic orbitals. Chromium, with an atomic number of 24, has the configuration $1s^{2}ext2s^{2}ext2p^{6}ext3s^{2}ext3p^{6}ext3d^{5}ext4s^1$before bonding. In the CrF₄⁻ complex, the oxidation state of chromium remains unchanged as 0, so the electron configuration stays the same.
In coordination chemistry, the focus is particularly on the d-orbitals, as these play a crucial role in bonding and determining the properties of the complex. In CrF₄⁻, the 3d orbitals are partially filled with five electrons. This is significant in analyzing how the ligands affect the metal's electron cloud, influencing the crystal field splitting and the field strength of the ligands.

Ligand Field Strength

Ligand field strength is a measure of how much a ligand can split the d-orbitals of a central metal ion in a complex. This is assessed through crystal field splitting, where d-orbitals are divided into different energy levels upon interaction with ligands.
Ligands can be classified as strong or weak field by their ability to cause larger or smaller splittings respectively. In tetrahedral complexes like CrF₄⁻, the splitting is generally less pronounced compared to octahedral complexes. Fluoride ($F^{-}$) is typically a weak field ligand. This means it only causes a small separation between the higher and lower energy d-orbital sets, resulting in more unpaired electrons.
In the CrF₄⁻ ion, this weak ligand field results in four unpaired d electrons, confirming the weak field nature of $F^{-}$ ligands within this complex structure. Understanding these differences in ligand field strength helps to predict magnetic and spectroscopic properties of coordination compounds.