Question

The \(\mathrm{CrF}_{6}{ }^{4-}\) ion is known to have four unpaired electrons. Does the \(\mathrm{F}^{-}\) ligand produce a strong or weak field?

Short answer

The $\mathrm{F}^{-}$ ligand produces a weak field in the $\mathrm{CrF}_{6}{ }^{4-}$ ion. This is because the ion has four unpaired electrons, which indicates a small energy gap between the t₂g and e_g orbitals, allowing the electrons to occupy the higher-energy orbitals without pairing up.

Step-by-step solution

Identify the central metal ion and its oxidation state

The complex ion, CrF₆⁴⁻, has chromium (Cr) as the central metal ion. To determine its oxidation state, we can use the fact that the overall charge of the complex ion is -4 and the charge ofeach fluoride ligand is -1. Let the oxidation state of Cr be x. Then, we can express the total charge as: x + 6(-1) = -4 Solving for x, we find that the oxidation state of Cr is +2.

Determine the electron configuration of the central metal ion

The atomic number of chromium is 24, which means its ground state electron configuration is [Ar] 3d⁵ 4s¹. Since Cr²⁺ has a +2 oxidation state, it loses two electrons, one from the 4s and one from the 3d orbitals. The electron configuration of Cr²⁺ is [Ar] 3d⁴.

Determine the effect of the ligand field

To determine if F⁻ produces a strong or weak field, we need to analyze the ligand field splitting in the octahedral complex. In a strong field, the d orbitals split into two groups: the lower-energy t₂g orbitals and the higher-energy e_g orbitals. This splitting results in a large energy gap (Δ) between the orbital levels. Electrons preferentially occupy the lower-energy t₂g orbitals before pairing up in the e_g orbitals. In contrast, a weak field has a smaller energy gap (Δ), and electrons can more easily occupy the higher-energy e_g orbitals. We are given that the CrF₆⁴⁻ ion has four unpaired electrons. This information suggests a weak ligand field, since a strong field would cause electron pairing, resulting in fewer unpaired electrons.

Conclude whether F⁻ is a strong or weak field ligand

Considering that the CrF₆⁴⁻ ion has four unpaired electrons, it indicates that the energy gap (Δ) between the t₂g and e_g orbitals is not large enough to force the electrons to pair up. Therefore, we can conclude that the F⁻ ligand in this complex produces a weak field.

Key concepts

Ligand Field Strength

Ligand field strength is a crucial concept in understanding how different ligands affect the electronic properties of a metal ion in a complex. The strength of the ligand field determines how the d orbitals of the metal ion will split into two sets of orbitals with different energies: the t₂g and e_g orbitals.
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In the octahedral complexes, such as \(\mathrm{CrF}_{6}{ }^{4-}\), the approach of ligands like fluoride ions (\(\mathrm{F}^{−}\)) affects how the metal ion's d orbitals split. Strong field ligands, like cyanide (\(\mathrm{CN}^{−}\)) or carbon monoxide (\(\mathrm{CO}\)), cause a significant splitting of these d orbitals. On the other hand, weak field ligands such as fluoride result in a smaller energy gap (Δ) between the t₂g and e_g orbitals.

• A strong ligand field causes more electron pairing.
• A weak ligand field results in more unpaired electrons.

The fact that the \(\mathrm{CrF}_{6}{ }^{4-}\) ion has four unpaired electrons indicates a weak ligand field because a strong field would promote electron pairing.

Electron Configuration

The electron configuration describes the distribution of electrons of an atom or ion in atomic or molecular orbitals. For the central metal ion chromium (Cr) in the complex \(\mathrm{CrF}_{6}{ }^{4-}\), understanding its electron configuration helps us predict its behavior in the complex.
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Chromium's ground state electron configuration is [Ar] 3d⁵ 4s¹. However, when Cr forms the \(\mathrm{Cr}^{2+}\) ion, it loses two electrons.

• One electron is removed from the 4s orbital.
• One electron is removed from the 3d orbital.

Thus, the electron configuration of Cr²⁺ becomes [Ar] 3d⁴. This reduced configuration plays a key role in determining the number of unpaired electrons and, consequently, the magnetic properties of the complex.

Oxidation States

Oxidation states are important for determining how electrons are distributed among the atoms in a chemical compound. In the \(\mathrm{CrF}_{6}{ }^{4-}\) ion, identifying the oxidation state of chromium helps in understanding the ion's electronic structure.
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To find the oxidation state of Cr in the complex, we use the overall charge of the ion and the charges of the ligands. The fluoride ion (\(\mathrm{F}^{-}\)) has a charge of -1, and since there are six of them in the complex, they contribute a total charge of -6. The overall charge of the complex is -4, indicating that the chromium must have a +2 oxidation state to balance the charges.

• Sum of charges: x + 6(-1) = -4
• Solving for x gives chromium an oxidation state of +2.

Recognizing this oxidation state is essential to deriving the correct electron configuration and understanding the behavior of the \(\mathrm{CrF}_{6}{ }^{4-}\) ion.

Unpaired Electrons

Unpaired electrons significantly influence the magnetic properties of a metal complex. In the case of \(\mathrm{CrF}_{6}{ }^{4-}\), the presence of four unpaired electrons gives important clues about the nature of the ligand field created by \(\mathrm{F}^{−}\) ions.
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Unpaired electrons result in a complex being paramagnetic, which means it is attracted to magnetic fields due to the lack of electron pairing. The number of unpaired electrons can be directly inferred from the electron configuration and ligand field strength.In weak field situations, such as with \(\mathrm{F}^{−}\), the energy difference (Δ) between the t₂g and e_g levels is too small to cause electron pairing within the t₂g orbitals. Consequently, you observe more unpaired electrons:

• Electrons fill all available t₂g orbitals before pairing in e_g orbitals.
• In \(\mathrm{CrF}_{6}{ }^{4-}\), this means four unpaired electrons are present, giving insight into the weak field nature of \(\mathrm{F}^{−}\).

Unpaired electrons not only affect magnetism but also provide evidence for the ligand field strength.