Question

The most stable ion is (a) \(\left[\mathrm{Fe}(\mathrm{OH})_{5}\right]^{3-}\) (b) \(\left[\mathrm{FeCl}_{6}\right]^{3-}\) (c) \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}\) (d) \(\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)\right]^{3+}\)

Short answer

The most stable ion is (c) [Fe(CN)_6]^{3-} due to strong field ligands.

Step-by-step solution

Analyze Electron Configuration of Iron

Iron (Fe) has the electron configuration of \( [Ar] 3d^6 4s^2 \). When it forms ions, it commonly loses electrons from the 4s orbital first. Thus, checking the electron count in each complex will help determine stability, typically those which allow for pairing or satisfy the 18-electron rule.

Complex Stability with Ligand Field Theory

Ligand field theory provides insight into the stability based on the ligand's ability to split the d-orbitals of the metal ion. Strong field ligands like CN^- lead to low-spin configurations, which can be more stable.

Configurations of Each Complex Ion

(a) \([\text{Fe(OH)}_5]^{3-}\) has weak field ligands. (b) \([\text{FeCl}_6]^{3-}\) also has weak field ligands. (c) \([\text{Fe(CN)}_6]^{3-}\) has strong field ligands, leading to a low-spin configuration. (d) \([\text{Fe(H}_2 \text{O)}]^{3+}\) with \text{H}_2 \text{O as a neutral, weak field ligand.}

Evaluate Electron Count and Spin State

The \([\text{Fe(CN)}_6]^{3-}\) complex has CN^- ligands which are strong field, causing the size splitting to be larger than pairing energy, leading to a low-spin state and satisfying the 18-electron rule more closely, thus stabilizing the ion.

Key concepts

Ligand Field Theory

Ligand Field Theory (LFT) helps us to understand the stability and properties of coordination complexes. It explains how the ligands surrounding a central metal ion can affect the energy levels of its d-orbitals.

• When ligands are nearby, they can cause the d-orbitals of the metal to split into different energy levels.
• This split creates what's called "crystal field splitting," labeled as \( \Delta \).

The degree of splitting depends largely on the nature of the ligand.
With strong field ligands, such as CN\(^-\), the gap \( \Delta \) is larger, leading to low spin states where electrons pair up in the lower energy orbitals rather than acting singly in both higher and lower orbitals. This can result in more stable configurations since paired electrons might be energetically favored.
In contrast, weak field ligands, like OH\(^-\) and H\(_2\)O, result in smaller \( \Delta \) and often lead to high spin states. High spin complexes have more unpaired electrons because electrons are more distributed across orbitals. This can influence both magnetic properties and potential reactivity.

Electron Configuration

Understanding electron configuration is key to predicting the behavior of metals in coordination complexes.
For iron, the base configuration is \([\text{Ar}] 3d^6 4s^2\). But when iron becomes a part of a compound or ion, configurations can change, particularly when electrons are lost.

• For instance, Fe\(^{3+}\) often results from losing three electrons, usually from the 4s orbital first, followed by the 3d orbital, leading to \([\text{Ar}] 3d^5\).

Different electron configurations affect how a metal interacts with its ligands, influencing the overall stability of complexes.
Along with understanding LFT, analyzing how many electrons are in each d-orbital plays a role in determining outcomes like magnetism, color, and stability. Low-spin configurations tend toward more stable, paired electron states due to lower energy states being filled first, as observed with strong field ligands.

18-Electron Rule

The 18-Electron Rule is a useful guideline in coordination chemistry that can predict the stability of metal complexes.
Essentially, stable transition metal complexes often achieve a total electron count of 18, considering both their own electrons and those donated by ligands.
This rule is akin to achieving a full valence shell like noble gases, where d, s, and p orbitals are completely filled.

• Complex ions like \([\text{Fe(CN)}_6]^{3-}\) can reach this stable electron count by utilizing strong-field ligands to fill available orbitals efficiently.
• This can provide insights into why certain metal complexes are more stable, as adhering to this rule reduces unwanted reactivity.

While not universal, as non-18 configurations also exist widely, it's a powerful tool for understanding many trends in metal complexes.