Problem 147 - A Complete Resource Book in Chemistry for JEE Main

Question

In the complexes \(\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+},\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}, \quad[\mathbf{2 0 0 2}]\) \(\left[\mathrm{Fe}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]^{3-}\) and \([\mathrm{FeCl}]^{3}\), more stability is shown by (a) \(\left[\mathrm{FeCl}_{6}\right]^{3-}\) (b) \(\left[\mathrm{Fe}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]^{3-}\) (c) \(\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}\) (d) \(\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}\)

Step-by-Step Solution

Answer

The most stable complex is \( \left[\mathrm{Fe} (\mathrm{CN})_{6}\right]^{3-} \).

Step 1: Identify the Complexes

The problem involves comparing the stability of different iron complexes. The complexes are:1. \( \left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+} \)2. \( \left[\mathrm{Fe} (\mathrm{CN})_{6}\right]^{3-} \)3. \( \left[\mathrm{Fe}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]^{3-} \)4. \( \left[\mathrm{FeCl}_{6}\right]^{3-} \)

Step 2: Evaluate Ligand Type

Different ligands affect the stability of complexes differently. Ligands can be weak field or strong field:- \( \text{H}_2\text{O} \) is a weak field ligand.- \( \text{Cl}^- \) is a weak field ligand.- \( \text{C}_2\text{O}_4^{2-} \) (oxalate) is a moderate field ligand.- \( \text{CN}^- \) is a strong field ligand.

Step 3: Apply Crystal Field Theory

According to crystal field theory, strong field ligands such as \( \text{CN}^- \) lead to greater splitting in the d-orbitals, which generally increases the stability of the complex. Thus, complexes with stronger field ligands are more stable due to greater \Delta_\text{o} splitting, reducing the energy level and promoting stability.

Step 4: Determine Stability Based on Ligand Field Strength

Using the information from Steps 2 and 3, we see:- The complex \( \left[\mathrm{Fe} (\mathrm{CN})_{6}\right]^{3-} \) contains the strongest field ligand, \( \text{CN}^- \), which indicates that this complex will have the greatest stability.

Key Concepts

Crystal Field Theory

Crystal Field Theory is a pivotal concept in coordination chemistry that describes how metal ions interact with surrounding ligands. When ligands approach a metal ion, they create an electric field that affects the d-orbitals of the metal. This interaction causes a split in the energy levels of the d-orbitals, a process known as crystal field splitting.
The degree of splitting depends on the type of ligands surrounding the metal ion. Stronger interactions lead to larger split levels, denoted as \( \Delta_{o} \). Crystal Field Theory helps predict the electronic structuring of a complex and explains the color, magnetism, and stabilization of complexes. A larger \( \Delta_{o} \) typically suggests greater stability within a complex, as it minimizes the energy of the electrons within the d-orbitals.

Ligand Field Strength

Different ligands exert different strengths of electric fields on the metal ion, which is quantified as ligand field strength. Ligands are classified based on their field strength into weak and strong field ligands.

• Weak field ligands: These include ligands such as \( \text{H}_{2}\text{O} \) and \( \text{Cl}^{-} \). They cause smaller splitting energies \( \Delta_{o} \).
• Strong field ligands: Ligands such as \( \text{CN}^{-} \) cause significant splitting in d-orbitals, with a larger \( \Delta_{o} \).

In our exercise, \( \text{CN}^{-} \) is a strong field ligand, while \( \text{H}_{2}\text{O} \) and \( \text{Cl}^{-} \) are weak field ligands. The oxalate ion \( \text{C}_{2}\text{O}_{4}^{2-} \) presents a moderate impact on the field strength. Hence, complexes with stronger field ligands will typically show more stability because the energy required for electron transition within the complex is minimized.

Complex Stability

Complex stability refers to the overall ability of a complex to maintain its structure in solution or solid state. Several factors contribute to complex stability, such as ligand field strength and geometric configuration.
A complex is considered more stable if it has a large \( \Delta_{o} \), as seen in the strong field ligand interactions. This stabilizes the configuration of the complex by lowering the energy levels of d-electrons.
In the given complexes, [Fe(CN)\(_6\)]\( ^{3-} \) is the most stable because it features the strong field ligand, \( \text{CN}^{-} \), causing maximal orbital splitting and lower energy configurations. Conversely, complexes containing weak field ligands like [Fe(H\(_2\)O)\(_6\)]\( ^{3+} \) are typically less stable due to minimal splitting of the d-orbitals.

Iron Complexes

Iron complexes are a type of coordination compound where iron serves as the central metal ion surrounded by ligands. Iron can form complexes in various oxidation states, commonly \( +2 \) and \( +3 \) states.
Coordination compounds of iron are significant in both biological systems and industrial applications. In biological systems, iron complexes play a crucial role in oxygen transport and electron transfer in proteins.
In the original exercise, iron is present in several states, and the stability is impacted by the type of ligands and their field strength. Specifically, the complex featuring \( \text{CN}^{-} \) showcases a significantly higher stability due to the strong ligand field, while those with \( \text{H}_2\text{O} \) and \( \text{Cl}^{-} \) illustrate weaker interactions and less stability.