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 \(\left[\mathrm{FeCl}_{6}\right]^{3-}\), more stability is shown by (a) \([\mathrm{FeCl}]^{3-}\) (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 \([\mathrm{Fe}(\mathrm{CN})_6]^{3-}\), due to strong field stabilization from \(\mathrm{CN}^-\).

Step 1: Identify the Ligands

Determine the ligands present in each complex. Ligands are the molecules or ions that surround the central metal ion in a coordination compound.- In \([\mathrm{Fe} \left(\mathrm{H}_2 \mathrm{O}\right)_6]^{3+}\), the ligand is \(\mathrm{H}_2 \mathrm{O}\).- In \([\mathrm{Fe}(\mathrm{CN})_6]^{3-}\), the ligand is \(\mathrm{CN}^-\).- In \([\mathrm{Fe}\left(\mathrm{C}_2 \mathrm{O}_4\right)_3]^{3-}\), the ligand is \(\mathrm{C}_2 \mathrm{O}_4^{2-}\) (oxalate).- In \([\mathrm{FeCl}_6]^{3-}\), the ligand is \(\mathrm{Cl}^-\).

Step 2: Consider Ligand Field Stabilization

Recognize that certain ligands can cause a greater splitting of the d-orbitals in the central metal, leading to increased stability in the complex.- \(\mathrm{CN}^-\) is a strong field ligand and causes a significant splitting of the d-orbitals.- \(\mathrm{C}_2 \mathrm{O}_4^{2-}\) is a moderate field ligand.- \(\mathrm{H}_2\mathrm{O}\) is a weak field ligand.- \(\mathrm{Cl}^-\) is also a weak field ligand.

Step 3: Apply the Chelate Effect

Evaluate the chelate effect, which explains how ligands that form rings with the central ion increase the stability of the complex.- \([\mathrm{Fe}(\mathrm{C}_2 \mathrm{O}_4)_3]^{3-}\) forms chelate rings because \(\mathrm{C}_2 \mathrm{O}_4^{2-}\) is a bidentate ligand.- No chelation occurs in \([\mathrm{Fe}(\mathrm{CN})_6]^{3-}\), \([\mathrm{Fe} \left(\mathrm{H}_2 \mathrm{O}\right)_6]^{3+}\), or \([\mathrm{FeCl}_6]^{3-}\).

Step 4: Compare Stabilization from Field Strength and Chelate Effect

Combine the effects of the ligand field and chelate effect to determine which complex is the most stable.- Strong field ligands increase stability due to higher ligand field stabilization energy; \(\mathrm{CN}^-\) is strongest.- The chelate effect strongly stabilizes \([\mathrm{Fe}(\mathrm{C}_2 \mathrm{O}_4)_3]^{3-}\) due to the formation of stable rings.- Given that \(\mathrm{CN}^-\) provides significant stabilization through strong field effects, \([\mathrm{Fe}(\mathrm{CN})_6]^{3-}\) is considered highly stable.

Key Concepts

Ligand Field Stabilization

The concept of ligand field stabilization is crucial in determining the stability of coordination compounds. It refers to the energy changes that occur when a metal ion interacts with surrounding ligands through its d-orbitals. Ligands can either be strong field or weak field, which affects how the d-orbitals of the metal ion are split.
- **Strong field ligands**, like cyanide ion ( ext{CN}^-), cause a large splitting of the d-orbitals. This results in greater stabilization energy. - **Weak field ligands**, such as water ( ext{H}_2 ext{O}) and chloride ( ext{Cl}^-), cause lesser splitting and therefore, provide less stabilization energy.
The degree of splitting is directly related to the nature of the ligands. Thus, complexes with strong field ligands are generally more stable. In our example,  ext{Fe}( ext{CN})_6^{3-} is stable because of the strong field effect of  ext{CN}^-, resulting in significant ligand field stabilization energy.

Chelate Effect

Chelate effect is another critical factor that influences the stability of coordination compounds. It refers to the increased stability of complexes containing multidentate ligands (ligands that can attach to a metal atom at several points).
One prime example is the oxalate ion ( ext{C}_2 ext{O}_4^{2-}), which is a bidentate ligand. This means it can bind to the central metal ion through two donor atoms, forming rings known as chelate rings. This multiple attachment creates a more stable complex.

• Bidentate or multidentate ligands tend to increase the entropy of the system because they replace more species in the coordination sphere.
• A chelate complex, such as  ext{Fe}( ext{C}_2 ext{O}_4)_3^{3-}, benefits from such a stabilization, making it more robust compared to complexes with similar monodentate ligands.

Thus, the chelate effect significantly contributes to the stability of complexes, as seen with oxalate forming multiple bonding interactions with iron in  ext{Fe}( ext{C}_2 ext{O}_4)_3^{3-}.

Complex Stability

Complex stability in coordination chemistry is determined by factors like ligand field stabilization and the chelate effect. A stable coordination compound is one where the individual components remain together under various conditions.
The concept of complex stability is integral to understanding why certain complexes are more robust than others. Specific factors include:

• **Field Strength of Ligands:** Strong field ligands provide increased stability due to higher ligand field stabilization energies.
• **Chelation:** Multidentate ligands like oxalate increase stability due to ring formation, which usually results in additional stability.

For example,  ext{Fe}( ext{CN})_6^{3-} is very stable because it contains a strong field ligand ( ext{CN}^-), leading to high stabilization. Conversely,  ext{Fe}( ext{C}_2 ext{O}_4)_3^{3-}, despite lacking strong field ligands, gains stability from the chelate effect. Therefore, both the field strength and chelation contribute to the overall stability of a complex.

Ligand Identification

Identifying ligands in a coordination compound is the first step in understanding its stability. Ligands are ions or molecules that donate a pair of electrons to the central metal ion, forming a coordination bond. Each ligand has its characteristics that influence the overall stability of the compound.
Examples from our exercise include:

•  ext{H}_2 ext{O} as a weak field ligand in  ext{Fe}( ext{H}_2 ext{O})_6^{3+}.
•  ext{CN}^- as a strong field ligand in  ext{Fe}( ext{CN})_6^{3-}.
•  ext{C}_2 ext{O}_4^{2-}, bidentate with its ability to form chelate rings, in  ext{Fe} ext{(C}_2 ext{O}_4 ext{)}_3^{3-}.
•  ext{Cl}^- as a weak field ligand in  ext{FeCl}_6^{3-}.

Recognizing ligands helps predict their effects on the metal ion's electron configuration and the complex's resulting stability. This helps chemists design more stable coordination compounds by selecting appropriate ligands for the desired stability and reactivity.