Problem 124 - A Complete Resource Book in Chemistry for JEE Main

Question

The most stable ion is \([\mathbf{2 0 0 2}]\) (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) \(\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}\)

Step-by-Step Solution

Answer

The most stable ion is (c) \([\mathrm{Fe} (\mathrm{CN})_{6}]^{3-}\) due to strong ligand field stabilization.

Step 1: Determine the Oxidation State of Iron

For each complex, we need to determine the oxidation state of iron (Fe). In all the given options, the charge on the complex is known, while ligands have specific charges: OH has a charge of -1, Cl has a charge of -1, CN has a charge of -1, and H2O is neutral. Let's calculate the oxidation state (OS) for Fe in each complex:(a) \([\mathrm{Fe} (\mathrm{OH})_{5}]^{3-}\): Let OS of Fe = x. \(x + 5(-1) = -3 \implies x = +2\).(b) \([\mathrm{FeCl}_{6}]^{3-}\): Let OS of Fe = x. \(x + 6(-1) = -3 \implies x = +3\).(c) \([\mathrm{Fe} (\mathrm{CN})_{6}]^{3-}\): Let OS of Fe = x. \(x + 6(-1) = -3 \implies x = +3\).(d) \([\mathrm{Fe}(\mathrm{H}_{2}\mathrm{O})_{6}]^{3+}\): Let OS of Fe = x. \(x + 6(0) = +3 \implies x = +3\).

Key Concepts

Iron complex oxidation state

In coordination chemistry, identifying the oxidation state of the central metal atom is crucial. The oxidation state gives insight into how many electrons are lost or gained by the atom in forming a compound.
For iron (Fe), we need to examine each ligand's charge within a complex ion. Ligands are atoms or molecules bound to a central metal atom, and they typically carry specific charges.

• In \([ ext{Fe}( ext{OH})_5]^{3-}\), each OH ligand has a charge of -1. The overall charge of the complex is -3, so the calculation for the oxidation state of Fe is: \(x + 5(-1) = -3\). Solving this gives \(x = +2\), meaning iron is in the +2 oxidation state here.
• For \([ ext{FeCl}_6]^{3-}\), with each Cl ion at -1, the equation is \(x + 6(-1) = -3\). Thus, \(x = +3\), indicating the iron is +3.
• Similarly, in \([ ext{Fe}( ext{CN})_6]^{3-}\), where each CN has a charge of -1, we find \(x = +3\) from \(x + 6(-1) = -3\).
• Ligands like \(H_2O\) in \([ ext{Fe}( ext{H}_{2} ext{O})_6]^{3+}\) are neutral, meaning the oxidation state is determined solely based on the overall positive charge, which directly gives \(x = +3\).

This detailed step allows you to calculate the iron's oxidation state in any given complex.

Iron coordination complexes

Coordination complexes involve a central metal atom, like iron, surrounded by molecules or ions known as ligands. Ligand selection and arrangement can greatly impact the properties and behavior of the coordination complex.
Iron coordination complexes, in particular, are crucial in various biological and chemical systems. These complexes exhibit unique characteristics based on:

• Type of Ligand: Ligands can be monodentate, binding through a single point, or multidentate, attaching at multiple points. For example, \(OH\), Cl, and CN are typically monodentate.
• Geometrical Configuration: The spatial arrangement of ligands around the central metal can affect its stability and reactivity. For example, octahedral is a common arrangement in these complexes.
• Charge and Size: Although the overall charge impacts solubility and reactivity, ligand size can influence the complex's sterics and overall stability.

Understanding these factors helps in predicting and manipulating the chemical behavior of iron coordination complexes.

Complex ion stability

Complex ion stability is determined by several factors, including ligand type, charge, and geometry. Stability is the tendency of a complex ion to remain intact without decomposing into its constituent parts.
In comparing the given iron complexes:

• Ligands like CN⁻ are strong field ligands, which can form very stable complexes by causing greater splitting in d-orbitals, leading to higher energy stabilization.
• Charge on the complex also plays a role. Higher positive charges can increase attraction between the ligand and metal ions, contributing to overall stability.
• Geometrically, stable configurations are often associated with maximizing ligand-metal interactions. An octahedral shape is commonly effective at achieving this in resonance with the number of interactions.

For the given complexes, \( [ ext{Fe}( ext{CN})_6]^{3-} \) is noted for its high stability due to the strong field nature of CN⁻ ligands and the favored electronic arrangement. Recognizing these aspects outlines why some complexes are favored over others in chemical reactions and applications.