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Q5.30:
Amongst the following, the most stable complex is

Solution :

Initial Data and Theoretical Foundation

To determine the most stable coordination complex among a series, we must evaluate the Chelate Effect and the nature of the ligands involved. Stability in coordination complexes is defined by the equilibrium constant for the formation of the complex ($K_f$).

The complexes under consideration for comparison typically involve different denticity levels of ligands. A chelate ring formation significantly increases stability compared to monodentate ligands due to a favorable change in entropy ($\Delta S > 0$) [Per the Second Law of Thermodynamics].

Step 1: Analyzing the Chelate Effect

The stability of a complex increases with the number of chelate rings formed. A polydentate ligand (such as ethylenediamine or EDTA) forms more stable complexes than monodentate ligands (such as $NH_3$ or $H_2O$) because the displacement of monodentate ligands by a polydentate ligand increases the number of free particles in the solution, thereby increasing the entropy of the system.

Step 2: Mathematical Justification of Stability

The Gibbs free energy change ($\Delta G^\circ$) for the formation of a complex is given by:

$\Delta G^\circ = \Delta H^\circ - T\Delta S^\circ = -RT \ln K_f$

As the number of chelate rings increases, $\Delta S^\circ$ becomes more positive, leading to a larger negative $\Delta G^\circ$, which corresponds to a significantly larger $K_f$ value [Per the thermodynamic definition of spontaneity].

Step 3: Comparative Analysis

Consider the common set of complexes compared in this academic context:

Complex Ligand Type Number of Rings Stability Trend
$[Fe(H_2O)_6]^{3+}$ Monodentate 0 Low
$[Fe(en)_3]^{3+}$ Bidentate 3 High
$[Fe(EDTA)]^{-}$ Hexadentate 5 Very High

Step 4: Geometric Representation of a Chelate Complex

Fe en (bidentate) en (bidentate)

Final Determination

Amongst typical coordination compounds, the complex with the highest denticity ligand, such as $[Fe(EDTA)]^{-}$ or complexes involving $en$ (ethylenediamine), is the most stable because it forms the maximum number of chelate rings, creating the most pronounced entropic stabilization effect [Per the Chelate Effect Principle].

Final Solution: The most stable complex is the one involving polydentate ligands (specifically those forming the highest number of chelate rings), as it maximizes entropic favorability and thermodynamic stability constant $K_f$.


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