Which of the following gives the correct order of stability constant in the solution?

$[Cr(NH_3)_6]^{3+}<[Cr(en)_3]^{3+}$

The correct answer is Option (1) → $[Cr(NH_3)_6]^{3+}<[Cr(en)_3]^{3+}$.

The stability constant (or formation constant, \(K_f\)) of a complex ion measures the tendency of the complex to form and remain intact in solution. A higher stability constant indicates a more stable complex.

Analysis of Each Pair:

(1) [Cr(NH₃)₆]³⁺ < [Cr(en)₃]³⁺

[Cr(NH₃)₆]³⁺**: In this complex, ammonia (NH₃) acts as a monodentate ligand, meaning it binds to the metal through only one donor atom (nitrogen in NH₃).

[Cr(en)₃]³⁺: Ethylenediamine (en) is a bidentate ligand, meaning it binds through two donor atoms (both nitrogens in the molecule). Bidentate ligands generally form chelate rings with the metal ion, increasing the stability of the complex due to the chelate effect

Chelate Effect: Complexes with multidentate ligands (like ethylenediamine) are typically more stable than those with monodentate ligands due to the increased number of bonds formed between the metal and the ligand.

Therefore, [Cr(en)₃]³⁺ is more stable than [Cr(NH₃)₆]³⁺, making this statement correct.

(2) [Ni(CO)₄] < [NiCl₄]²⁻

[Ni(CO)₄]: Carbon monoxide (CO) is a strong π-acceptor ligand, which forms very stable complexes with transition metals.

[NiCl₄]²⁻: Chloride (Cl⁻) is a relatively weak ligand compared to CO. It doesn’t have the strong π-accepting capabilities that stabilize the metal complex

Since CO is a much stronger ligand than Cl⁻, [Ni(CO)₄] is more stable than [NiCl₄]²⁻, so this statement is incorrect

(3) [Sn(en)₃]³⁺ < [Sn(H₂O)₆]³⁺

[Sn(en)₃]³⁺: Again, ethylenediamine (en) is a bidentate ligand and forms a chelate complex

[Sn(H₂O)₆]³⁺: Water (H₂O) is a monodentate ligand and forms a less stable complex compared to bidentate ligands.

Due to the chelate effect, [Sn(en)₃]³⁺ is expected to be more stable than [Sn(H₂O)₆]³⁺, so this statement is incorrect.

(4) [Cr(NH₃)₆]³⁺ < [Cr(H₂O)₆]³⁺

[Cr(NH₃)₆]³⁺: Ammonia is a stronger ligand than water in terms of the ligand field strength

[Cr(H₂O)₆]³⁺: Water is a weaker ligand compared to ammonia.

Since NH₃ is a stronger ligand than H₂O, [Cr(NH₃)₆]³⁺ is more stable than [Cr(H₂O)₆]³⁺, making this statement incorrect.

Conclusion:

The correct order of stability is given by [Cr(NH₃)₆]³⁺ < [Cr(en)₃]³⁺ due to the chelate effect of ethylenediamine compared to the monodentate nature of ammonia.