The thermodynamic stability of a coordination compound in aqueous...

The thermodynamic stability of a coordination compound is indicated by its overall formation constant ($\beta$). Higher stability corresponds to a higher formation constant.

Among the given ligands, ethylenediamine ($en$) is a bidentate ligand, while $NH_3$, $H_2O$, and $Cl^-$ are monodentate ligands.

When a bidentate or polydentate ligand coordinates to a metal ion, it forms a ring structure called a chelate ring. The formation of chelate rings significantly increases the stability of the complex compared to similar complexes with monodentate ligands. This phenomenon is known as the chelate effect, which is primarily an entropy-driven process.

In the formation of $[Ni(en)_3]^{2+}$, three $en$ molecules replace six water molecules from the coordination sphere of the aqueous nickel ion, increasing the total number of particles in the system and leading to a highly positive change in entropy ($\Delta S$).

Therefore, due to the chelate effect, $[Ni(en)_3]^{2+}$ is the most stable complex and has the highest overall formation constant.

Answer: $[Ni(en)_3]^{2+}$