Which complex compound is the most stable?

Solution & Explanation

\textbf{Answer:} (C) $[\mathrm{CoCl}{}_2(\mathrm{en}){}_2]\mathrm{NO}{}_3$. \textbf{Solution:} The key factor is the \textbf{chelate effect}: complexes containing bidentate (chelating) ligands that form rings are markedly more stable than those with only monodentate ligands. In $[\mathrm{CoCl}{}_2(\mathrm{en}){}_2]\mathrm{NO}{}_3$, the two ethylenediamine (en) ligands are bidentate and each forms a stable five-membered chelate ring with the cobalt centre. This chelation gives a large positive entropy contribution and a high stability constant. The other options contain only monodentate ligands ($\mathrm{NH}{}_3$, $\mathrm{H}{}_2\mathrm{O}$, $\mathrm{Br}{}^{-}$, $\mathrm{NO}{}_3{}^{-}$) and lack chelate rings, so they are less stable. Hence the chelated complex $[\mathrm{CoCl}{}_2(\mathrm{en}){}_2]\mathrm{NO}{}_3$ is the most stable, option (C).