To determine which compound is most stable, we need to consider the factors that contribute to the stability of coordination compounds.$\newline$Stability of coordination compounds is influenced by:$\newline$• The nature of the ligands: Strong field ligands form more stable complexes.$\newline$• The oxidation state of the metal: Higher oxidation states generally lead to more stable complexes.$\newline$• The chelate effect: Chelating ligands form more stable complexes compared to monodentate ligands.$\newline$Let's analyze each option:$\newline$Option 1: [Co(NH$_3$)$_4$Br$_2$]NO$_3 \newline$• Contains $NH_3$ (a neutral ligand) and Br$^-$ (a weak field ligand).$\newline$• No chelating ligands present.$\newline$Option 2: [Co(NH$_3$)$_5($NO$_3$)$_3] \newline$• Contains $NH_3$ and NO$_3^-$ (a weak field ligand).$\newline$• No chelating ligands present.$\newline$Option 3: [CoCl$_2$(en)$_2$]NO$_3 \newline$• Contains $Cl^-$ (a weak field ligand) and $en$ (ethylenediamine, a bidentate ligand).$\newline$• The presence of $en$ provides a chelate effect, increasing stability.$\newline$Option 4: [Co(NH$_3$)$_6]_2($SO$_4$)$_3 \newline$• Contains only $NH_3$ ligands, no chelating effect.$\newline$Analyzing the options, Option 3 is the most stable due to the chelate effect provided by the bidentate ligand $en. \newline$Therefore, the correct option is Option 3.