Out of the following complex compounds, which compound will have the minimum conductance in solution?

Solution & Explanation

\textbf{Answer:} (C) $[\mathrm{Co}(\mathrm{NH}{}_3){}_3\mathrm{Cl}{}_3]$. \textbf{Solution:} Molar conductance depends on the number of ions a complex releases in solution. Only chloride ions outside the coordination sphere ionise; those bonded to the metal do not. $[\mathrm{Co}(\mathrm{NH}{}_3){}_6]\mathrm{Cl}{}_3$ $\to$ 1 cation + 3 $\mathrm{Cl}{}^{-}$ = 4 ions (highest conductance). $[\mathrm{Co}(\mathrm{NH}{}_3){}_5\mathrm{Cl}]\mathrm{Cl}{}_2$ $\to$ 1 cation + 2 $\mathrm{Cl}{}^{-}$ = 3 ions. $[\mathrm{Co}(\mathrm{NH}{}_3){}_4\mathrm{Cl}{}_2]\mathrm{Cl}$ $\to$ 1 cation + 1 $\mathrm{Cl}{}^{-}$ = 2 ions. $[\mathrm{Co}(\mathrm{NH}{}_3){}_3\mathrm{Cl}{}_3]$ $\to$ all three $\mathrm{Cl}{}^{-}$ are inside the sphere, giving a neutral non-electrolyte with 0 ions. With no ions in solution, $[\mathrm{Co}(\mathrm{NH}{}_3){}_3\mathrm{Cl}{}_3]$ has the \textbf{minimum conductance}, option (C). Note: the source key lists (d); however as written here $[\mathrm{Co}(\mathrm{NH}{}_3){}_4\mathrm{Cl}{}_2]\mathrm{Cl}$ ionises into 2 ions, so the fully neutral non-electrolyte $[\mathrm{Co}(\mathrm{NH}{}_3){}_3\mathrm{Cl}{}_3]$ (Werner's classic) is the chemically correct minimum-conductance answer, (C).