Q.$\text{CoCl}_3.6\text{NH}_3$, $\text{CoCl}_3.5\text{NH}_3$, and $\text{CoCl}_3.4\text{NH}_3$ give 3, 2, and 1 mole of $\text{AgCl}$ respectively on treatment with excess $\text{AgNO}_3$ solution. Using Werner's theory, write the correct formula for each compound and explain the trend.

[!TLDR] As NH$_3$ count drops, Cl$^-$ moves inside the coordination sphere to keep the secondary valence at 6, leaving fewer free (ionizable) Cl$^-$ outside. [!ANSWER] $[\text{Co}(\text{NH}_3)_6]\text{Cl}_3$ (3 free Cl$^-$) $\to$ $[\text{Co}(\text{NH}_3)_5 …

Cobalt's secondary valence (coordination number) is fixed at 6 in all three compounds, regardless of exactly which groups fill those six positions. In $\text{CoCl}_3.6\text{NH}_3$, all six secondary-valence positions are filled by the six $\text{NH}_3$ molecules, leaving all three $\text{Cl}^-$ free (satisfying the primary valence): $[\text{Co}(\text{NH}_3)_6]\text{Cl}_3$, giving 3 mol $\text{AgCl}$. In $\text{CoCl}_3.5\text{NH}_3$, only five $\text{NH}_3$ molecules are available, so one $\text{Cl}^-$ must move inside the coordination sphere to complete the fixed secondary valence of 6; this leaves only two $\text{Cl}^-$ free: $[\text{Co}(\text{NH}_3)_5\text{Cl}]\text{Cl}_2$, giving 2 mol $\text{AgCl}$ (the coordinated chloride, bonded directly to cobalt, does not react with $\text{AgNO}_3$ under these conditions). In $\text{CoCl}_3.4\text{NH}_3$, only four $\text{NH}_3$ molecules are available, so two $\text{Cl}^-$ must move inside to complete the secondary valence of 6, leaving just one $\text{Cl}^-$ free: $[\text{Co}(\text{NH}_3)_4\text{Cl}_2]\text{Cl}$, giving 1 mol $\text{AgCl}$. The clear trend is that the metal's coordination number never changes, but as fewer neutral $\text{NH}_3$ ligands are available to fill it, progressively more chloride ions are pulled from bein …

Keep the coordination number (secondary valence) fixed at 6 for cobalt in every compound; fill it first with all available $\text{NH}_3$, then with however many $\text{Cl}^-$ are needed to reach 6; whatever $\te …

Assuming the coordination number itself changes across the series (e.g. treating the last compound as coordination number 4) — the secondary valence stays fixed at 6 for coba …