Werner's Theory of Coordination Compounds

Long before any electronic theory of bonding existed, the Swiss chemist Alfred Werner correctly worked out the structure of coordination compounds in 1893, using purely chemical evidence: how many ions a given compound produces when dissolved, measured by its electrical conductivity and by how many moles of $\text{AgCl}$ precipitate when it is treated with excess silver nitrate solution.

Werner's key postulate was that a metal in a coordination compound exhibits two distinct kinds of valence simultaneously:

The primary valence is the ordinary, ionizable valence — it corresponds directly to the oxidation state of the metal, is satisfied only by negative ions, and (crucially, in Werner's original formulation) is non-directional, meaning it is not associated with any fixed geometric position in space. Groups satisfying the primary valence are free to dissociate as simple ions in solution.

The secondary valence is a fixed, non-ionizable valence that corresponds to what is now called the coordination number. It is satisfied by neutral molecules or by negative ions, is always a fixed number for a given metal (6 for $\text{Co}^{3+}$ or $\text{Cr}^{3+}$, for example), and — unlike the primary valence — is directional, meaning the groups satisfying it occupy definite, fixed positions in space around the metal, giving rise to a specific geometric shape (an octahedron, for a secondary valence of 6). Every group satisfying the secondary valence sits inside the coordination sphere and does not dissociate as a free ion in solution.

Applying this to $\text{CoCl}_3.6\text{NH}_3$: cobalt's primary valence is 3 (matching its $+3$ oxidation state) and its secondary valence is 6. All six $\text{NH}_3$ molecules satisfy the secondary valence — they occupy the six fixed octahedral positions directly bonded to cobalt — while all three $\text{Cl}^-$ ions satisfy the primary valence, remaining as free, ionizable counter ions outside the coordination sphere. The correct formula is therefore $[\text{Co}(\text{NH}_3)_6]\text{Cl}_3$, and consistent with this, the compound precipitates all three chlorides as $\text{AgCl}$ (3 moles) when treated with excess $\text{AgNO}_3$, and its solution conducts as a 1:3 electrolyte (four ions total per formula unit: one complex cation and three free $\text{Cl}^-$). …