Animated Solution for Chemistry - Coordination Compounds: The secondary valency and the number of hydrogen bonded water molecules in ${\text{CuSO}}_4\cdot 5{\text{H}}_2\text{O}$, respectively, are

When we look at the simple chemical formula of blue vitriol, ${\text{CuSO}}_4\cdot 5{\text{H}}_2\text{O}$, it is easy to assume that all five water molecules are identical in their behavior and bonding. However, the microscopic reality is far more fascinating. To truly understand this molecule, we must dive into the realm of coordination chemistry and Werner's theory.

According to Alfred Werner, the father of coordination chemistry, central metal ions possess two types of valencies: primary and secondary. The primary valency corresponds to the oxidation state of the metal (which is $+2$ for copper here), while the secondary valency corresponds to the coordination number—the number of ligands directly attached to the metal via coordinate covalent bonds.

In the crystal structure of copper sulfate pentahydrate, the ${\text{Cu}}^{2+}$ ion is not surrounded by all five water molecules. Instead, it is directly bonded to exactly four water molecules in a square planar arrangement. These four water molecules reside inside the coordination sphere. Therefore, the true coordination complex is $[\text{Cu}({\text{H}}_2\text{O}{)}_4{]}^{2+}$.

Because there are exactly four water molecules directly coordinated to the copper ion, the secondary valency of copper in this compound is $4$.

If only four water molecules are coordinated to the copper ion, what happens to the fifth one?

This is where the beauty of hydrogen bonding comes into play. The fifth water molecule sits outside the primary coordination sphere. It acts as a structural bridge within the crystal lattice. On one side, its oxygen atom forms hydrogen bonds with the hydrogen atoms of the coordinated water molecules. On the other side, its own hydrogen atoms form hydrogen bonds with the oxygen atoms of the sulfate ion (${\text{SO}}_4^{2-}$).

Because this single water molecule is held in the lattice exclusively by hydrogen bonds (and not by a direct coordinate bond to the copper ion), the number of hydrogen-bonded water molecules is exactly $1$.

By dissecting the structural formula $[\text{Cu}({\text{H}}_2\text{O}{)}_4]{\text{SO}}_4\cdot {\text{H}}_2\text{O}$, we can clearly see the distinct roles of the water molecules. Four are coordinated, fulfilling the secondary valency, and one is hydrogen-bonded, stabilizing the crystal lattice.

Thus, the secondary valency is $4$, and the number of hydrogen-bonded water molecules is $1$.