Step 1: Understanding the Concept:
In hydrated copper(II) sulfate (\( CuSO_4 \cdot 5H_2O \)), the five water molecules are not bonded identically to the central metal ion or the lattice.
Step 2: Detailed Explanation:
The actual structure of blue vitriol is represented as \( [Cu(H_2O)_4]SO_4 \cdot H_2O \).
1. Four water molecules are coordinated directly to the \( Cu^{2+} \) ion in a square planar arrangement, forming coordinate covalent bonds.
2. The fifth water molecule is not directly attached to the copper ion. Instead, it is trapped in the crystal lattice.
3. This fifth water molecule is held in place by hydrogen bonds to the oxygen atoms of the sulfate (\( SO_4^{2-} \)) ion and the coordinated water molecules.
Step 3: Final Answer:
The number of hydrogen-bonded water molecules is 1.