The number of water molecule(s) directly bonded to the metal centre in \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}\) is ___.

Copper(II) sulfate pentahydrate is a vibrant blue crystal commonly used in chemistry labs and various industrial processes. What makes it distinct is not just its color, but its structure: the ‘pentahydrate’ part of the name tells us that each copper sulfate unit is associated with five water molecules.

The formula c(CuSO4 cdot 5H2O) unveils the composition: copper (IICu2n), sulfate (xxSO4nn), and the five water molecules (5H2O). When looking at this compound, it’s tempting to think that the water is merely mixed with the copper sulfate, but that’s not the case; instead, these water molecules are in a coordinated dance with the copper ions, directly influencing the compound's properties and behavior.

Coordination compounds, such as copper(II) sulfate pentahydrate, are defined by the specific arrangement of their molecules and ions around a central metal atom or ion. In these compounds, the central metal ion — in this case, copper (IICu2n) — acts like a hub for surrounding ligands (molecules or ions that donate pairs of electrons).

In copper(II) sulfate pentahydrate, water serves as the ligand, creating a coordination complex with the copper ion at the center. This intimate relationship is designated by the dot separating the copper sulfate part of the formula from the water molecules. It signifies that the water molecules are directly bonded to the copper, not loosely associated as in a mixture. These coordination bonds are integral to the chemical's characteristic behavior and properties.

A crystal lattice is the three-dimensional arrangement of atoms, ions, or molecules in a crystalline material. Imagine it like a precisely organized grid in which each point on the grid is occupied by an atomic or ionic component. The crystal lattice defines the structural integrity and the physical properties of the material.

In the crystal lattice of copper(II) sulfate pentahydrate, the copper ions, sulfate ions, and water molecules form a specific geometric arrangement. This arrangement is not random; the positions are dictated by the interactions between these units - like the coordination bonds between copper ions and water molecules. In this structured network, the water molecules are coordinated directly to the copper, which impacts how the substance will behave, such as in its solubility, formation of hydrates, and interactions with other chemicals.