How to Calculate a Coordination Number

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In solid matter, atoms and molecules form a variety of geometrical structures depending on the way they combine. In each structure, a central atom shares electrons with other atoms or ionic molecules, and the shape of the structure depends on how the electrons are shared. The coordination number for the central atom is an indicator of how many atoms or molecules form bonds with it, and that is a determinant of the molecular shape and ultimately the properties of the solid. For covalently bonded molecules and transition metal complexes, chemists derive the coordination number from the chemical formula. They calculate the coordination number for metallic solids by examining the lattice structure.

Covalently Bonded Molecules

In a covalently bonded molecule, chemists determine the coordination number of the central atom by counting the number of bonded atoms. For example, in the methane molecule, the central carbon atom is bonded to four hydrogen atoms, so its coordination number is 4. This number can be readily determined from the chemical formula for methane: CH4.

The same relationship holds for ionic compounds. For example, the coordination number of the carbon trioxide molecule (CO3)2- is 3, and the charge of the ion is -2.

Transition Metal Complexes

Transition metals, which occupy columns 3 through 12 of the periodic table, form complexes with groups of atoms called ligands. The coordination of the transition metal is again given by the number of atoms with which the central atom is bonded. For example, the coordination number of the ionic compound CoCl2(NH3)4+ is 6, because the central cobalt atom bonds with two chlorine atoms and four nitrogen atoms. In FeN42+, the coordination number is 4 because that's the number of bonds formed by the central iron atom, even though the nitrogen atoms form a lattice complex by bonding with each other.

Metallic Solids

In metallic solids, there is no clear bond between pairs of atoms, so chemists determine the coordination of the structure by choosing a single atom and counting the number of atoms immediately surrounding it. For example, an atom that is part of a layer structure may have three atoms below it, three above it and six surrounding it in the same layer. The coordination number for that atom would be 12.

The atoms in a solid crystal often form themselves into geometrical structures called cells, and these cells repeat themselves ad infinitum to create the crystal structure. Deciphering the shape of the cell makes it possible to calculate the coordination number, which is the same for each atom in the structure. For example, a cubic structure has one atom in the middle surrounded by one on each corner, for a total of eight, so the coordination number is 8.

Ionic Solids

Sodium chloride (NaCl) is an example of an ionic solid, which is one formed by a cation (Na+) and an anion (Cl-). In an ionic metal, the coordination number of the cation is equal to the number of anions in close proximity to it. NaCl is a cubic structure, and each sodium cation is surrounded by four chlorine ions on the same plane, as well as one below and one above, so the coordination number is 6. For the same reason, the coordination of each chlorine anion is also 6.