Many transition metals exhibit multiple oxidation numbers contributing to their unique properties, such as colors. But how is the metal’s oxidation number determined?

Coordination compounds are electrically neutral species consisting of a coordination complex and counterions with a primary and secondary valence.

The primary valence is the oxidation number of the metal ion. To find the oxidation number start by identifying the charges contributed by the ligands and counter ions. 

Next, sum up the charges and determine the oxidation number of the metal ion. If all ligands are neutral, the complex ion charge becomes the oxidation number of the metal ion.

The secondary valence refers to the number of ligands directly bonded to the central metal ion, also called the coordination number. Here, the coordination number of rhodium is six.

Some metal ions possess one coordination number only. Cobalt(III) and platinum(II) have a coordination number of 6 and 4. However, for many metal ions, the coordination number varies ranging from 2 to 6.

The relative size of ligands and metal ions influences the coordination number. For instance, smaller ligands like fluorine coordinate six times to iron(III), compared to the larger chlorine, which coordinates only four times. 

Negative charges imparted by ligands to the metal ion also influence the coordination number. The coordination number of nickel(II) with neutral water molecules is 6, which is reduced to 4 with anionic chloride ions.

The geometric shape of the complex ion partially depends on the coordination number of a metal ion. A complex with a coordination number of two has a linear geometry, where two ligands are 180° apart on either side of the metal ion.

A complex with a coordination number of 4 exhibits two types of geometry based on the valence electron in the d-subshell. Metal ions with eight d-electrons, such as palladium(II), are square planar. While metal ions with ten d-electrons, such as zinc(II), exhibit a tetrahedral geometry. 

A complex with a coordination number of 6 is octahedral. The six ligands occupy six vertices, four ligands form the corners of a square, and the remaining two the planes above and below at an equivalent distance. Thus, an octahedron appears as two pyramids with a common square base and eight faces.