Occasionally, it may be necessary to determine the oxidation state or valence of an ion in a compound from its formula. This situation is often encountered with compounds or polyatomic complexes containing transition metal ions, which may have multiple oxidation states. A simple algebraic equation solves the problem, as illustrated in Example 1.4.

Example 1.4

Find the oxidation state or valence of each underlined atom.

A. KMnO4

B. (Cr2O7)^{2-}

Solution

Here, it is necessary to know the oxidation states assigned to common “fixed” elements. Some guidelines include the following:

• Alkali metals are 1+.

• Alkaline earth metals are 2+.

• Oxygen is generally 2-.

• Halides are generally 1-.

Set up a simple algebraic equation based on the principle that the sum of known charges of individual atoms in the formulas, multiplied by their respective subscripts, must total the net charge on the formula unit of the compound or polyatomic ion.

A. For KMnO4:

Note that x represents the unknown oxidation state of the Mn atom. The total is set to zero because the formula unit is electronically neutral or uncharged.

Solve for x: x = +7

Thus, the oxidation state of Mn in KMnO4 is +7.

B. For (СГ2О7)^{2-}:

Note that the x represents the unknown oxidation state of the Cr atom. The total is set to -2 because the net charge on the complex is -2.

Solve for x: x = +6.

Thus, the oxidation state of Cr in (&2O7)^{2-} is +6.