Assigning Oxidation States Example Problem

The oxidation state of an atom in a molecule refers to the degree of oxidation of that atom. Oxidation states are assigned to atoms by a set of rules based on the arrangement of electrons and bonds around that atom. This means each atom in the molecule has its own oxidation state which could be different from similar atoms in the same molecule.
These examples will use the rules outlined in Rules for Assigning Oxidation Numbers.

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What Are the Rules for Assigning Oxidation Numbers?

By Anne Marie Helmenstine, Ph.D.

Problem: Assign oxidation states to each atom in H₂O
According to rule 5, oxygen atoms typically have an oxidation state of -2.
According to rule 4, hydrogen atoms have an oxidation state of +1.
We can check this using rule 9 where the sum of all oxidation states in a neutral molecule is equal to zero.
(2 x +1) (2 H) + -2 (O) = 0 True
The oxidation states check out.
Answer: The hydrogen atoms have an oxidation state of +1 and the oxygen atom has an oxidation state of -2.
Problem: Assign oxidation states to each atom in CaF₂.
Calcium is a Group 2 metal. Group IIA metals have an oxidation of +2.
Fluorine is a halogen or Group VIIA element and has a higher electronegativity than calcium. According to rule 8, fluorine will have an oxidation of -1.
Check our values using rule 9 since CaF₂ is a neutral molecule:
+2 (Ca) + (2 x -1) (2 F) = 0 True.
Answer: The calcium atom has an oxidation state of +2 and the fluorine atoms have an oxidation state of -1.
Problem: Assign oxidation states to the atoms in hypochlorous acid or HOCl.
Hydrogen has an oxidation state of +1 according to rule 4.
Oxygen has an oxidation state of -2 according to rule 5.
Chlorine is a Group VIIA halogen and usually has an oxidation state of -1. In this case, the chlorine atom is bonded to the oxygen atom. Oxygen is more electronegative than chlorine making it the exception to rule 8. In this case, chlorine has an oxidation state of +1.
Check the answer:
+1 (H) + -2 (O) + +1 (Cl) = 0 True
Answer: Hydrogen and chlorine have +1 oxidation state and oxygen has -2 oxidation state.
Problem: Find the oxidation state of a carbon atom in C₂H₆. According to rule 9, the sum total oxidation states add up to zero for C₂H₆.
2 x C + 6 x H = 0
Carbon is more electronegative than hydrogen. According to rule 4, hydrogen will have a +1 oxidation state.
2 x C + 6 x +1 = 0
2 x C = -6
C = -3
Answer: Carbon has a -3 oxidation state in C₂H₆.
Problem: What is the oxidation state of the manganese atom in KMnO₄?
According to rule 9, the sum total of oxidation states of a neutral molecule equal zero.
K + Mn + (4 x O) = 0
Oxygen is the most electronegative atom in this molecule. This means, by rule 5, oxygen has an oxidation state of -2.
Potassium is a Group IA metal and has an oxidation state of +1 according to rule 6.
+1 + Mn + (4 x -2) = 0
+1 + Mn + -8 = 0
Mn + -7 = 0
Mn = +7
Answer: Manganese has an oxidation state of +7 in the KMnO₄ molecule.
Problem: What is the oxidation state of the sulfur atom in the sulfate ion - SO₄^2-.
Oxygen is more electronegative than sulfur, so the oxidation state of oxygen is -2 by rule 5.
SO₄^2- is an ion, so by rule 10, the sum of the oxidation numbers of the ion is equal to the charge of the ion. In this case, the charge is equal to -2.
S + (4 x O) = -2
S + (4 x -2) = -2
S + -8 = -2
S = +6
Answer: The sulfur atom has an oxidation state of +6.
Problem: What is the oxidation state of the sulfur atom in the sulfite ion - SO₃^2-?
Just like the previous example, oxygen has an oxidation state of -2 and the total oxidation of the ion is -2. The only difference is the one less oxygen.
S + (3 x O) = -2
S + (3 x -2) = -2
S + -6 = -2
S = +4
Answer: Sulfur in the sulfite ion has an oxidation state of +4.