What is an oxidation number and how can you calculate it?

Answer

Dear Ariana,

In principle, the answer is simple, but some caveats need to be made:

The oxidation number is a (hypothetical) net charge of an atom in a molecule, obtained by assigning the electrons in each chemical bond between two different elements to the most electronegative atom.

This is a tricky sentence that becomes easier to understand if we break the definition down into a few steps:

1. Draw the Lewis structure of the molecule and determine the formal charges of the atoms. (I assume you already can.)

2. To get the oxidation number of each atom in a molecule, start from the formal charges and perform a charge transfer for each bond between two different elements as follows:

• Count a charge -N on the most electronegative element in the bond.
• Add a charge +N to the least electronegative element in the bond.

Here N is the bond order: 1 for a single bond, 2 for a double bond, 3 for a triple bond. The Pauling electronegativity scale is usually used, see for example http://ptable.com/#Property/Electronegativity. The oxidation state is just a concept, introduced mainly to understand redox reactions.

If you need to calculate oxidation numbers for your exam or for homework, use a few rules of thumb to check your result:

• The sum of the formal charges is equal to the net charge of the molecule.
• The sum of the oxidation numbers is also equal to the net charge of the molecule.
• Oxygen almost always has oxidation stage -2.
• Hydrogen almost always has oxidation stage +1.
• If you are allowed to use a Mendeleev table, you will usually find the possible oxidation states of each element there. If you arrive at an oxidation state for a given element that is not on Mendeleev’s table, then your solution may be wrong.

A few caveats are now in order, because the above definition is not foolproof! Here are the two biggest problems:

1. One cannot draw a clear Lewis structure in all cases. The Lewis model for the chemical bond is only a very simplified description. In practice, there are many molecules and materials where not all chemical bonds can be located as a pair of electrons between two atoms. In such cases, you cannot simply apply the above rules.
2. There are many different electronegativity scales, for example those of Pauling, those of Allen, those of Mulliken, etc. These different scales are not compatible with each other and therefore the concept of oxidation number is not rigorously defined. Most textbooks work with the Pauling scale, but that’s just an arbitrary choice.

In an effort to solve the second problem, the IUPAC (International Union of Pure and Applied Chemistry) has introduced a different definition. (See http://goldbook.iupac.org/O04365.html) This IUPAC calculation does not use electronegativity, but relies on ad hoc conventions and agreements. This definition also has its problems. It is not applicable to many molecules; For example, things already go wrong with the simplest molecule, the hydrogen gas cation (H₂⁺). (This is a molecule with only 1 electron and is therefore often called the simplest molecule, especially in theoretical chemistry.) An additional flaw of the IUPAC definition is that it takes away all insight into the underlying concepts such as electronegativity.

The ambiguity of the concept of oxidation number is also nicely illustrated by a recent attempt to introduce a rigorous definition in the scientific literature, see http://dx.doi.org/10.1103/physrevlett.108.166403. The authors of this article claim to have found a completely conclusive definition, but the arguments in this article remain debatable. You also notice it in the meta-data of the article: it took three years of discussion before the article was accepted for publication. (This is unusually long. Normally this takes up to several months.)

From a purely philosophical point of view, it also makes little sense to introduce a rigorous definition for a “hypothetical” charge. It is also a quantity that cannot really be measured (in the quantum mechanical sense). In experimental chemical research one usually “measures” the oxidation state of an atom, which is also not strictly correct. Rather, one measures a property (typically a spectrum) that one associates ad hoc with an oxidation state.

I hope this helps!

Kind regards,

Prof. dr. Show Verstraelen

PS Don’t let all this ambiguity be a reason to put you off chemistry. This just makes it interesting!