# Chemistry - Is it possible for one specific atom in a molecule to have a non-integer oxidation state?

## Solution 1:

It depends. Consider various radicals such as the superoxide anion $\ce{O2^{.-}}$ or $\ce{NO2^{.}}$. For both of these, we can draw simple Lewis representations:

In these structures, the oxygen atoms would have different oxidation states ($\mathrm{-I}$ and $\pm 0$ for superoxide, $\mathrm{-II}$ and $\mathrm{-I}$ for $\ce{NO2}$). That is the strict, theoretical IUPAC answer to the question.

However, we also see that the oxygens are symmetry-equivalent (homotopic) and should thus be identical. Different oxidation states violate the identity rule. For each compound, we can imagine an additional resonance structure that puts the radical on the other oxygen. (For $\ce{NO2}$, we can also draw resonance structures that locate a radical on both oxygens and another one that expands nitrogen’s octet and localises the radical there.) To better explain this physical reality theoretically, we can calculate a ‘resonance-derived average oxidation state’ which would be $-\frac{1}{2}$ for superoxide and $-\frac{3}{2}$ for $\ce{NO2}$. This is not in agreement with IUPAC’s formal definition but closer to the physical reality.

## Solution 2:

IUPAC recognizes that there are fractional oxidation states, but asks that you avoid writing them.

IR 4.6.1 says not to write an oxidation state "where it is not feasible or reasonable to define" because:

This avoids the use of fractional oxidation states.

Examples:

1. $$\ce{O2-}$$

2. $$\ce{Fe4S4^3+}$$

See also IR-5.4.2.2 which says "oxidation numbers are no longer recommended when naming homopolyatomic ions" because "ions such as pentabismuth(4+) (see Section IR-5.3.2.3) and dioxide(1—) (see Section IR-5.3.3.3), with fractional formal oxidation numbers, could not be named at all"

## Solution 3:

According to the IUPAC Gold Book[1], oxidation state is defined as:

A measure of the degree of oxidation of an atom in a substance. It is defined as the charge an atom might be imagined to have when electrons are counted according to an agreed-upon set of rules ...

Since the definition explicitly involves counting electrons, it is not possible for an individual atom to have a fractional oxidation state since it cannot have a non-integer number of electrons.