# What is the difference between oxidation number and oxidation state?

Jun 3, 2016

Oxidation number might be easier to understand at the high school level, but oxidation state and oxidation number are synonymous in many cases.

The only time I can think of where they are different are in coordination complexes.

In ["Ti"("CO")_6]^(2-), or hexacarbonyltitanate(II), the oxidation state is $- 2$ but the oxidation number is $\text{II}$. The "-ate" indicates the negative overall charge of the complex.

On the other hand, ["Ti"("CO")_6]^(2+), or hexacarbonyltitanium(II), would have the same oxidation number but a $+ 2$ oxidation state.

OXIDATION STATE EXAMPLE

The oxidation state is the hypothetical charge if the bond that the atom makes with a second atom is 100% ionic in character, and if after accounting for electronegativities, the more electronegative atom in the pair has the more negative oxidation state.

It isn't ever exactly the case for a real bond to have 100% ionic character (i.e. to transfer 100% of the electron density into another atom's valence orbitals), but oxidation states turn out to be a good charge accounting scheme.

Consider the following ${E}^{\circ}$ vs. $\text{pH}$ (Pourbaix) diagram. For example, if we are at $\text{pH}$ $2$, then we can apply some positive voltage to ${\text{Fe}}^{3 +}$ at $\text{1 atm}$ pressure, $\text{273.15 K}$, and constant $\text{pH}$ as follows:

$\setminus m a t h b f \left(\stackrel{\textcolor{b l u e}{+ 3}}{{\text{Fe"^(3+))(aq) + 4stackrel(color(blue)(+1))("H")_2stackrel(color(blue)(-2))("O")(l)-> stackrel(color(blue)(+6))("Fe")stackrel(color(blue)(-2))("O"_4^(2-))(aq) + 8stackrel(color(blue)(+1))("H}}^{+}} \left(a q\right) + 3 {e}^{-}\right)$

${E}_{\text{ox"^@ > "0.8 V}}$

(We started in the ${\text{Fe}}^{3 +}$ region on the upper left side of the graph, and we moved upwards to oxidize.)

For this half-reaction, we've oxidized iron(III) $\left(\stackrel{+ 3}{\text{Fe}}\right)$to iron(VI) $\left(\stackrel{+ 6}{\text{Fe}}\right)$ in acidic conditions.

So, iron attains a $+ 6$ oxidation state, and its oxidation number is represented as $\text{VI}$.

OXIDATION NUMBER VS. STATE EXAMPLE

One difference I can find is in ["Ti"("CO")_6]^(2-). This is called hexacarbonyltitanate(II).

The oxidation number of titanium here is written as $\text{II}$, but the oxidation state of titanium is actually $- 2$ (making it a ${d}^{6}$ metal). The negative overall charge of the complex is conveyed by the "-ate" in the name, and the negative oxidation state is deduced.

This compound has a ${t}_{2 g}^{6}$ configuration, being low spin, and is a stable 18-electron complex (as it should be for a coordination complex with six $\pi$-acceptor ligands).