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Iron's oxidation state in $\ce{Fe3O4}$. I really can't get the logic behind this.

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The formula of $\ce{Fe3O4}$ is a shorthand for $\ce{Fe^{II}Fe^{III}2O4}$, so there are two sorts of atoms of iron here in +2 and +3 oxidation state.

However, it is still possible to gain truly fractional oxidation states. The simplest example probably would be potassium superoxide, $\ce{KO2}$. Here, the anion is symmetrical $\ce{O2^{-}}$ anion, so obviously both oxygen atoms are in $\ce{-1/2}$ oxidation state. There are more complicated examples as well.

Often fractional oxidation state comes from symmetrical structures with charge, that would have unpaired electrons otherwise. However, systems with truly fractional oxidation states usually have bonding, hard to describe in terms of common Lewis structures (and with little relevance of idea of oxidation state), and mostly are considered in semi-advanced organic chemistry and advanced inorganic chemistry.

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Your assumption that all iron atoms in magnetite ($\ce{Fe3O4}$) have the same oxidation state is wrong.

It is a mixed $\ce{Fe(II,III)}$ oxide.

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The iron atoms in magnetite, $\ce{Fe3O4}$, are not all in the same oxidation state: per Michael's comment, while it is not a spinel-type material, it has a spinel structure (strictly, an inverse spinel structure), with one Fe(II) center and two Fe(III) centers.

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    $\begingroup$ Actually, it is not spinel. It has a spinel structure, and to be even more precise, it has the anti-spinel structure. $\endgroup$ – Gimelist Jan 1 '15 at 15:02
  • $\begingroup$ Good to have someone better versed in materials to make that correction. I wasn't even aware of the existence of an anti-spinel. $\endgroup$ – hBy2Py Jan 1 '15 at 16:06
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Analyzing the structure:(All other answers tell you why $\ce{Fe3O4}$ has a fractional oxidation state, but without having a look at the structure you wont be able to tell if there are two $\ce{Fe}$ atoms in +3 state or one, thus it makes it important to analyze the structure of $\ce{Fe3O4}$)

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Here the two Iron atoms that are bonded to three oxygen atoms have an oxidation state of +3 each, and the Iron atom that is bonded to two oxygen atom has an oxidation state of +1.

Thus taking the average (3+3+2)/3 = 8/3;

You would have got the same if you used the fact that $\ce{Fe3O4}$ is neutral.If you assume the oxidation state of Iron to be x, then 3x+4(-2)=0. Solving you would get x as 8/3(However this oxidation state would be the average oxidation state of Iron).

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