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Many times I encounter oxidation numbers like -1 in the peroxide for oxygen, -1/2 in superoxide, and in some other compounds some elements have 8/3 or such like that...what is the physical meaning of fractional oxidation numbers and how can i imagine that to be at the molecular level

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The main issue here is that you are asking for all atoms to have the oxidation states. One thing that pushes us in this direction is that our specification for chemical formulae does not differentiate in general different kinds of the same atom.

Suppose you have a compound where half the oxygen atoms have oxidation state -1 and the other half have oxidation state -2. This is not captured in our notion of a chemical formula. For example, sodium superoxide is $\ce{NaO2}$. If you want all of the oxygen atoms to have the same oxidation number, your best bet is to average over all oxygen atoms. In this case, the average is $-\frac{1}{2}$.

We can take this a step further. Why should we require that each atom have an integral oxidation state? The logic behind this is that electrons are atomic components and can't be split. But molecular ions and molecules are complicated, and some times you need to share one electron over the entire system. A fractional oxidation state may be the most accurate way to describe atoms of this system.

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  • $\begingroup$ Okay thank you but please tell how oxidation numbers in different integer are different from others and what is their physical meaning? $\endgroup$ – Tanmay Siddharth Jun 10 at 15:28
  • $\begingroup$ One of cases is the element have multiple oxidation states within the compound, that has, or even has not a stoichiometric composition given by small integers. $\endgroup$ – Poutnik Jun 10 at 15:50
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Oxidation number is a formal chemist invention of expected charge of an atom, if a molecule or a substance is hypothetically torn apart to particular atoms, according to the conventional electronegativity.

Some compounds would lead, by this mental operation, to sharing an electron among multiple atoms, like superoxides, what formally lead to oxidation state -1/2, as both atoms are

Some compounds have a particular element in a mixed bonding state, leading to different formal oxidation states in distinguished molecules like thiosulphates, or to a mixed, average state, like some oxides as $\ce{Pb3O4, Fe3O4}$.

Some compounds, have non stoichiometric composition, typically solid metal oxides, with elements of multiple oxidation states, leading to even a rational number of the formal oxidation state. It is usually caused by some vacant oxygen or metal atoms in the oxide matrix.

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