what is the difference between oxidation state and oxidation number?
To assist in determining the precise degree of oxidation (or reduction) of an atom in a species (ion, element or molecule), the idea of oxidation number or oxidation state is used. The two terms are usually used interchangeably so that an atom may have a particular oxidation number or, be in a particular oxidation state. Oxidation number is residual charge (positive or negative) an atom appears to possess in a molecule when the shared electrons are counted towards the more electronegative atom. Oxidation state refers to the broad degree of oxidation of an atom in a molecule. Most of the time, it doesn't matter if the term oxidation state or oxidation number is used.
In coordination chemistry, however, a slight differentiation between these two closely related terms is done. Oxidation numbers are conventionally represented with Roman numerals (without any charge) while oxidation states use Indo-Arabic numerals (charge included).
In organic chemistry too, a subtle differentiation has to be done in order to avoid apparent absurdities while applying the concept of oxidation numbers rigidly. Consider the molecules Ethane (C2H6), Propane (C3H8) and Butane (C4H10). Technically speaking, they have the oxidation numbers – 3.00, – 2.67, and – 2.50; although organic chemists seldom think of these three compounds as being in different oxidation states. Here the sense of oxidation state is broader, which depends upon the nature of functional groups or electronegative substituents in the molecule. Oxidation (or reduction) is considered based upon the conversion of a functional group in a molecule from one category to a higher (or lower) one.