Oxidation state ($\mathrm{OS}$)

An oxidation state is an electron-bookkeeping assignment to a chemical atom: its electric charge number after the ionic approximation of bonds. It helps identify oxidation and reduction and determine stoichiometry, even for covalent bonds without separate charged ions. In water, each hydrogen has oxidation state $+1$ and oxygen has $-2$; this does not assert that a water molecule contains two free protons and a free oxide ion.^[ref]

Three conventions answer different questions. Formal charge divides each bonding electron pair equally in a chosen Lewis structure. Oxidation state uses the ionic approximation of bonds. Partial atomic charge instead partitions the actual electron density and depends on that partition. In the ordinary water Lewis structure, every formal charge is zero although the oxidation states are not. Neither bookkeeping convention supplies numerical partial atomic charges.

For the routine examples here, assign all bonding electrons between different chemical elements to the more electronegative partner; divide bonding electrons between identical chemical elements equally. Retain each lone pair on its original chemical atom. Subtract the assigned valence electron count $N_i^{\mathrm{assigned}}$ from the neutral chemical atom's valence electron count $v_i$. The IUPAC convention uses Allen electronegativity, based on free-chemical atom valence electron energies. Close electronegativity comparisons and some reversibly bound chemical compounds require care beyond this simple rule.^[ref]

The examples explain exceptions to memorized rules:

These drawings record allocations, not molecular geometry or a physical process of breaking the chemical bonds. In particular, the O–O line in the molecular oxygen panel only marks the connection; it does not assert a complete Lewis structure or spin state.

Sum oxidation states over all chemical atoms of the specified molecule, ion or formula unit, including multiplicities:Here $q$ is the net electric charge and $e$ the positive elementary charge. For a neutral entity the sum is zero; for an ion it equals its signed electric charge number $z$. The reason is simple: the allocation assigns every valence electron exactly once, so the sum is the neutral electron budget minus the actual electron count.

For water, $2(+1)+(-2)=0$; for hydrogen peroxide, $2(+1)+2(-1)=0$. In permanganate, ${\mathrm{MnO}}_4^{-}$, assigning each oxygen $-2$ gives $x+4(-2)=-1$, so manganese has oxidation state $+7$. This is not a free ${\mathrm{Mn}}^{7+}$ ion: the entire permanganate anion has net electric charge $-e$. The sum rule supplies a constraint; without additional assignments it cannot determine every individual oxidation state.

An increase in oxidation state records oxidation; a decrease records reduction. Thus ${\mathrm{Fe}}^{2+}\to {\mathrm{Fe}}^{3+}$ raises the iron oxidation state by one, while ${\mathrm{MnO}}_4^{-}\to {\mathrm{Mn}}^{2+}$ lowers the manganese oxidation state from $+7$ to $+2$. Five iron ions supply the five-electron inventory required per permanganate ion.

In an acidic chemical solution, the complete half-reactions areFirst balance oxygen with four water molecules, then hydrogen with eight protons, and finally electric charge with five electrons. Multiply the iron half-reaction by five and add; the exchanged electrons cancel:Both sides contain one manganese, four oxygen, eight hydrogen and five iron chemical atoms, with net electric charge $+17e$. The ${\mathrm{H}}^{+}$ notation represents the acidic aqueous proton inventory; it does not imply bare protons moving independently of water. These half-reactions and their sum are the acidic balance used in the documented permanganate-iron titration.^[ref]

The coefficients predict amounts consumed, not a collision of five ions or an elementary reaction. Bulk chemical solution also contains compensating counterions, which are omitted from this net chemical equation. The hydrogen and oxygen oxidation states are unchanged; balancing their inventories remains essential even though they do not account for the exchanged electrons.