Oxidation Number Rules

Free Elements Rule: The oxidation number of any atom in its elemental form is always zero, regardless of the complexity of the molecule. For example, a single atom of sodium ($Na$) and a molecule of sulfur ($S_8$) both have oxidation states of $0$ because there is no net transfer of electrons between identical atoms.

Monatomic Ions Rule: For any simple monatomic ion, the oxidation number is exactly equal to the ionic charge. This means an aluminum ion ($Al^{3+}$) has an oxidation state of $+3$, while a sulfide ion ($S^{2-}$) has an oxidation state of $-2$.

Group Specificity: In all their compounds, Group 1 metals (alkali metals) are assigned $+1$, and Group 2 metals (alkaline earth metals) are assigned $+2$. These values are highly consistent due to the low electronegativity and stable valence configurations of these metals.

Hydrogen Assignments: Hydrogen is typically assigned an oxidation state of $+1$ when it is bonded to nonmetals, such as in $H_2O$ or $CH_4$. However, when bonded to metals in binary compounds known as hydrides (e.g., $LiH$), hydrogen takes an oxidation state of $-1$ because it is more electronegative than the metal.

Oxygen Assignments: Oxygen is almost always assigned an oxidation state of $-2$ in its compounds. This rule reflects oxygen's high electronegativity and its tendency to attract two electrons to complete its valence shell.

Oxygen Exceptions: There are two critical exceptions to the oxygen rule: in peroxides (like $H_2O_2$), oxygen is $-1$, and when bonded to fluorine (the only element more electronegative than oxygen), it can have a positive oxidation state such as $+2$ in $OF_2$.

Neutral Compounds: The sum of the oxidation numbers of all atoms in a neutral molecule must equal zero. This principle allows for the calculation of an unknown oxidation state by setting up a simple algebraic equation based on the known rules for other elements in the molecule.

Polyatomic Ions: For a polyatomic ion, the sum of the oxidation numbers must equal the overall net charge of the ion. For instance, in a sulfate ion ($SO_4^{2-}$), the sum of the oxidation state of sulfur and the four oxygen atoms must equal $-2$.

Algebraic Application: To find an unknown state, multiply the oxidation number of each known element by its subscript, sum them, and set the total equal to the charge of the species. This method is the primary way to determine the states of transition metals and nonmetals with variable oxidation states.

The Hierarchy Strategy: Always apply rules in order of priority: start with free elements, then Group 1/2 metals and Fluorine, then Hydrogen, then Oxygen. Only use the summation rule at the very end to find the remaining 'flexible' element.

Sign Importance: In chemistry, the sign of an oxidation number is mandatory; writing '2' instead of '+2' or '-2' is technically incorrect. Always double-check that the sign reflects the relative electronegativity of the atoms involved.

Subscript Awareness: A common mistake is forgetting to multiply the oxidation number by the number of atoms (the subscript) in the formula. If a molecule has three oxygens, you must contribute $-6$ (from $3 \times -2$) to the total sum calculation.

Sanity Check: After calculating, ensure the resulting oxidation state is chemically reasonable. Most elements do not exceed oxidation states of $+7$ or $+8$, and nonmetals rarely go below $-4$.