Oxidation numbers and electron transfer

Use oxidation numbers as bookkeeping

Oxidation numbers assign electrons according to a formal accounting convention. They help track electron transfer even when a reaction involves covalent compounds rather than isolated ions. A monatomic ion has an oxidation number equal to its charge. An element in its uncombined form has oxidation number zero, whether it is written as individual metal atoms or as a molecule such as oxygen gas. The sum of oxidation numbers, each multiplied by the relevant atom count, equals the species' overall charge.

Common rules simplify the calculation. Hydrogen is usually +1 when bonded to non-metals; oxygen is usually −2 in ordinary compounds. Group 1 metals are normally +1 and group 2 metals +2 in their compounds. These rules have exceptions: oxygen in a peroxide is −1, and hydrogen in a metal hydride is −1. A question about an ordinary oxide and a question about a peroxide therefore need different starting assumptions. State which rule is applicable before solving for an unknown value.

For an unknown oxidation number, write a short equation. In a neutral molecule, the total must be zero; in a polyatomic ion, it must equal the ion's charge. Multiply oxygen's value by the number of oxygen atoms and include all other contributions. Solving the resulting linear equation prevents mistakes with negative ionic charge. Do not confuse a central atom's oxidation number with the charge of the whole ion: the ion's charge is the sum over every atom.

Identify both changes before naming the agents

Oxidation is loss of electrons and corresponds to an increase in oxidation number. Reduction is gain of electrons and corresponds to a decrease. The two changes occur together. A species that is oxidised provides electrons and acts as the reducing agent. A species that is reduced accepts electrons and acts as the oxidising agent. The agent name describes its effect on the other participant, which is why the naming can initially feel reversed.

Consider a metal atom that becomes a doubly positive ion. It has lost two electrons and is oxidised. If another ion gains those electrons and becomes a neutral metal, it is reduced. The original metal atom is the reducing agent, while the ion accepting electrons is the oxidising agent. Identify the actual reactant species carrying the changing atom. A spectator ion that appears unchanged on both sides does not become an oxidising agent simply because it has a negative charge.

Balance electrons as well as material

A half-equation isolates one electron change. For example, a neutral atom forming a +2 ion releases two electrons. A +3 ion becoming a +2 ion consumes one electron. To combine such changes, multiply the second half-equation by two so that the electron counts match. Add the half-equations and cancel electrons appearing on opposite sides. The final equation must conserve every element and total electrical charge. A balanced atom count alone is not enough for an ionic equation.

For aqueous reactions, water, hydrogen ions or hydroxide ions may participate depending on the specified conditions. These species are accounting tools with chemical meaning, not arbitrary corrections. In an acidic medium, hydrogen ions can balance hydrogen after water balances oxygen. In a basic medium, hydroxide and water are used consistently. Do not import hydrogen ions into a final basic-medium equation merely because an earlier intermediate calculation used them. For introductory problems, a supplied pair of simple half-equations often avoids this extra complication.

Connect electron transfer with reacting amounts

Once the equation is balanced, its coefficients give mole ratios just as in other stoichiometry. If one atom loses two electrons while each accepting ion gains one, two accepting ions are required per donor atom. Convert masses to moles before applying this ratio. Multiplying a half-equation changes its coefficient and total electrons, but not the oxidation number assigned to each atom. Check the finished result through two independent balances: the same number of atoms on each side and the same total charge on each side. This catches an omitted coefficient that either check alone might miss.