Balancing Redox Reactions by the Oxidation-Number Method

The oxidation-number method balances a redox equation directly, by tracking the total change in oxidation number for every atom that changes state, without ever splitting the equation into separate half-reactions. It is often the fastest method when the skeletal (unbalanced) equation is already fairly simple.

The procedure, in order:

1. Write the skeletal (unbalanced) ionic or molecular equation, and assign oxidation numbers to every atom that could plausibly change.
2. Identify the atom(s) undergoing an increase in oxidation number (oxidation) and the atom(s) undergoing a decrease (reduction), and compute the magnitude of change per atom.
3. Multiply each formula by a small whole-number coefficient so that the total increase equals the total decrease — this is the same electron-conservation requirement as the ion-electron method, just expressed as oxidation-number units instead of explicit electrons.
4. Balance all atoms other than H and O by inspection.
5. Balance oxygen atoms by adding $\text{H}_2\text{O}$, then balance hydrogen atoms by adding $\text{H}^+$ (acidic medium) — or, for basic medium, balance with $\text{H}_2\text{O}$ and $\text{OH}^-$ as described in the next section.
6. Check that the net ionic charge is equal on both sides — this confirms the electron balance was applied correctly.

Worked example: $\text{Fe}^{2+} + \text{Cr}_2\text{O}_7^{2-} \to \text{Fe}^{3+} + \text{Cr}^{3+}$ (acidic medium).

Iron changes from $+2$ to $+3$: an increase of $1$ per Fe atom (oxidation). Chromium changes from $+6$ (in $\text{Cr}_2\text{O}_7^{2-}$, two Cr atoms per formula) to $+3$: a decrease of $3$ per Cr atom, so $2 \times 3 = 6$ per formula of dichromate (reduction).

To equalize total increase and total decrease, 6 Fe atoms (total increase $6 \times 1 = 6$) must react per 1 dichromate ion (total decrease $= 6$): $6\text{Fe}^{2+} + \text{Cr}_2\text{O}_7^{2-} \to 6\text{Fe}^{3+} + 2\text{Cr}^{3+}$. …