balancing redox half-reactions

Balancing a messy redox equation by trial and error is maddening. The half-reaction method tames it by splitting the reaction into two separate stories — the oxidation half and the reduction half — balancing each one fully on its own, and only then sewing them back together so that the electrons one side loses exactly match the electrons the other side gains. It is a recipe, and like all good recipes you follow the steps in order.

Within each half-reaction the steps go: balance the main element; balance oxygen by adding H2O; balance hydrogen by adding H+; balance the charge by adding electrons (e-). That gives you, for example, the reduction of permanganate in acid as MnO4- + 8 H+ + 5 e- -> Mn2+ + 4 H2O. You then scale the two halves so their electron counts are equal, add them, and cancel anything that appears on both sides. If the reaction runs in base instead of acid, you finish by adding OH- to both sides to neutralize the H+ into water — a small extra step.

This method is the workhorse of analytical and inorganic chemistry, behind every titration calculation, every battery half-cell, and every electrolysis. Its great virtue is that the electron count is explicit: you literally see how many electrons move, which is exactly the number you need for stoichiometry and for the Nernst equation. The honest caveat is that a balanced equation only tells you the conservation arithmetic — it says nothing about whether the reaction actually goes, or how fast. For 'whether', you turn to cell potentials.