Half-Reaction Method:

1. Write the oxidation and reduction half-reactions, adding electrons (e^-) on the right side of the oxidation half-reaction and on the left side of the reduction half reaction to balance the changes in ON.

2. By inspection balance the half-reactions, adding H₂O(l), H⁺(aq) or OH^-(aq) as required. Adjust the coefficients in the two half-reactions so that the numbers of electrons are equal in each, and add the two half-reactions (the electrons cancel).

3. For either method, check the final equation to make sure that atoms and charge are balanced.

The rules by themselves are no doubt confusing. Let's see how they work with some examples.

Example 1

Balance the oxidation-reduction equation for the oxidation of H₂S(aq) by HNO₃(aq) to produce NO(g) and S(s) in aqueous acidic solution (thus H⁺ and H₂O may be involved).

  (1)

(2) In NO₃-, ON(N) = +5; in NO, ON(N) = +2, ΔON = -3. In H₂S, ON(S) = -2; in S, ON(S) = 0, ΔON = +2.

ON Method:

(3') Multiply the coefficients of N-containing species by 2 to get a 6-electron overall reduction; multiply the coefficients of S-containing species by 3 to get a 6 electron overall oxidation:

(4') Balance O by adding 4 H₂O to the right; then balance H by adding 2 H⁺ to the left:

2 H⁺(aq) + 2 NO₃^-(aq) + 3 H₂S(aq) → 2 NO(g) + 3 S(s) + 4 H₂O(l)

Half-Reaction Method:

(3") The oxidation and reduction skeletal half-reactions are:

(4") Balance half-reactions with H+ and H₂O:

Multiply the coefficients of the first equation by 3 and the second by 2, and add, canceling the electrons:

The H+ also cancel in part, leaving

2 H⁺(aq) + 2 NO₃^-(aq) + 3 H₂S(aq) → 2 NO(g) + 3 S(s) + 4 H₂O(l)

(5) The two methods give the same result. Check that the atoms balance—2 N, 3 S, 6 O, and 8 H on each side—and that the charges balance—0 net charge on each side.