What is the coefficient of H2O in the balanced equation obtained by using oxidation numbers?

Question

HNO₃(aq) + H₂S(aq) → NO(g) + S(s) + H₂O(l)

Answer 1

Since O has a usual standard oxidation number of -2, and H is +1 (refer to texts for the few exceptions), and the sum of oxidation numbers for a molecule must be 0, the oxidation numbers of N are +5 and +2 in the reactants and products, respectively, and S is -2 in reactants and 0 as an element in the products. Therefore, N is being reduced by 3 charges, and S is gaining 2 by oxidation. In order to balance these changes, the N coefficients will be 2, and S coefficients will be 3 (giving 6 plus for oxidation and 6 minus for reduction). Also, water will have a coefficient of 4, since the reactants will have 2H and 6H. The O will also be balanced, since there are 6 in the reactants, and 2 + 4 in the products.