Concepts: oxidation number rules and calculations

3.1 The rules

Assigning oxidation numbers follows a small set of rules. An element in its free state has oxidation number zero. A monoatomic ion has its charge as its oxidation number. Oxygen usually has minus two, hydrogen plus one, and fluorine minus one in all its compounds. The sum of the oxidation numbers is zero in a neutral compound and equals the charge in a polyatomic ion.

The rules have exceptions that matter in examination questions. Oxygen has plus two in fluorine compounds such as OF2, because fluorine is more electronegative, and minus one in peroxides such as H2O2. Hydrogen has minus one in metal hydrides such as sodium hydride. The exception is decided by which atom is more electronegative, and the rule of the more electronegative atom taking the negative number settles most of them.

For an element that can show several oxidation states, the rules give the average number in a compound with several atoms of that element. In a compound where the same element has different environments, the average can hide the individual values, and separate assignments are needed for each site. For example, the two nitrogen atoms in ammonium nitrate have different oxidation numbers even though the formula shows one compound. The worked examples below apply these rules to common compounds and ions, and the method is the same for every one of them.

3.2 Worked examples

In sulphuric acid, H2SO4, hydrogen contributes plus two and oxygen contributes minus eight, so sulphur must be plus six for the total to be zero. In potassium permanganate, KMnO4, potassium is plus one and the four oxygen atoms give minus eight, so manganese is plus seven. In potassium dichromate, K2Cr2O7, potassium gives plus two and oxygen minus fourteen, so the two chromium atoms together are plus twelve and each is plus six.

For a polyatomic ion the sum equals the charge. In the permanganate ion, MnO4 minus, four oxygen atoms give minus eight, so manganese is plus seven for the total to be minus one. In the dichromate ion, Cr2O7 two minus, seven oxygen atoms give minus fourteen, and the two chromium atoms are plus twelve in total, so each is plus six, with the ion charge of minus two satisfied. In the sulphate ion, SO4 two minus, sulphur is plus six.

In a compound where one element shows two oxidation states, the average is not enough. In ammonium nitrate, NH4NO3, the ammonium nitrogen is minus three and the nitrate nitrogen is plus five. The average is plus one, which is meaningless chemically. This is why the rules should be applied to each part of the formula rather than to the formula as a whole.

3.3 Oxidation number and reaction types

A rise in oxidation number is oxidation and a fall is reduction. Comparing the oxidation numbers of the same element in reactants and products therefore tells at a glance whether the element is oxidised or reduced. If the same element both rises and falls in one reaction, the reaction is a disproportionation.

Some compounds carry fractional oxidation numbers when the average is taken, and the fraction is a sign that the element sits in different environments. In magnetite, Fe3O4, the average oxidation number of iron is plus eight over three, which is best understood as one iron two plus and two iron three plus ions. In a compound such as sodium thiosulphate the average sulphur number is plus two, but the two sulphur atoms are in different oxidation states. Examination questions often ask for the average, and the safe method is to apply the sum rule first and then, if the question asks about a particular atom, to write the structural formula and assign each site separately.

For organic compounds the oxidation number of carbon is found by treating hydrogen as plus one and oxygen as minus two, and then applying the sum rule to the whole molecule. Carbon in methane is minus four, in methanol minus two, in methanal zero, in methanoic acid plus two and in carbon dioxide plus four. The series shows the progressive oxidation of carbon as the number of oxygen atoms increases, which is why organic oxidation reactions fit the same electron accounting as inorganic ones.

In the decomposition of hydrogen peroxide, oxygen goes from minus one in H2O2 to minus two in water and zero in oxygen gas. The same element is both reduced and oxidised, which is the signature of disproportionation. In the reaction of chlorine with cold dilute sodium hydroxide, chlorine goes from zero to minus one in chloride and plus one in hypochlorite, again a disproportionation.

The oxidation number also helps to balance redox equations. The total increase in oxidation number must equal the total decrease, which gives the coefficients of the two species. This method is quicker than counting electrons for complicated equations, though the electron and half reaction methods are more reliable when the medium is specified.