Oxidation States

Carbon in carbon dioxide has an oxidation state of +4. It does not carry a charge of +4. It does not carry a charge anywhere near +4 — careful calculations put the actual charge on that carbon atom at well under +1.

This is not a flaw in the system. It is what the system is for. An oxidation state is a deliberate fiction: a number produced by pretending that every bond in a molecule is completely ionic, so that every shared pair is handed outright to whichever atom is more electronegative. Nobody believes the pretence. It survives because it makes electron transfer countable, and counting electron transfer is the only way to make sense of an enormous class of reactions.

Accepting that it is bookkeeping resolves most of the confusion in this topic — including how an atom can have a fractional oxidation state, which would be nonsense for a real charge.

The rules only work in order

Most textbooks give the assignment rules as an unordered list, which leaves you stuck the first time two of them disagree. They are a priority sequence, and applied in order they never conflict.

1. An element in its free state is 0. This covers Fe, O₂, P₄, S₈ and graphite alike — being diatomic does not change it.
2. A monatomic ion equals its charge. Na⁺ is +1, S²⁻ is −2.
3. The states must sum to zero for a neutral compound, or to the charge for a polyatomic ion. This is the equation you solve; the remaining rules supply its known terms.
4. Fluorine is always −1 in compounds. No exceptions exist, because nothing outranks fluorine in electronegativity.
5. Group 1 is +1 and group 2 is +2 in compounds, without practical exception.
6. Hydrogen is +1, except when bonded to a metal, where it is −1. Sodium hydride is Na⁺H⁻.
7. Oxygen is −2, except in peroxides, where it is −1; in superoxides, where it is −½; and when bonded to fluorine, where it is positive.
8. Other halogens are −1 unless bonded to oxygen or to a halogen above them.

Rule 4 outranking rule 7 is what makes the ordering necessary. In oxygen difluoride, OF₂, both fluorines are −1 by rule 4, so oxygen must be +2 — one of the few compounds in which oxygen is positive. Applying the oxygen rule first would have given a contradiction with no way out.

Sulfuric acid and dichromate, worked

The method is always the same: fill in every atom you have a rule for, let the unknown be x, and solve.

Sulfuric acid, H₂SO₄. Two hydrogens at +1 give +2. Four oxygens at −2 give −8. The molecule is neutral:

(+2) + x + (−8) = 0
x = +6

Sulfur is +6, which is the highest it can reach — group 16 has six valence electrons and there is nothing further to give away.

Dichromate, Cr₂O₇²⁻. Seven oxygens at −2 give −14, and the ion carries a 2− charge, so the sum must be −2 rather than 0:

2x + (−14) = −2
2x = +12
x = +6

Each chromium is +6. Note that the equation solves for 2x because there are two chromium atoms, and forgetting to divide is the single most common slip in these problems.

Potassium superoxide, KO₂. Potassium is +1 by rule 5, so the two oxygens must total −1, which makes each −½. That is not an error, and it leads directly to the next section.

When the answer is +2.67

Magnetite is Fe₃O₄. Four oxygens at −2 total −8, so three irons must total +8, and each iron comes out at +8/3, or +2.67.

No atom has a charge of two-thirds of an electron. What the fraction means is that the formula unit contains iron in more than one state, and the calculation has produced their average. Magnetite genuinely contains one Fe²⁺ and two Fe³⁺ per formula unit: 2 + 3 + 3 = 8, exactly as required. The fractional answer was the average of a mixture all along, in the same way that an average atomic mass is.

Tetrathionate, S₄O₆²⁻, makes the same point more starkly. Six oxygens give −12 and the charge is −2, so the four sulfurs total +10 and average +2.5. The actual structure has two sulfur atoms in the middle of a chain, each at 0, and two on the outside bonded to oxygen, each at +5. Not one sulfur atom in the ion is at +2.5.

So a fractional oxidation state is a signal, not a problem. It tells you that the atoms of that element in the substance are not all equivalent, and the average is concealing the difference.

Three different numbers for the same carbon atom

The clearest way to see that oxidation state is one convention among several is to compute all three descriptions of one atom.

For the carbon in CO₂:

• Oxidation state: +4. Assume both double bonds are fully ionic, give all eight bonding electrons to oxygen, and carbon is left four short.
• Formal charge: 0. Assume the opposite extreme — every bond split exactly evenly. Carbon then owns four of the eight bonding electrons, which is precisely how many valence electrons it brought.
• Actual partial charge: somewhere below +1, depending on the computational method used, and no method gives a unique answer because partial atomic charge is not an observable quantity.

Three numbers, one atom, all legitimate. Oxidation state is the maximally ionic assumption, formal charge the maximally covalent one, and reality lies between them. Use oxidation states for tracking redox, formal charges for deciding which Lewis structure is best, and neither as a claim about where the electrons actually are.

Following electrons through a reaction

The payoff is redox. An increase in oxidation state is oxidation; a decrease is reduction. That definition works even when no ion is visibly formed and no oxygen is involved.

Take zinc metal displacing copper from solution:

Zn + Cu²⁺ → Zn²⁺ + Cu

Zinc goes from 0 to +2 and is oxidised. Copper goes from +2 to 0 and is reduced. Two electrons have moved, and the counting confirms it.

The vocabulary for the participants runs backwards from intuition, which is worth stating plainly: the oxidising agent is the species that gets reduced, because it does the oxidising to something else. In that reaction the copper ion is the oxidising agent and zinc is the reducing agent.

Permanganate shows why the method is worth the trouble. In MnO₄⁻, manganese solves to +7; in acidic conditions its usual product is Mn²⁺. Manganese has dropped five oxidation states, so each permanganate ion has accepted five electrons — a number you could not have obtained by looking at the formulas, and one that fixes the coefficients of the whole equation.

The Roman numeral is not a count

In a name like iron(III) chloride, the III is the oxidation state of the iron, not the number of chlorines and not a subscript. It happens to give FeCl₃ here only because chloride is 1−.

Manganese(VII) oxide is Mn₂O₇, where the numeral is 7 and no subscript is 7. Reading the numeral as an atom count would produce a formula that does not exist. The convention exists because most transition metals form several compounds with the same partner, and the name has to say which.

The records at both ends

Two boundary facts make good checks on an answer.

The maximum oxidation state a main-group element can reach is its number of valence electrons, because that is all it has to give: +7 for chlorine in perchlorate, +6 for sulfur in sulfate. Compute +8 for a group 16 element and you have made an arithmetic error, not a discovery.

Across the whole periodic table the record is +9, held by iridium in the [IrO₄]⁺ cation identified in the gas phase in 2014. At the other extreme, metals can go negative when bonded to things less electronegative than themselves: iron is −2 in the tetracarbonylferrate ion, and gold forms a genuine Au⁻ auride ion in cesium auride, a compound that is, remarkably, a semiconductor rather than an alloy.