Oxidation Numbers

An oxidation number (or oxidation state) is a bookkeeping value assigned to an atom to track how electrons are distributed in a compound or ion. This subtopic covers the standard rules for assigning oxidation numbers — to free elements, monatomic ions, specific groups of the periodic table, hydrogen, oxygen, and any atom whose oxidation number must be solved for using the sum rule.

Key Takeaways

• An oxidation number is a bookkeeping value that treats every bond as ionic, assigning electrons to the more electronegative atom.

• A free element has an oxidation number of zero; a monatomic ion's oxidation number equals its charge.

• Group IA is always +1, Group IIA is always +2, and Group VIIA is -1 except when bonded to a more electronegative element.

• Hydrogen is usually +1 (nonmetals) but -1 in metal hydrides; oxygen is usually -2 but -1 in peroxides and +2 in OF₂.

• The sum rule: oxidation numbers sum to zero in a neutral compound, or to the overall charge in a polyatomic ion — used to solve for sulfur in SO₄²⁻ (+6) and nitrogen in NO₃⁻ (+5).

• Oxidation is an increase in oxidation state; reduction is a decrease in oxidation state.

What Is an Oxidation Number?

An oxidation number is a bookkeeping technique for keeping track of electrons. It treats every one of an atom's bonds as if it were fully ionic, assigning the shared electrons in each bond to whichever atom is more electronegative. This doesn't mean the bond is actually ionic — it's an accounting convention that makes it possible to track which atoms gain or lose electron density as a reaction proceeds.

Assigning oxidation numbers correctly matters because it lets you determine which atoms are oxidized and which are reduced in a reaction, and how many electrons each atom gains or loses in the process.

Oxidation Numbers of Free Elements and Monatomic Ions

Free element rule: the oxidation number of an atom in its elemental form is zero, since it hasn't gained or lost any electrons. This applies to diatomic and polyatomic elemental forms as well as single atoms — each nitrogen atom in N₂ has an oxidation number of zero, and the same is true for phosphorus in P₄ and sulfur in S₈.

Monatomic ion rule: the oxidation number of a monatomic ion equals the charge of that ion. For example:

• Sodium ion (Na⁺): oxidation number +1

• Copper(II) ion (Cu²⁺): oxidation number +2

• Iron(III) ion (Fe³⁺): oxidation number +3

• Chloride ion (Cl⁻): oxidation number -1

• Nitride ion (N³⁻): oxidation number -3

Oxidation Numbers of Groups IA, IIA, and VIIA

Certain groups of the periodic table follow predictable oxidation number patterns in compounds, based on how many electrons they characteristically lose or gain:

• Group IA (alkali metals): always +1 in a compound, since alkali metals lose one electron to reach a stable configuration. For example, sodium (Na) is +1 in NaCl.

• Group IIA (alkaline earth metals): always +2 in a compound, since these metals lose two electrons to form stable cations. For example, calcium (Ca) is +2 in calcium chloride (CaCl₂).

• Group VIIA (halogens): -1 in a compound, since halogens typically gain one electron to form a stable anion — except when bonded to an element of higher electronegativity, in which case the halogen is assigned the positive number instead. Chlorine is -1 in hydrogen chloride (HCl), but in hypochlorous acid (HOCl), chlorine is bonded to the more electronegative oxygen, so chlorine's oxidation number flips to +1.

Oxidation Number of Hydrogen

Hydrogen's oxidation number depends on what it's bonded to:

• +1 when bonded to nonmetals, since hydrogen is less electronegative than most nonmetals. In hydrochloric acid (HCl), hydrogen is +1.

• -1 when bonded to metals in metal hydrides, since hydrogen becomes the more electronegative element in that bond. In sodium hydride (NaH), hydrogen is -1.

Oxidation Number of Oxygen

Oxygen's oxidation number is usually -2, since oxygen typically gains two electrons to complete its valence shell — in water (H₂O), each oxygen atom is -2. There are two standard exceptions:

• Peroxides, such as hydrogen peroxide (H₂O₂), contain an O-O single bond. Because the two oxygens share that bond's electrons equally with each other rather than with a more electronegative partner, each oxygen atom is assigned -1 instead of -2.

• Oxygen difluoride (OF₂) bonds oxygen to fluorine, the only element more electronegative than oxygen itself. In this one compound, oxygen is assigned the positive oxidation number, +2.

The Sum Rule: Neutral Compounds and Polyatomic Ions

The oxidation numbers of every atom in a species must add up to that species' overall charge:

• In a neutral compound, the oxidation numbers of all atoms must sum to zero. In water (H₂O), the sum is 2(+1 for hydrogen) + (-2 for oxygen) = 0.

• In a polyatomic ion, the oxidation numbers of all atoms must sum to the ion's charge.

Worked example — the sulfate ion (SO₄²⁻): each of the four oxygen atoms is -2, contributing 4 × (-2) = -8 total. Since the ion's overall charge is -2, sulfur's oxidation number must make up the difference: -2 - (-8) = +6. Checking: 4(-2) + (+6) = -2, which matches the ion's charge.

Worked example — the nitrate ion (NO₃⁻): each of the three oxygen atoms is -2, contributing 3 × (-2) = -6 total. Since the ion's overall charge is -1, nitrogen's oxidation number must be -1 - (-6) = +5. Checking: (+5) + 3(-2) = -1, which matches the ion's charge.

The sum rule is the tool to reach for whenever a compound or ion contains an atom whose oxidation number isn't fixed by one of the rules above — assign the known atoms first, then solve for the unknown.

Oxidation Numbers and Redox Direction

Oxidation numbers are also what define oxidation and reduction directly: oxidation is an increase in oxidation state, and reduction is a decrease in oxidation state. A substance is oxidized when it moves from a lower oxidation number to a higher one, and reduced when it moves from a higher oxidation number to a lower one — the same electron-loss/electron-gain relationship covered in the previous subtopic, now expressed in terms of the numbers themselves.

Common MCAT Mistakes

• Applying the halogen rule without checking electronegativity. Group VIIA elements are -1 in a compound except when bonded to something more electronegative than themselves — chlorine is +1 in HOCl, not -1, because oxygen is more electronegative.

• Assuming oxygen is always -2. Oxygen is -2 in most compounds, but -1 in peroxides (O-O bond) and +2 in OF₂, the one compound where oxygen bonds to a more electronegative element.

• Forgetting hydrogen flips sign in metal hydrides. Hydrogen is +1 when bonded to nonmetals but -1 in metal hydrides like NaH, since hydrogen becomes the more electronegative atom in that bond.

• Setting the sum rule to zero for polyatomic ions. Oxidation numbers only sum to zero in a neutral compound — in a polyatomic ion, they must sum to the ion's actual charge (e.g., -2 for SO₄²⁻, not 0).

MCAT-Style Concept Check

Question: What is the oxidation number of chromium in the dichromate ion, Cr₂O₇²⁻?

• A) +3

• B) +6

• C) +7

• D) +12

Answer: B

Explanation: Using the sum rule, the seven oxygen atoms each contribute -2, for a total of 7 × (-2) = -14. Since the ion's overall charge is -2, the two chromium atoms together must contribute -2 - (-14) = +12, so each individual chromium atom has an oxidation number of +12 ÷ 2 = +6.

FAQ

What is an oxidation number, in simple terms?

It's a bookkeeping value assigned to an atom that treats every bond as fully ionic, assigning the shared electrons to whichever atom is more electronegative — it tracks how electron density shifts during a reaction, not literal ionic charge.

Why is oxygen -1 instead of -2 in hydrogen peroxide?

Hydrogen peroxide (H₂O₂) contains an oxygen-oxygen single bond. Because the two oxygen atoms share that bond's electrons equally with each other rather than with a more electronegative atom, each oxygen is assigned -1 rather than the usual -2.

When is hydrogen's oxidation number -1 instead of +1?

Hydrogen is -1 only in metal hydrides, such as sodium hydride (NaH), where hydrogen is bonded to a metal that is less electronegative than itself — making hydrogen the more electronegative atom in that particular bond.

How do you use the sum rule to find an unknown oxidation number?

Assign oxidation numbers to every atom whose value is fixed by a rule, multiply each by how many of that atom are present, and set the total equal to the compound's overall charge (zero for a neutral compound, the ion's charge for a polyatomic ion). Whatever value makes the sum correct is the unknown atom's oxidation number.