Assigning Oxidation Numbers
An iron gate gets covered in rust on the coast of Veracruz, but a stainless steel spoon does not. In both cases there is iron and oxygen nearby, so what changes? To follow the trail of electrons passing from one atom to another, chemists use a "marker" for each atom: the oxidation number. On this page you will learn the rules for assigning it, and at the end we will return to the rust.
What is the oxidation number?
In a chemical reaction, electrons sometimes change owners. To keep track, we imagine that in each bond the electrons stay with the atom that attracts them most (the most electronegative one). The charge each atom would have with that split is its oxidation number.
It is written with the sign first: $+2$, $-1$, $0$. The charge of an ion is written with the sign after: $\text{Ca}^{2+}$, $\text{Cl}^-$. For example, calcium in $\text{Ca}^{2+}$ has a charge of $2+$ and an oxidation number of $+2$.
The oxidation number is an accounting model: in molecules like water the electrons are shared, not transferred completely. Even so, the model is extremely useful for knowing who loses and who gains electrons.
Assign the oxidation number of each atom in these species and justify each one with a rule: oxygen in O₂, sodium in Na⁺, hydrogen in H₂O, and oxygen in H₂O.
Assign the oxidation number of each atom in these species and justify each one with a rule: oxygen in O₂, sodium in Na⁺, hydrogen in H₂O, and oxygen in H₂O.
Rules for elements and ions
The first two rules are the simplest.
Why? The two atoms in $\text{O}_2$ are identical and attract electrons with the same strength: neither one keeps more, so the assigned charge is zero.
Assign the oxidation number of each atom in these species and justify each one with a rule: oxygen in O₂, sodium in Na⁺, hydrogen in H₂O, and oxygen in H₂O.
Assign the oxidation number of each atom in these species and justify each one with a rule: oxygen in O₂, sodium in Na⁺, hydrogen in H₂O, and oxygen in H₂O.
Rules for hydrogen and oxygen
In compounds, two elements appear so often that it pays to memorize their usual number.
The reason: oxygen is very electronegative and takes the electrons of the bond; it ends up almost as if it had two extra electrons ($-2$). Hydrogen, when bonded to a more electronegative nonmetal, gives up its electron in this split ($+1$).
Assign the oxidation number of each atom in these species and justify each one with a rule: oxygen in O₂, sodium in Na⁺, hydrogen in H₂O, and oxygen in H₂O.
Assign the oxidation number of each atom in these species and justify each one with a rule: oxygen in O₂, sodium in Na⁺, hydrogen in H₂O, and oxygen in H₂O.
The total sum rule
The rule that lets you calculate unknown numbers is conservation of charge.
It makes sense: the total charge of the species cannot change just because of how we distribute it among the atoms.
With the three results we can order sulfur: $\text{H}_2\text{S}$ ($-2$) < $\text{SO}_2$ ($+4$) < $\text{SO}_3$ ($+6$).
Polyatomic ions and transition metals
When the species is an ion, the sum is not $0$: it is the charge of the ion. And when a metal has several possible numbers, the sum tells you which one it has in that compound.
Order the oxidation number of sulfur in these three substances from lowest to highest: H₂S, SO₂, and SO₃. Show the calculation of each oxidation number using the rules…
Order the oxidation number of sulfur in these three substances from lowest to highest: H₂S, SO₂, and SO₃. Show the calculation of each oxidation number using the rules (hydrogen $+1$, oxygen $-2$, total sum 0).
An order for applying the rules
When you have a new species, follow this path:
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Is it a simple substance (a single element)? Then every atom is $0$.
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Is it a single-atom ion? It equals its charge.
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If not, first assign $\text{O} = -2$ and $\text{H} = +1$.
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Set up the total sum equal to the charge of the species and solve for the missing number.
Order the oxidation number of sulfur in these three substances from lowest to highest: H₂S, SO₂, and SO₃. Show the calculation of each oxidation number using the rules…
Order the oxidation number of sulfur in these three substances from lowest to highest: H₂S, SO₂, and SO₃. Show the calculation of each oxidation number using the rules (hydrogen $+1$, oxygen $-2$, total sum 0).
Back to the rust
At the beginning we asked about the iron gate. In metallic iron, $\text{Fe}$, the oxidation number is $0$. In rust, $\text{Fe}_2\text{O}_3$, with $\text{O} = -2$: $2x + 3(-2) = 0$, so $x = +3$. The iron went from $0$ to $+3$: it lost electrons and was oxidized. Following oxidation numbers lets you see that change, and it is what we will do in the next sections.