Oxidation numbers

Following electrons we cannot see

When zinc becomes $\text{Zn}^{2+}$, the electrons clearly leave. But in $\text{H}_2 + \text{Cl}_2 \rightarrow 2\text{HCl}$ the electrons are shared, not handed over. Is this a redox reaction? We need a way to follow the electrons even when they are only shared.

Chemists use a bookkeeping number called the oxidation number, or oxidation state. It is the charge an atom would have if all its bonding electrons were given to the more electronegative atom. In hydrogen chloride, chlorine is more electronegative, so we count the shared pair as chlorine's. Hydrogen gets $+1$ and chlorine gets $-1$.

The rules

1. An atom in a free element has oxidation number 0. This is true for $\text{H}_2$, $\text{O}_2$, $\text{P}_4$, $\text{S}_8$ and for metals such as Na and Fe.
2. A simple ion has an oxidation number equal to its charge: $+1$ for $\text{Na}^+$, $+3$ for $\text{Al}^{3+}$, $-1$ for $\text{Cl}^-$.
3. Fluorine is $-1$ in all its compounds, because it is the most electronegative element.
4. Hydrogen is $+1$ when it is bonded to non-metals. It is $-1$ in metal hydrides such as NaH and $\text{CaH}_2$.
5. Oxygen is $-2$ in most compounds. It is $-1$ in peroxides such as $\text{H}_2\text{O}_2$ and $\text{Na}_2\text{O}_2$, and $-\tfrac{1}{2}$ in superoxides such as $\text{KO}_2$. In $\text{OF}_2$ it is $+2$, because fluorine wins.
6. Alkali metals are $+1$, alkaline earth metals are $+2$, and aluminium is $+3$ in their compounds.
7. The other halogens are $-1$ in halides. They are positive when combined with oxygen or with a more electronegative halogen.
8. The oxidation numbers of all the atoms in a species add up to its charge: 0 for a neutral compound, and the charge for an ion.

When two rules seem to disagree, the one earlier in the list wins.

Finding an oxidation number

Call the unknown number $x$. Write an equation for the total, and solve it.

Sulfur in $\text{H}_2\text{SO}_4$. The sum is zero: $2(+1) + x + 4(-2) = 0$. So $x = +6$.

Nitrogen in $\text{NO}_3^-$. The sum is $-1$: $x + 3(-2) = -1$. So $x = +5$.

Chromium in $\text{Cr}_2\text{O}_7^{2-}$. The sum is $-2$: $2x + 7(-2) = -2$. So $2x = 12$ and $x = +6$.

Notice that each atom is counted as many times as its subscript. Forgetting the 2 in $\text{Cr}_2$ is a common slip.

Set the ion to $\text{SO}_4^{2-}$: four oxygen atoms and a charge of 2. Does the bar for X match the sulfur you found above? Now try three oxygen atoms and a charge of 1.

Fractional oxidation numbers

Sometimes the rules give a fraction.

• In $\text{Fe}_3\text{O}_4$: $3x + 4(-2) = 0$, so $x = +\tfrac{8}{3}$.
• In $\text{Na}_2\text{S}_4\text{O}_6$: $2(+1) + 4x + 6(-2) = 0$, so $x = +\tfrac{5}{2}$.
• In $\text{C}_3\text{O}_2$: $3x + 2(-2) = 0$, so $x = +\tfrac{4}{3}$.

A fraction is an average. In $\text{Fe}_3\text{O}_4$ one iron atom is $+2$ and two are $+3$, and $\dfrac{2 + 3 + 3}{3} = \dfrac{8}{3}$. In the tetrathionate ion two sulfur atoms are 0 and two are $+5$, and the average is $\dfrac{5}{2}$. An oxidation number may be a fraction, but the charge on an ion never is.

Stock notation

Many metals show more than one oxidation number. A Roman numeral in brackets after the metal's name says which one is meant. This is the Stock notation.

• $\text{FeCl}_3$ is iron(III) chloride, and $\text{FeCl}_2$ is iron(II) chloride.
• $\text{Cu}_2\text{O}$ is copper(I) oxide, and CuO is copper(II) oxide.
• $\text{MnO}_2$ is manganese(IV) oxide.
• $\text{SnCl}_2$ is tin(II) chloride.

Older names, such as ferric and ferrous, are still found in books.

Using oxidation numbers to spot redox

An atom that is oxidised has an oxidation number that rises. An atom that is reduced has one that falls. Look at the reaction of zinc with hydrochloric acid:

Zinc goes from 0 to $+2$, so it is oxidised. Hydrogen goes from $+1$ to 0, so it is reduced. Chlorine stays at $-1$. The substance that contains the element reduced is the oxidising agent, here HCl. The substance that contains the element oxidised is the reducing agent, here zinc.

A reaction is a redox reaction only if some oxidation number changes. In $\text{NaOH} + \text{HCl} \rightarrow \text{NaCl} + \text{H}_2\text{O}$, nothing changes, so it is not.

Which agents can only go one way?

An element in its highest oxidation state cannot lose more electrons. Its compounds can only be oxidising agents. Examples are $\text{KMnO}_4$ (Mn is $+7$), $\text{K}_2\text{Cr}_2\text{O}_7$ (Cr is $+6$), $\text{HNO}_3$ (N is $+5$) and $\text{H}_2\text{SO}_4$ (S is $+6$).

An element in its lowest state cannot gain more electrons. Its compounds can only be reducing agents. Examples are $\text{H}_2\text{S}$ (S is $-2$) and $\text{NH}_3$ (N is $-3$).

An element in an intermediate state can do either. Examples are $\text{SO}_2$ (S is $+4$), $\text{H}_2\text{O}_2$ (O is $-1$) and $\text{HNO}_2$ (N is $+3$).

Practise with new numbers

Try it in Python

The program solves for the oxidation number of one element in a formula, using the fixed values for hydrogen, oxygen and the metals.

Common mistakes

• Forgetting the subscript. In $\text{Cr}_2\text{O}_7^{2-}$ there are two chromium atoms, so divide by 2 at the end.
• Using $-2$ for oxygen in a peroxide. It is $-1$ in $\text{H}_2\text{O}_2$.
• Using $+1$ for hydrogen in a metal hydride. It is $-1$ in $\text{CaH}_2$.
• Mixing up oxidation number and charge. The oxidation number of carbon in methane is $-4$, but there is no $\text{C}^{4-}$ ion.
• Saying that an oxidation number cannot be a fraction. It can, as an average.

Remember these

• The oxidation numbers of all the atoms add up to the charge of the species.
• A rise in oxidation number means oxidation. A fall means reduction.
• Free elements are 0, fluorine is $-1$, and oxygen is usually $-2$, hydrogen usually $+1$.
• The highest state can only oxidise. The lowest can only reduce.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. What is the oxidation number of phosphorus in $\text{PO}_4^{3-}$?

2. What is the oxidation number of oxygen in $\text{Na}_2\text{O}_2$?

3. Can $\text{H}_2\text{S}$ act as an oxidising agent?

4. In $\text{Fe}_3\text{O}_4$, how many iron atoms are $+3$ and how many are $+2$?