Determining Empirical Formulae

What an empirical formula tells you

A chemical formula uses element symbols and small numbers called subscripts to represent the elements present and their proportions. For example, $\mathrm{C_2H_6}$ represents two carbon atoms and six hydrogen atoms in one ethane molecule. When no subscript is written, it means one.

A molecular formula gives the actual number of atoms of each element in one molecule. An empirical formula gives the simplest whole-number ratio of those atoms. It describes their proportions rather than the size of the molecule.

For ethane, the carbon-to-hydrogen ratio is $2:6$. Dividing both numbers by two gives $1:3$, so its empirical formula is $\mathrm{CH_3}$. This does not mean that an ethane molecule contains only one carbon and three hydrogen atoms: it means that there are three hydrogen atoms for every carbon atom.

Turning atom counts into a formula

Start by writing the numbers of atoms as a ratio, keeping the elements in a clear, stated order. Then divide every number by their highest common factor: the largest whole number that divides exactly into all the counts. Use the simplified numbers as the formula’s subscripts, leaving out any subscript of one.

Suppose a diagram represents a molecule containing four carbon atoms, eight hydrogen atoms and two oxygen atoms. The ratio is:

$$\mathrm{C:H:O}=4:8:2$$

The highest common factor is two. Dividing all three counts by two gives:

$$\mathrm{C:H:O}=2:4:1$$

The empirical formula is therefore $\mathrm{C_2H_4O}$. The oxygen matters when simplifying: although four divides both the carbon and hydrogen counts, it does not divide the oxygen count to give a whole number.

Reading models and diagrams

In a ball-and-stick model, the balls represent atoms and the sticks represent bonds. Use the key to identify each element, then count its atoms. In a displayed formula, count each written element symbol. Once you have the counts, the ratio method is the same.

The diagram below separates the atoms into groups to make counting clear; it does not show their positions or bonds within a molecule.

The four-carbon, eight-hydrogen, two-oxygen inventory gives the ratio worked through above. Grouping the symbols helps you see that simplifying a ratio changes how you describe the proportions, not which atoms the molecule actually contains.

You can also start directly from a molecular formula. Glucose, $\mathrm{C_6H_{12}O_6}$, has the ratio . Dividing every count by six gives , so its is . Some molecular formulae cannot be simplified: the ratio in water, , is already , so its empirical formula is also .

Working backwards from an empirical formula

An empirical formula lets you check whether a model has the correct proportions. For $\mathrm{CH_2}$, a matching model must contain twice as many hydrogen atoms as carbon atoms. Two carbon atoms and four hydrogen atoms fit; two carbon atoms and six hydrogen atoms do not.

To generate possible atom counts, multiply every subscript by the same whole number. Thus $\mathrm{CH_2}$ is compatible with molecular formulae such as $\mathrm{C_2H_4}$ and , the formulae of ethene and propene respectively. Both have the same simplest .

This also shows the limit of an empirical formula: it cannot, on its own, tell you the molecule’s actual atom counts, identify the compound uniquely or show how its atoms are arranged.

Find an empirical formula

Atom counts → ratio → simplest whole-number ratio → formula.

Divide every count by the highest common factor. Omit subscripts of one.