An empirical formula gives the simplest whole-number ratio of the atoms in a compound. Glucose, \mathrm{C_6H_{12}O_6}, contains carbon, hydrogen and oxygen atoms in the ratio 6 : 12 : 6, which is 1 : 2 : 1, so its empirical formula is \mathrm{CH_2O}.
A molecular formula gives the actual number of each kind of atom in one molecule. Ethene, \mathrm{C_2H_4}, has the empirical formula \mathrm{CH_2} and benzene, \mathrm{C_6H_6}, has \mathrm{CH}, while for water the two formulae are the same.
Ionic compounds and covalent network crystals are not made of molecules, so their formulae, such as \mathrm{NaCl} and \mathrm{SiO_2}, are always empirical formulae.
An oxide of iron contains 69.9 % iron by mass. In 100 g of the oxide there are therefore 69.9 g of iron and 30.1 g of oxygen.
Dividing each mass by its molar mass gives the amounts: 69.9 g ÷ 55.8 g/mol = 1.25 mol of iron and 30.1 g ÷ 16.0 g/mol = 1.88 mol of oxygen. The ratio of the atoms is the ratio of these amounts.
Dividing both by the smaller amount gives 1 : 1.50, which is not yet a ratio of whole numbers. Doubling gives 2 : 3, so the empirical formula is \mathrm{Fe_2O_3}, iron(III) oxide, which is found in the ore haematite.
Blue crystals of copper(II) sulfate contain water molecules held in the crystal, known as water of crystallization. On heating, this water leaves as steam and white anhydrous copper(II) sulfate remains.
Heating 2.50 g of the blue crystals until the mass stops changing leaves 1.60 g of white powder, so 0.90 g of water has been driven off.
The amounts are 1.60 g ÷ 159.6 g/mol = 0.0100 mol of \mathrm{CuSO_4} and 0.90 g ÷ 18.0 g/mol = 0.050 mol of water, a ratio of 1 : 5. The formula of the blue crystals is therefore \mathrm{CuSO_4 \cdot 5H_2O}.
Different compounds can share an empirical formula. Methanal, ethanoic acid and glucose all have the empirical formula \mathrm{CH_2O}, and one \mathrm{CH_2O} unit has a relative mass of 30.0.
The molecular formula is a whole number of these units. Dividing the relative molecular mass by 30.0 gives that number: 30.0 for methanal gives 1, 60.0 for ethanoic acid gives 2, and 180.0 for glucose gives 6.
The molecular formulae are therefore \mathrm{CH_2O}, \mathrm{C_2H_4O_2} and \mathrm{C_6H_{12}O_6}. The relative molecular mass itself is measured separately, for example from the density of the compound as a gas.
To find the empirical formula of a compound of carbon, hydrogen and oxygen, a weighed sample is burned completely in dry oxygen over hot copper(II) oxide. The water formed is absorbed by calcium chloride and the carbon dioxide by soda lime, and both tubes are weighed.
The calcium chloride tube must come first. Soda lime absorbs water as well as carbon dioxide, so in the other order the water would be counted as carbon dioxide.
A 4.60 mg sample gave 8.80 mg of carbon dioxide and 5.40 mg of water, which contain 2.40 mg of carbon and 0.600 mg of hydrogen. The oxygen is the rest: 4.60 - 2.40 - 0.600 = 1.60 mg.
The molar masses give C : H : O = 0.200 : 0.600 : 0.100 = 2 : 6 : 1, so the empirical formula is \mathrm{C_2H_6O}. Since the relative molecular mass is 46.0, this is also the molecular formula, that of ethanol or methoxymethane.