Empirical formulae

The empirical formula of a substance is the simplest whole number ratio of the atoms of each element present.

Calculating an empirical formula

Information about reacting masses is used to calculate empirical formulae. This is obtained from experiments.

Example

A hydrocarbon contains 4.8 g of carbon and 1.0 g of hydrogen. Calculate its empirical formula. (Ar of C = 12, Ar of H = 1)

Ar refers to the relative atomic mass of an element.

StepActionResultResult
1Write the element symbolsCH
2Write the masses4.8 g1.0 g
3Write the Ar values121
4Divide masses by Ar4.8 ÷ 12 = 0.41.0 ÷ 1 = 1
5Divide by the smallest number0.4 ÷ 0.4 = 11.0 ÷ 0.4 = 2.5
6Multiply (if needed) to get whole numbers1 × 2 = 22.5 × 2 = 5
7Write the formulaC2H5C2H5

The action at step 5 usually gives the simplest whole number ratio straightaway. Sometimes it does not, so both numbers may need to be multiplied to get a whole number (step 6). For example, multiply by 2 if there is a .5, by 3 if the number has a .33, or by 4 if it has a .25 in a number.

Question

3.2 g of sulfur reacts completely with oxygen to produce 6.4 g of an oxide of sulfur. Calculate the empirical formula of the oxide of sulfur. (Ar of S = 32, Ar of O = 16)

StepActionResultResult
1Write the element symbolsSO
2Write the masses3.2 g6.4 g - 3.2 g = 3.2 g
3Write the Ar values3216
4Divide masses by Ar3.2 ÷ 32 = 0.13.2 ÷ 16 = 0.2
5Divide by the smallest number0.1 ÷ 0.1 = 10.2 ÷ 0.1 = 2
6Multiply (if needed) to get whole numbers(not needed - already have whole numbers)(not needed - already have whole numbers)
7Write the formulaSO2SO2

Examples of empirical formula

The empirical formula can worked out from diagrams of molecules. Here is a diagram showing a molecule of butane:

Covalent structure of butane.

The molecular formula of butane is C4H10. This is the actual number of atoms of each element in a molecule of butane. This formula does not show the simplest whole number ratio because each number can be divided by 2. This gives the empirical formula of butane - C2H5.

The molecular formula and empirical formula of some substances are the same. For example, both types of formula for carbon dioxide are CO2.

The formulae used for ionic compounds, giant molecules and metals are all empirical formulae. This is because the actual numbers of ions and atoms they contain is so huge.