Empirical and molecular formulae

Empirical and molecular formulae are ratios

The empirical formula gives the smallest whole number ratio of atoms of each element in a compound.

The molecular formula gives the actual number of atoms of each type of element in a molecule.

The molecular formula is made up of a whole number of empirical units.

Empirical formulae are calculated from experiments

Ex: When a hydrocarbon is burnt in excess oxygen, 4.4g of carbon dioxide and 1.8g of water are made. What is the empirical formula of the hydrocarbon.

No. of moles of CO₂ = Mass/M = 4.4/ 12.0+(2×16.0) = 4.4/44.0 = 0.10 moles

1 Mole of CO₂ contains 1 Mole of carbon atoms, so you must have started with 0.10 moles of carbon atoms.

No. of moles of H₂O: 1.8/ (2×1.0) + 16.0 = 1.8/ 18.0 = 0.10 moles

1 moles of H₂O contains 2 moles of hydrogen atoms (H), so you must have started with 0.20 moles of hydrogen atoms.

Ratio: C:H = 0.10:0.20. Now you divide both numbers by the smallest - here it’s 0.10.

So, the ratio C:H =1:2. So the empirical formula must be CH₂.

Molecular formulae are calculated from experimental data too

Ex: When 4.6g of an alcohol, with molar mass 46gmol^-1 , is burnt in excess oxygen, it produces 8.8g of carbon dioxide and 5.4g of water. Calculate the empirical formula for the alcohol and then its molecular formula.

No. of moles of CO₂ = mass/M = 8.8/ 44 = 0.2 moles

1 mole of CO₂ contains 1 mole of C. So, 0.2 moles of CO₂ contains 0.2 moles of C.

No. of moles of H₂O = mass/ M = 5.4/18 = 0.3 moles

1 mole of H₂O contains 2 moles of H. So, 0.3moles of H₂O contains 0.6 moles of H.

Mass of C = No. of moles x M = 0.2 ×12.0 = 2.4g

Mass of H = No. of moles x M = 0.6 × 1.0 = 0.6 g

Mass of O = 4.6 - (2.4+0.6) = 1.6g

Number of moles O = mass/M = 1.6/16.0 = 0.1 moles

Molar ratio = 0.2 : 0.6 : 0.1 = 2 : 6 : 1

Empirical formula = C₂H₆O

Mass of empirical formula = (2×12.0) + (6×1.0.) + 16.0 = 46.0g

In this example, the mass of the empirical formula equals the molecular mass, so the empirical and molecular formulae are the same,

Molecular formula = C₂H₆O