Empirical & Molecular Formulae (Cambridge International A-Level Chemistry)

Empirical & Molecular Formulae

• The molecular formula is the formula that shows the number and type of each atom in a molecule

  • Eg. the molecular formula of ethanoic acid is C₂H₄O₂

• The empirical formula is the simplest whole number ratio of the elements present in one molecule or formula unit of the compound

  • Eg. the empirical formula of ethanoic acid is CH₂O

• Organic molecules often have different empirical and molecular formulae

• Simple inorganic molecules however have often similar empirical and molecular formulae

• Ionic compounds always have similar empirical and molecular formulae

Empirical & Molecular Formulae Calculations

Empirical formula

• The empirical formula is the simplest whole-number ratio of the elements present in one molecule or formula unit of the compound
• It is calculated from knowledge of the ratio of masses of each element in the compound
• The empirical formula can be found by determining the mass of each element present in a sample of the compound
• It can also be deduced from data that gives the percentage compositions by mass of the elements in a compound

Worked Example Calculating empirical formula from mass

Determine the empirical formula of a compound that contains 10 g of hydrogen and 80 g of oxygen.

Answer:

Elements	Hydrogen	Oxygen
Mass of each element (g)	10	80
Atomic mass	1.0	16.0
Moles = mass / Ar	$\frac{10}{1.0}$ = 10	$\frac{80}{16.0}$ = 5
Ratio (divide by smallest value)	$\frac{10}{5}$ = 2	$\frac{5}{5}$ = 1

• So, the empirical formula of the compound is H₂O

Worked Example Calculating empirical formula from %

Determine the empirical formula of a compound that contains 85.7% carbon and 14.3% hydrogen.

Answer:

Elements	Carbon	Hydrogen
Mass of each element (%)	85.7	14.3
Atomic mass	12.0	1.0
Moles = mass / Ar	$\frac{85.7}{12.0}$ = 7.14	$\frac{14.3}{1.0}$ = 14.3
Ratio (divide by smallest value)	$\frac{7.14}{7.14}$ = 1	$\frac{14.3}{7.14}$ = 2.00

• So, the empirical formula of the compound is CH₂

Molecular formula

• The molecular formula gives the exact number of atoms of each element present in the formula of the compound
• The molecular formula can be found by dividing the relative formula mass of the molecular formula by the relative formula mass of the empirical formula
• Multiply the number of each element present in the empirical formula by this number to find the molecular formula

Worked Example Calculating molecular formula

The empirical formula of X is C₄H₁₀S and the relative formula mass of X is 180.

What is the molecular formula of X?

Relative atomic mass Carbon: 12 Hydrogen:1 Sulfur:32

Answer:

• Step 1: Calculate the relative formula mass of the empirical formula

  • Relative formula mass = (C x 4) + (H x 10) + (S x 1)
  • Relative formula mass = (12 x 4) + (1 x 10) + (32 x 1)
  • Relative formula mass = 90

• Step 2: Divide the relative formula mass of X by the relative formula mass of the empirical formula

  • Ratio between M_r of X and the M_r of the empirical formula = 180/90
  • Ratio between M_r of X and the M_r of the empirical formula = 2

• Step 3: Multiply each number of elements by 2

  • (C_{4 x 2}) + (H_{10 x 2}) + (S_{1 x 2}) = (C₈) + (H₂₀) + (S₂)
  • The molecular formula of X is C₈H₂₀S₂