Percentage composition and formulas

Percentage composition tells us how much of each element a compound contains, by mass:

Mass % of an element = (mass of that element in one mole of the compound ÷ molar mass of the compound) × 100.

For example, carbon dioxide, CO₂ (molar mass 44 g mol⁻¹), contains 12 g of carbon per mole, so it is 12 ÷ 44 × 100 = 27.3% carbon, and the rest, 72.7%, is oxygen. The percentages always add up to 100.

Two kinds of formula:

• The empirical formula gives the simplest whole-number ratio of the atoms.
• The molecular formula gives the actual number of each kind of atom in one molecule.

Hydrogen peroxide is H₂O₂ (molecular), but its simplest ratio is HO (empirical).

To find a formula from the percentages, follow five steps:

• Step 1: assume 100 g of the compound, so each percentage becomes a mass in grams.
• Step 2: divide each mass by the element's atomic mass, to get the number of moles.
• Step 3: divide every mole number by the smallest one.
• Step 4: if the ratios are not whole numbers, multiply them all by a small whole number. A ratio of 1 : 1.33 becomes 3 : 4 when multiplied by 3. This gives the empirical formula.
• Step 5: find n = molar mass ÷ empirical formula mass. The molecular formula is n times the empirical formula. For example, an empirical formula CH₂Cl (mass 49.5) and a molar mass of 99 give n = 2, so the molecular formula is C₂H₄Cl₂.

Notice that the percentages alone can only give the empirical formula; to get the molecular formula, you also need the molar mass.