Percentage composition gives the mass of each element per 100 g of a compound. Converting those masses to moles gives the simplest atom ratio, the empirical formula. The molar mass then gives the molecular formula.
The percentage composition of a compound gives the mass of each element as a percentage of the total mass. For a known formula it is found from one mole:
mass % of element = (mass of element in 1 mol ÷ molar mass) × 100
Water, H₂O: using H = 1.008 and O = 16.00, the molar mass is 18.02 g/mol. One mole contains 2.016 g of hydrogen and 16.00 g of oxygen. So water is (2.016 ÷ 18.02) × 100 = 11.2% hydrogen and (16.00 ÷ 18.02) × 100 = 88.8% oxygen by mass. By the law of definite proportions, every sample of pure water has this composition.
Carbon dioxide, CO₂, has molar mass 44 g/mol. What percentage of its mass is carbon?
One mole of CO₂ contains 12 g of carbon out of 44 g.
Mass % of carbon = (12 ÷ 44) × 100 = 27.3%. The other 72.7% is oxygen, 32 g out of 44 g.
The molecule has one carbon atom and two oxygen atoms, and each oxygen atom has a larger mass than a carbon atom. So oxygen accounts for most of the mass.
A chemical analysis can measure the percentage composition of an unknown compound. A formula states the ratio of numbers of atoms. Numbers of atoms are proportional to numbers of moles. So the formula is found by converting the masses to moles.
The method:
The method gives the empirical formula: the simplest whole-number ratio of atoms. The molecular formula gives the actual number of each atom in one molecule. It is the empirical formula multiplied by a whole number n.
Glucose has empirical formula CH₂O. A glucose molecule is C₆H₁₂O₆, so n = 6. To find n, compare the molar mass with the empirical formula mass: n = molar mass ÷ empirical formula mass.
From percentages to a formula. Mass percentages become moles. The simplest mole ratio is the empirical formula. Dividing the molar mass by the empirical formula mass gives the multiplier for the molecular formula.
A compound contains 4.07% hydrogen, 24.27% carbon and 71.65% chlorine. Its molar mass is 98.96 g/mol. Find its formulae.
An oxide of carbon has empirical formula CO and molar mass 28 g/mol. What is its molecular formula?
The empirical formula mass of CO is 12 + 16 = 28 g/mol. n = 28 ÷ 28 = 1.
So the molecular formula is CO, the same as the empirical formula. This happens whenever one molecule contains exactly the simplest ratio of atoms. Water, H₂O, and carbon dioxide, CO₂, are other examples.
1The percentage composition of a compound gives…
2What percentage of the mass of CO₂ (molar mass 44 g/mol) is carbon?
3An empirical formula gives…
4Glucose is C₆H₁₂O₆. Its empirical formula is ____.
5What is the first step in finding a formula from percentage composition?
6The empirical formula is CH₂Cl (49.48 g/mol) and the molar mass is 98.96 g/mol. The molecular formula is…
Next: stoichiometry — using a balanced equation to calculate amounts, and finding which reactant runs out first.
Noescio