Percent Composition and Empirical Formulas

Core Idea

Percent composition describes the mass percentage of each element in a compound. Empirical formula is the simplest whole-number ratio of atoms in a compound, determined from percent composition or experimental data. Molecular formula is the actual number of atoms, found by dividing molecular mass by empirical formula mass.

Explainer

Building on your understanding of molar mass, you can now ask a quantitative question about any compound: what fraction of its mass comes from each element? This is percent composition, calculated by dividing the total mass contributed by each element (number of atoms × molar mass of that element) by the compound's molar mass, then multiplying by 100%. For water (H₂O, molar mass 18.02 g/mol), hydrogen contributes 2 × 1.008 = 2.016 g/mol, so its percent composition is (2.016 / 18.02) × 100% = 11.19%. Oxygen accounts for the remaining 88.81%. This calculation works for any compound whose formula you know.

The more powerful application runs in reverse. Suppose a chemist analyzes an unknown compound and finds it is 40.0% carbon, 6.7% hydrogen, and 53.3% oxygen by mass. To find the empirical formula, assume a 100-gram sample so the percentages become grams directly: 40.0 g C, 6.7 g H, 53.3 g O. Convert each to moles using molar masses: 40.0 / 12.01 = 3.33 mol C, 6.7 / 1.008 = 6.65 mol H, 53.3 / 16.00 = 3.33 mol O. Divide each by the smallest value (3.33) to get the simplest ratio: C₁H₂O₁, or CH₂O. This is the empirical formula — the simplest whole-number ratio of atoms.

The empirical formula tells you the ratio but not the actual count. The compound could be CH₂O (formaldehyde, molar mass 30.03), C₂H₄O₂ (acetic acid, 60.05), or C₆H₁₂O₆ (glucose, 180.16) — all share the same empirical formula. To determine the molecular formula, you need one additional piece of data: the compound's actual molar mass, typically obtained from mass spectrometry or another experimental method. Divide the measured molar mass by the empirical formula mass to get a whole-number multiplier, then multiply each subscript in the empirical formula. If the measured molar mass is 180 g/mol and the empirical formula mass (CH₂O) is 30 g/mol, the multiplier is 6, giving C₆H₁₂O₆. This two-step process — percent composition to empirical formula, then empirical formula to molecular formula — is how chemists identify unknown compounds from experimental mass data.