What is it made of?

Percentage composition

The percentage by mass of an element is the mass of that element in one mole of the compound divided by the molar mass, times 100. Caffeine, C₈H₁₀N₄O₂, has M = 194.20 g mol⁻¹ and contains 4 × 14.01 = 56.04 g of nitrogen per mole, so it is 28.9% nitrogen by mass.

From masses to an empirical formula

An empirical formula is the simplest whole-number ratio of atoms. To find it: convert each mass (or percentage, using 100 g) into moles, divide every value by the smallest, and multiply by 2 or 3 if a value ends in .5, .33 or .67. A sugar that is 40.0% C, 6.71% H and 53.3% O gives 3.33 : 6.66 : 3.33 mol, a ratio of 1 : 2 : 1, so its empirical formula is CH₂O.

Combustion analysis

The sample is burned in excess pure oxygen. The gases pass first through a water absorber (anhydrous calcium chloride) and then a carbon dioxide absorber (sodium hydroxide). The increase in mass of each absorber is the mass of H₂O and CO₂ formed. Nitrogen can be converted to NO₂ and collected in the same way.

• m(C) = m(CO₂) × 12.01 ÷ 44.01, because all the carbon ends up in CO₂;
• m(H) = m(H₂O) × 2.016 ÷ 18.016;
• m(O) is found by difference, because some of the oxygen in the products came from the O₂ gas, not from the sample.

Run the analysis yourself. Choose a sample, burn it, then reveal the calculation.

The order of the absorbers matters: sodium hydroxide also absorbs water, so if it came first, the carbon would be overestimated.

Molecular formula

The empirical formula is only a ratio. To find the molecular formula, divide the molar mass by the empirical formula mass and multiply the subscripts by the result. The molar mass can come from a mass spectrometer, or from gas measurements: n = PV ÷ RT, then M = m ÷ n. An ester with empirical formula C₂H₄O and M = 88 g mol⁻¹ is C₄H₈O₂.

Hydrates and gravimetric analysis

Many salts crystallise with water of crystallisation. Heating CuSO₄·xH₂O to constant mass drives off all the water: the mass lost gives moles of water, and x = n(H₂O) ÷ n(salt). In gravimetric analysis an element is converted into a pure precipitate of known formula, such as AgCl or Fe₂O₃, and its mass is found from the fraction of the precipitate that is that element.

Parts per million

Trace amounts are reported in ppm: mg of solute per kg of solution. For dilute aqueous solutions 1 L has a mass of about 1 kg, so 1 ppm ≈ 1 mg L⁻¹. Australian drinking water may contain at most 0.010 ppm of lead.