Quantitative analysis

Quantitative analysis finds how much of each element a compound contains, as a percentage by mass. The general idea: % of element = mass of element ÷ mass of compound × 100.

Carbon and hydrogen (Liebig's method): a known mass, m, of the compound is burnt in oxygen. The CO₂ is absorbed in potassium hydroxide, and the water in anhydrous calcium chloride; both are weighed.

• C% = 12 × m(CO₂) × 100 / (44 × m)
• H% = 2 × m(H₂O) × 100 / (18 × m)

For example, 0.20 g of a compound gives 0.44 g of CO₂: C% = 12 × 0.44 × 100 / (44 × 0.20) = 60%.

Nitrogen can be found in two ways:

• Dumas' method: the compound is heated with copper oxide in an atmosphere of CO₂. The nitrogen formed is collected (over KOH, which absorbs the CO₂), its volume is corrected to STP (subtracting the aqueous tension, the pressure of water vapour), and N% = 28 × V(STP) × 100 / (22 400 × m).
• Kjeldahl's method: the compound is heated with concentrated sulphuric acid, turning its nitrogen into ammonium sulphate. Alkali then liberates ammonia, which is passed into a known volume of standard acid; the leftover acid is found by titration. N% = 1.4 × M × 2(V – V₁/2) / m. It does not work for nitro and azo compounds, or for nitrogen in a ring (as in pyridine), because their nitrogen does not change into ammonium sulphate.

Halogens (Carius method): the compound is heated with fuming nitric acid and silver nitrate, and the silver halide formed is weighed. X% = atomic mass of X × m(AgX) × 100 / (molar mass of AgX × m). Sulphur is turned into sulphuric acid and precipitated as barium sulphate: S% = 32 × m(BaSO₄) × 100 / (233 × m).

Phosphorus is weighed as ammonium phosphomolybdate, or as Mg₂P₂O₇: P% = 62 × m₁ × 100 / (222 × m). Oxygen is usually found by difference: 100 minus the sum of all the other percentages.