1.3 Elemental Composition of Pure Substances

A pure substance has only one kind of particle. Some are made of separate molecules, such as H₂O or CO₂. Others, like NaCl, are huge 3-D arrays of ions with no separate molecules; for these, the formula describes a formula unit, the simplest ratio of ions (one Na⁺ for every Cl⁻).

The law of definite proportions says any pure sample of a compound has the same mass ratio of its elements. Water from a glacier and water made in a lab are both 11.19% hydrogen and 88.81% oxygen by mass. If a sample's mass ratio is different, it's either a different compound or not pure.

Percent by mass of an element = (mass of that element in the compound ÷ total mass) × 100.

Using a formula, take the mass of the element in one mole of the compound and divide by the molar mass. For glucose, C₆H₁₂O₆ (180.16 g/mol), carbon is 6(12.01) ÷ 180.16 × 100 = 40.00% C.

The empirical formula is the lowest whole-number ratio of atoms. Subscripts count atoms, not grams, so you always have to convert masses to moles before comparing.

• If you're given percentages, assume a 100 g sample so each percent becomes grams.
• Convert each mass to moles using the atomic mass.
• Divide every mole value by the smallest one.
• If a ratio ends in about .5, .33 or .25, multiply all ratios by 2, 3 or 4 to get whole numbers. Don't round 1.5 to 2.
• Write the formula with those whole numbers as subscripts.

In the lab, you rarely start with percentages. A common experiment heats a hydrate, a salt with water molecules built into its crystals, such as CuSO₄·5H₂O. The mass lost on heating is the water. Convert the mass of water and the mass of dry salt left behind to moles, and their ratio gives the number of water molecules per formula unit.

The same idea works for any data: find the mass of each element, convert to moles, and compare. If some water stays behind because the sample wasn't heated long enough, the measured water mass is too small, and the calculated ratio of water to salt comes out too low.

Different compounds can share an empirical formula. Formaldehyde (CH₂O), acetic acid (C₂H₄O₂) and glucose (C₆H₁₂O₆) all reduce to CH₂O, so they have identical percent compositions. Percent composition alone can't tell them apart.

If you also know the molar mass, you can find the molecular formula: divide the molar mass by the empirical formula's mass, then multiply every subscript by that whole number. For ionic compounds, the empirical formula is the formula you write.