Composition of mixtures

A pure substance — an element or a compound — is built from a single kind of particle, so its composition is fixed. Water is always two hydrogens to one oxygen; no sample of pure water is ever 20% hydrogen. Its percent composition is a fingerprint.

A mixture contains more than one kind of particle, physically combined, and its proportions can vary from sample to sample. Salt water can be barely salty or nearly saturated and still be salt water. That is the defining difference: a mixture's composition is not fixed, and the components keep their own identities and can be separated by physical means.

Because a mixture's composition varies, you cannot look it up — you have to measure it. The usual route is to separate the components physically, weigh them, and compare each mass to the total. Since separation neither creates nor destroys matter, the component masses always add back to the starting mass.

Composition problems for mixtures come down to bookkeeping with conserved mass. The steps rarely change.

1. Separate by a physical property. Dissolving, filtering, evaporating, or magnetism splits the mixture without changing what each component is. Salt dissolves and sand does not, so filtering divides them.
2. Weigh each recovered component. The masses you recover must sum to the mass you started with. If they don't, you lost some material, not made or destroyed any.
3. Divide each part by the whole. Mass percent of a component = (mass of that component ÷ total mass) × 100. The percentages of all components add to 100%.
4. Use a component's back to grams when needed. Given a percent and a total mass, multiply to recover a component's mass: 40% of 10.0 g is 4.0 g. The percent is a ratio; the grams depend on how much you took.

A useful shortcut: if a mixture has only two components, finding one immediately gives the other. Recover 6.0 g of sand from a 10.0 g mixture and the salt must be 4.0 g — no separate measurement needed.

Quick reference card. Sort what has fixed composition from what does not.

Question. A 10.0 g mixture of table salt and sand is stirred into water, filtered, and the filtrate evaporated. You recover 4.0 g of salt. What is the mixture's composition by mass?

Step 1 — separate. Salt dissolves; sand does not. Filtering keeps the sand on the paper and the salt in solution — a physical separation that changes neither substance.

Step 2 — weigh and check conservation. Evaporating the filtrate leaves 4.0 g of salt. By mass conservation, the sand is 10.0 − 4.0 = 6.0 g.

Step 3 — divide each part by the whole. Salt: 4.0 ÷ 10.0 × 100 = 40% salt. Sand: 6.0 ÷ 10.0 × 100 = 60% sand. They add to 100%, as they must.

Sanity check. A different scoop of the same salt-and-sand pile could easily be 25% salt or 55% salt — the 40% is a property of this sample, not of "salt-and-sand mixtures" in general. That variability is exactly what makes it a mixture rather than a compound.