Topic 1.4 Composition of Mixtures: distinguish pure substances from mixtures and use elemental analysis and mass relationships to determine the composition of a mixture.

What this topic is asking

The College Board (Topic 1.4) wants you to tell a pure substance from a mixture, and to use mass relationships and elemental analysis to work out the composition of a mixture. Pure substances have a fixed composition and fixed properties; mixtures vary, and that variability is what these calculations quantify.

Pure substances versus mixtures

The decisive difference is variability. Carbon dioxide is always $\text{CO}_2$ with the same melting point and density. A salt-water solution can be made stronger or weaker, and its freezing point changes with concentration, because it is a mixture. Mixtures can be homogeneous (uniform throughout, like a solution or a metal alloy) or heterogeneous (non-uniform, like sand in water), but in either case the components are not chemically bonded and can in principle be separated by physical means.

Mass percent of a component

A common way to describe a mixture's composition is the mass percent of each component:

For a solution, the related quantity is the concentration (for example molarity), but for solid mixtures and for AP-style stoichiometry problems, mass percent is the usual target. The mass percents of all components add to $100\%$, which gives you a built-in check.

Solving mixture problems with mass relationships

Many AP mixture problems give you a total mass and one measured quantity (such as the total mass of a particular element, or the mass of a product formed) and ask for the make-up of the mixture.

The skill being tested is connecting an analytical measurement back to composition. Elemental analysis, the experimental technique behind it, burns or otherwise decomposes the sample and measures how much of one element it contained. Because each component contributes that element in a different, calculable proportion, the measured total constrains the mixture's make-up. If a problem gives you two independent measurements (for example total mass and total moles), you can even handle a mixture with two unknowns by solving two simultaneous equations.

Distinguishing the question types

Watch for the phrase that signals which calculation is wanted. "Percent composition of the compound" (Topic 1.3) asks about a single pure substance's formula. "Composition of the mixture" asks what fraction of the sample is each separate substance. They use the same mole and mass tools but answer different questions, so read carefully.

Try this

Q1. Classify each as a pure substance or mixture: (a) distilled water, (b) bronze, (c) oxygen gas. [3 points]

• Cue. (a) pure substance (compound); (b) mixture (alloy); (c) pure substance (element).

Q2. A $2.00$ g sample of a mixture is $30\%$ copper by mass. Calculate the mass of copper present. [1 point]

• Cue. $0.30 \times 2.00 = 0.60$ g of copper.