Solutions and concentration

A solution is a homogeneous mixture of two or more substances: its composition is the same all the way through. Sugar in water, air, and brass (copper with zinc) are all solutions. The substance present in the larger amount is usually called the solvent; the others are solutes.

Chemists describe how much solute a solution holds, its concentration, in several ways:

• Mass percentage = (mass of the component ÷ total mass of the solution) × 100. A 10% glucose solution has 10 g of glucose in every 100 g of solution.
• Parts per million (ppm) is used when the amount is tiny, such as a pollutant in water: grams of the component in a million grams of solution.
• Mole fraction x = moles of one component ÷ total moles of all the components. The mole fractions of all the components always add up to 1.
• Molarity M = moles of solute in one litre of solution.
• Molality m = moles of solute in one kilogram of solvent.

Watch the difference between the last two. Molarity uses a volume, and liquids expand when warmed, so molarity changes with temperature. Molality uses only masses, which do not change, so molality does not depend on temperature.

When a mass of solvent is given in grams, change it to kilograms first (or multiply the top by 1000). If a question gives 75 g of benzene, the molality is moles of solute × 1000 ÷ 75.

A useful number: 1 L (1 kg) of water is about 55.5 mol of water molecules (1000 ÷ 18). It turns up in many questions.