Concentration of solutions

Most reactions in the laboratory happen in solutions. The substance dissolved is the solute; the one it is dissolved in is the solvent. Concentration tells how much solute is present, and can be expressed in four ways:

• Mass per cent = mass of solute ÷ mass of solution × 100. (Mass of solution = mass of solute + mass of solvent.) 5 g of salt in 45 g of water is 5 ÷ 50 × 100 = 10%.
• Mole fraction of A = moles of A ÷ total moles (nA + nB). The mole fractions of all the parts add up to 1.
• Molarity (M) = moles of solute ÷ litres of solution. 0.4 mol of glucose in 2 L of solution is 0.2 M.
• Molality (m) = moles of solute ÷ kilograms of solvent.

There is an important difference between the last two. A liquid expands when heated, so the volume of a solution changes with temperature, and so does its molarity. Molality uses the mass of the solvent, which does not change with temperature, so molality stays the same.

When a solution is diluted (more solvent is added), the moles of solute stay the same; they just spread through more volume. So M₁V₁ = M₂V₂. For example, 50 mL of 2 M acid made up to 500 mL: M₂ = 2 × 50 ÷ 500 = 0.2 M.