Solutions and concentration: study guide

Key ideas

A concentration says how much solute is in a given amount of solution or solvent. Which unit you use depends on whether volume or temperature changes matter.

• Molarity is moles of solute per liter of solution: M = n ÷ V. It changes slightly with temperature because volume does.
• Molality is moles of solute per kilogram of solvent. It does not depend on temperature.
• When you dilute, the amount of solute stays the same: M₁V₁ = M₂V₂.
• Colligative properties such as boiling-point elevation depend on the number of dissolved particles: ΔT = i × K × m.

Key equations

• M = n ÷ V
• M₁V₁ = M₂V₂
• molality = mol solute ÷ kg solvent
• ppm = mg solute ÷ kg solution
• ΔT = i × K × m

Worked example

Make 250 mL of 0.10 M NaCl (58.44 g/mol): mass = 0.10 mol/L × 0.250 L × 58.44 g/mol = 1.46 g. To dilute 50.0 mL of a 2.0 M solution to 0.50 M, V₂ = 2.0 × 50.0 ÷ 0.50 = 200 mL, so add water up to 200 mL, which is 150 mL of water.

Common mistakes

• Using the volume of solvent instead of the volume of solution in molarity.
• Adding the new volume of water to the volume of concentrate before the dilution formula. V₂ is the final volume.
• Forgetting the van ’t Hoff factor i for salts that dissociate into several ions.

Practice

Test yourself with practice questions on this topic: Solutions and concentration