Types of solutions and ways to express concentration
A solution is a homogeneous mixture. Its concentration can be given as percentage, ppm, mole fraction, molarity or molality; molality does not change with temperature, molarity does.
Solute and solvent
A solution is a homogeneous mixture: its composition and properties are the same all through. A binary solution has two components. The solvent is the component present in the larger amount, and it decides the physical state of the solution (solid, liquid or gas). The other component is the solute. Most of this chapter is about liquid solutions.
Types of solutions
| Type of solution | Solute | Solvent | Example |
|---|---|---|---|
| Gaseous | Gas | Gas | Oxygen and nitrogen mixed together (air) |
| Gaseous | Liquid | Gas | Chloroform vapour mixed with nitrogen |
| Gaseous | Solid | Gas | Camphor vapour in nitrogen |
| Liquid | Gas | Liquid | Oxygen dissolved in water |
| Liquid | Liquid | Liquid | Ethanol dissolved in water |
| Liquid | Solid | Liquid | Glucose or sugar dissolved in water |
| Solid | Gas | Solid | Hydrogen dissolved in palladium |
| Solid | Liquid | Solid | Amalgam of mercury with sodium |
| Solid | Solid | Solid | Copper dissolved in gold (gold jewellery) |
Ways to express concentration
| Term | How it is worked out | Unit | Changes with temperature? |
|---|---|---|---|
| Mass percentage (w/w) | (Mass of component ÷ total mass of solution) × 100 | % | No |
| Volume percentage (V/V) | (Volume of component ÷ total volume of solution) × 100 | % | Yes |
| Mass by volume percentage (w/V) | Mass of solute in g per 100 mL of solution | g per 100 mL | Yes |
| Parts per million (ppm) | (Parts of component ÷ total parts of solution) × 10⁶ | ppm | No, when by mass |
| Mole fraction (x) | Moles of the component ÷ total moles | None | No |
| Molarity (M) | Moles of solute ÷ volume of solution in L | mol L⁻¹ | Yes |
| Molality (m) | Moles of solute ÷ mass of solvent in kg | mol kg⁻¹ | No |
Molarity vs molality
That is why the boiling point and freezing point formulas use molality.
Worked example: one solution, three ways
23 g of ethanol (C₂H₅OH, M = 46 g mol⁻¹) is dissolved in 90 g of water (M = 18 g mol⁻¹). Find (a) the mass percentage of ethanol, (b) the mole fraction of each component and (c) the molality of the solution.
- Moles of ethanol, n₂ = 23 g ÷ 46 g mol⁻¹ = 0.5 mol. Moles of water, n₁ = 90 g ÷ 18 g mol⁻¹ = 5 mol.
- (a) Mass percentage = 23 ÷ (23 + 90) × 100 = 23 ÷ 113 × 100 = 20.4%.
- (b) x(ethanol) = 0.5 ÷ (0.5 + 5) = 0.5 ÷ 5.5 = 0.091.
- x(water) = 5 ÷ 5.5 = 0.909. Check: 0.091 + 0.909 = 1.
- (c) Molality = 0.5 mol ÷ 0.090 kg = 5.56 mol kg⁻¹.
(a) 20.4% ethanol by mass; (b) x(ethanol) = 0.091, x(water) = 0.909; (c) 5.56 mol kg⁻¹
Worked example: molarity and ppm
(a) 2.0 g of NaOH (M = 40 g mol⁻¹) is dissolved in water and the volume is made up to 250 mL. Find the molarity. (b) A 500 g sample of well water contains 0.75 mg of fluoride ions. Express this in ppm.
- (a) n = 2.0 g ÷ 40 g mol⁻¹ = 0.050 mol. V = 250 mL = 0.250 L.
- M = 0.050 mol ÷ 0.250 L = 0.20 mol L⁻¹.
- (b) Mass of F⁻ = 0.75 mg = 0.75 × 10⁻³ g. Mass of sample = 500 g.
- ppm = (0.75 × 10⁻³ g ÷ 500 g) × 10⁶ = 1.5 × 10⁻⁶ × 10⁶ = 1.5 ppm.
(a) 0.20 M; (b) 1.5 ppm of fluoride
A hospital drip of normal saline is a 0.9% (mass by volume) solution of NaCl, and the fluoride in drinking water is reported in ppm. Every label on a medicine bottle is a concentration statement.
2 marks: “Define molarity and molality. Which of the two is preferred when the temperature changes, and why?” Molarity = moles of solute per litre of solution; molality = moles of solute per kilogram of solvent. Molality is preferred because it depends on mass, which does not change with temperature; volume does.
3 marks: “18 g of glucose (C₆H₁₂O₆, M = 180 g mol⁻¹) is dissolved in 90 g of water. Find the mole fraction of glucose and the molality of the solution.” n(glucose) = 18 ÷ 180 = 0.1 mol; n(water) = 90 ÷ 18 = 5 mol. x(glucose) = 0.1 ÷ 5.1 = 0.0196. Molality = 0.1 mol ÷ 0.090 kg = 1.11 mol kg⁻¹.
1 marks: “Name two ways of expressing concentration that do not depend on temperature.” Any two of: mass percentage, mole fraction, molality, ppm by mass.
Capital M for the Measuring flask (litres of solution); small m for mass (kilograms of solvent). Masses never change with temperature, so mass %, mole fraction and molality stay fixed.