Solutions: concentration, dilution and colligative properties
How substances dissolve, molarity, molality and mole fraction, dilution, boiling point elevation, freezing point depression and osmotic pressure.
A solution is a homogeneous mixture: a solute dissolved in a solvent. Almost all laboratory chemistry, and a good part of industrial chemistry, happens in aqueous solution. This lesson covers how substances dissolve, the ways of expressing concentration and the properties that depend only on the number of dissolved particles.
Why things dissolve
The rule of thumb is “like dissolves like”: polar solvents such as water dissolve salts and polar substances; non-polar ones such as hexane dissolve fats and oils. When a salt dissolves in water, water molecules surround each ion with the right pole facing it (solvation): the partially negative oxygen towards cations, the hydrogens towards anions.
The solubility of solids usually grows with temperature, that of gases decreases (a warm soft drink quickly loses its carbon dioxide). For gases Henry’s law holds: solubility is proportional to the partial pressure of the gas above the liquid.
Concentrations
| Quantity | Definition | Unit |
|---|---|---|
| Molarity M | moles of solute / litres of solution | mol/L |
| Molality m | moles of solute / kg of solvent | mol/kg |
| Mole fraction χ | moles of a component / total moles | dimensionless |
| Mass percent | mass of solute / mass of solution · 100 | % |
| ppm | parts per million by mass | mg/kg |
Molality does not change with temperature, because it does not depend on volume: that is why it is used for colligative properties.
Dilution example. The moles of solute do not change when solvent is added: M1·V1 = M2·V2. To prepare 500 mL of 0.10 M HCl from a 2.0 M solution you need V1 = 0.10 · 500 / 2.0 = 25 mL, made up to 500 mL with water (always pour the acid into the water, never the other way round).
Colligative properties
Some properties of a solution depend only on how many solute particles there are, not on which ones. For electrolytes what counts is the number of ions produced: the van ‘t Hoff factor i is 1 for sugar, about 2 for NaCl, about 3 for CaCl2.
- Vapour pressure lowering (Raoult’s law): P = χsolvent · P°.
- Boiling point elevation: ΔTb = i · Kb · m, with Kb = 0.512 °C·kg/mol for water.
- Freezing point depression: ΔTf = i · Kf · m, with Kf = 1.86 °C·kg/mol for water.
- Osmotic pressure: π = i · M · R · T.
Example. Dissolving 58.4 g of NaCl (1 mol) in 1 kg of water, with i ≈ 2, lowers the freezing point by 2 · 1.86 · 1 ≈ 3.7 °C: that is why salt is spread on roads. The real value is a little smaller, because at high concentration the ions are not fully independent.
Solutions and electricity
Pure water conducts very little; with a dissolved salt it conducts because the ions move in the electric field. This is the principle of conductivity meters, which measure water purity (the deionised water used in chip manufacturing has a resistivity of about 18 MΩ·cm), and of the electrolytes in batteries and electrolytic capacitors.
