What is a solution?
A solution is a homogeneous mixture of two or more substances. The component present in the larger amount is usually the solvent, and the others are solutes. Solutions can be solid, liquid or gaseous: air is a gaseous solution, and brass is a solid solution of zinc in copper.
Concentration terms
Term | Definition | Depends on temperature? |
|---|---|---|
Mass percentage | (mass of component / mass of solution) × 100 | no |
ppm | parts of component per million parts of solution | no (when by mass) |
Mole fraction x | moles of component / total moles | no |
Molarity M | moles of solute per litre of solution | yes |
Molality m | moles of solute per kg of solvent | no |
Solubility of gases: Henry's law
The partial pressure of a gas above a solution is proportional to its mole fraction in the solution: p = K_H x
A higher value of K_H means lower solubility. Gas solubility decreases as temperature increases.
Applications:
Soft drinks are bottled under high CO₂ pressure, so more CO₂ dissolves.
Deep-sea divers can suffer the bends: at depth, extra nitrogen dissolves in the blood, and it forms bubbles if they surface too quickly. Their air tanks therefore use helium diluted with oxygen.
At high altitude the partial pressure of oxygen is low, which causes anoxia (weakness and difficulty thinking clearly).
Raoult's law
For a solution of volatile liquids, the partial vapour pressure of each component equals its mole fraction times the vapour pressure of the pure component: p₁ = x₁ p₁°
The total vapour pressure is p = p₁°x₁ + p₂°x₂.
For a non-volatile solute in a solvent, the vapour pressure of the solution is lower than that of the pure solvent, and the relative lowering equals the mole fraction of the solute:
(p° − p)/p° = x_solute
Ideal and non-ideal solutions
Ideal | Positive deviation | Negative deviation | |
|---|---|---|---|
Obeys Raoult's law? | yes, at all concentrations | no: vapour pressure is higher | no: vapour pressure is lower |
Interactions | A–B same as A–A and B–B | A–B weaker | A–B stronger |
ΔH_mix, ΔV_mix | 0, 0 | positive | negative |
Example | n-hexane + n-heptane | ethanol + acetone | chloroform + acetone |
Non-ideal solutions can form azeotropes: mixtures that boil at a constant temperature with the same composition in liquid and vapour, so they cannot be separated by fractional distillation. A minimum-boiling azeotrope shows positive deviation (about 95% ethanol in water). A maximum-boiling azeotrope shows negative deviation (about 68% nitric acid in water).
Colligative properties
Colligative properties depend only on the number of solute particles, not on their identity. For a dilute solution of a non-volatile solute:
Property | Formula |
|---|---|
Relative lowering of vapour pressure | Δp/p° = x_solute |
Elevation of boiling point | ΔT_b = K_b m |
Depression of freezing point | ΔT_f = K_f m |
Osmotic pressure | π = C R T |
K_b and K_f are constants characteristic of the solvent. For water, K_f = 1.86 K kg mol⁻¹.
Osmosis is the flow of solvent through a semipermeable membrane from the dilute side to the concentrated side. Osmotic pressure is the pressure needed to stop it. Because it can be measured at room temperature and gives large values even for dilute solutions, it is the best method for finding the molar masses of proteins and polymers.
Isotonic solutions have the same osmotic pressure. A 0.9% (mass/volume) NaCl solution is isotonic with blood, so it is used as normal saline.
Reverse osmosis: applying pressure greater than the osmotic pressure pushes solvent from the concentrated side to the dilute side. It is used to desalinate seawater.
Example. 1.8 g of glucose (M = 180 g/mol) is dissolved in 100 g of water. Find the depression in freezing point. m = (1.8/180)/0.1 = 0.1 mol/kg. ΔT_f = 1.86 × 0.1 = 0.186 K.
Abnormal molar masses and the van't Hoff factor
Electrolytes dissociate, producing more particles, while some solutes (such as acetic acid in benzene) associate, producing fewer. The van't Hoff factor i corrects for this:
ΔT_f = i K_f m, and π = i C R T
For NaCl in water, i ≈ 2. For K₂SO₄, i ≈ 3. For a solute that dimerises completely, i = ½.