A solution is a homogeneous mixture of two or more substances, made up of a solute (present in smaller amount) and a solvent (present in larger amount). Solutions can be classified by the physical state of the solute and solvent — gas in gas, liquid in liquid, solid in liquid, and so on.
Solubility is the maximum amount of solute that can dissolve in a given amount of solvent at a given temperature, forming a saturated solution. For solids in liquids, solubility generally increases with temperature; for gases in liquids, solubility decreases with rising temperature and increases with pressure.
The partial pressure of a gas above a liquid is proportional to its mole fraction ($x$) dissolved in the liquid, where $K_H$ is Henry's law constant — a higher $K_H$ means lower solubility.
The pressure exerted by a vapour in equilibrium with its liquid at a given temperature. Adding a non-volatile solute to a solvent lowers the solvent's vapour pressure, because solute particles occupy some of the surface, reducing the fraction of solvent molecules that can escape.
The partial vapour pressure of each component in a solution equals its mole fraction ($x_i$) multiplied by its vapour pressure in the pure state ($p_i^0$). Total vapour pressure of the solution is the sum of all partial pressures (Dalton's law).
Obey Raoult's law across the entire range of concentration; solute-solvent interactions are essentially identical to solute-solute and solvent-solvent interactions. $\Delta H_{mixing} = 0$ and $\Delta V_{mixing} = 0$. E.g., benzene + toluene.
| Deviation Type | Interactions | ΔH_mixing | Example |
|---|---|---|---|
| Positive deviation | Weaker A-B than A-A/B-B | Positive (absorbed) | Ethanol + acetone |
| Negative deviation | Stronger A-B than A-A/B-B | Negative (released) | Chloroform + acetone |
Solutions with large deviations from Raoult's law can form azeotropes — mixtures that boil at a constant temperature and distil over without any change in composition, making the components impossible to separate by simple distillation.
Colligative properties depend only on the number of solute particles present in a solution, not on their chemical identity. The four classic colligative properties are: relative lowering of vapour pressure, elevation of boiling point, depression of freezing point, and osmotic pressure.
where $p_1^0$ = vapour pressure of pure solvent, $p_1$ = vapour pressure of solution, and $x_2$ = mole fraction of the (non-volatile) solute.
Since adding a non-volatile solute lowers a solvent's vapour pressure, a higher temperature is needed for the solution's vapour pressure to reach atmospheric pressure — so the boiling point rises.
where $K_b$ = molal elevation constant (ebullioscopic constant) of the solvent, and $m$ = molality of the solution.
1 g of a non-volatile solute (molar mass 60) is dissolved in 100 g of water ($K_b = 0.52\ \text{K kg/mol}$). Calculate the elevation in boiling point.
Moles of solute $= 1/60 = 0.0167\ \text{mol}$. Molality $= 0.0167 / 0.1\ \text{kg} = 0.167\ \text{mol/kg}$
$\Delta T_b = (0.52)(0.167) = 0.087\ \text{K}$
A solute lowers the freezing point of a solvent because the solution's vapour pressure curve intersects the solid's vapour pressure curve at a lower temperature than for the pure solvent.
where $K_f$ = molal depression constant (cryoscopic constant) of the solvent.
This is why salt is spread on icy roads in winter — it lowers water's freezing point below 0°C, melting ice at temperatures where pure water would normally freeze.
Calculate the freezing point depression when 6 g of urea (molar mass 60) is dissolved in 200 g of water ($K_f = 1.86\ \text{K kg/mol}$).
Moles of urea $= 6/60 = 0.1\ \text{mol}$. Molality $= 0.1 / 0.2\ \text{kg} = 0.5\ \text{mol/kg}$
$\Delta T_f = (1.86)(0.5) = 0.93\ \text{K}$
Osmosis is the spontaneous flow of solvent molecules through a semi-permeable membrane from a region of lower solute concentration (or pure solvent) to a region of higher solute concentration. Osmotic pressure (π) is the external pressure that must be applied to the solution side to exactly stop this net flow of solvent.
where $C$ = molar concentration of solution, $R$ = gas constant, $T$ = absolute temperature. This equation has the same form as the ideal gas equation.
Two solutions with equal osmotic pressure are called isotonic. A solution with higher osmotic pressure than another is hypertonic; one with lower osmotic pressure is hypotonic. Placing cells in a hypertonic solution causes them to shrink (crenation), while a hypotonic solution causes them to swell and possibly burst.
Colligative properties depend on the number of particles in solution — but electrolytes dissociate into ions (increasing particle count), while some solutes associate into larger units like dimers (decreasing particle count). The van't Hoff factor (i) corrects for this.
$i > 1$ for solutes that dissociate (e.g., NaCl, i ≈ 2); $i < 1$ for solutes that associate (e.g., dimerised acetic acid in benzene, i ≈ 0.5); $i = 1$ for non-electrolytes that neither dissociate nor associate.
0.1 mol of NaCl is dissolved in 1 kg of water. If NaCl dissociates completely, calculate the expected freezing point depression ($K_f = 1.86\ \text{K kg/mol}$).
NaCl → Na⁺ + Cl⁻ gives $i = 2$ (complete dissociation into 2 ions).
$\Delta T_f = i K_f m = (2)(1.86)(0.1) = 0.372\ \text{K}$