Vapor pressure and solutions
Every liquid gives off vapor, and in a closed container that vapor builds up to an equilibrium pressure, the vapor pressure, which depends only on the liquid and its temperature. When something is dissolved in the liquid, the vapor pressure drops. In 1887 the French chemist François-Marie Raoult showed that the drop follows a simple rule for ideal solutions.
The formulas
- Raoult’s law: P = x × P°, where x is the mole fraction of the component in the liquid and P° its vapor pressure when pure
- Mole fraction: x_A = n_A ÷ (n_A + n_B)
- Vapor pressure lowering by a nonvolatile solute: ΔP = P° − P = x_solute × P°
- Two volatile liquids: P_total = x_A × P°_A + x_B × P°_B, and the vapor contains a mole fraction y_A = x_A × P°_A ÷ P_total of A
Example: sugar in water
Dissolve 0.5 mol of sucrose in 100 g of water, which is 5.55 mol, at 25 °C, where pure water has a vapor pressure of 3.17 kPa:
- Mole fraction of water: 5.55 ÷ 6.05 = 0.9174
- Vapor pressure of the solution: 0.9174 × 3.17 = 2.908 kPa
- Lowering: 0.262 kPa, or 8.26% of the pure-water value
For a salt such as sodium chloride, count the moles of ions, about twice the moles of salt, because the effect depends on the number of dissolved particles.
Example: an ideal mixture
At 25 °C, benzene has a vapor pressure of about 12.7 kPa and toluene about 3.8 kPa. In a liquid with equal moles of both, the total pressure is 0.5 × 12.7 + 0.5 × 3.8 = 8.25 kPa, and the vapor holds 6.35 ÷ 8.25 = 77% benzene. The vapor is richer in the more volatile liquid, which is the principle behind fractional distillation.
Colligative properties
Vapor pressure lowering is one of four colligative properties, which depend on the number of solute particles rather than their nature. The others, boiling point elevation, freezing point depression and osmotic pressure, all follow from it. They explain why salted water boils slightly hotter, why road salt melts ice and why seawater evaporates more slowly than fresh water.
Real solutions
Raoult’s law holds for dilute solutions and for mixtures of chemically similar liquids. Mixtures such as acetone and chloroform, which attract each other, show negative deviations, and those such as ethanol and hexane show positive deviations. Strong deviations lead to azeotropes, mixtures that boil without changing composition, like 95.6% ethanol in water.