Liquids, solutions and phase behaviour

Lesson 3 treated gases, whose molecules are far apart and nearly independent. Liquids and solids are condensed phases: their molecules are held close together by the intermolecular forces of Lesson 2. Most engineering processes involve a change between these phases or a mixture of substances in one of them: water boils in a power-plant boiler and condenses in a cooling tower, moisture condenses inside walls and on cold pipes, road salt melts ice, reverse osmosis turns seawater into drinking water, and oxygen dissolved in a river keeps fish alive. This lesson covers vapour pressure and boiling, the Clausius–Clapeyron equation, humidity and dew point, phase diagrams, solutions and their concentration units, the colligative properties (vapour pressure lowering, freezing point depression, boiling point elevation and osmotic pressure), and the solubility of gases described by Henry's law.

Vapour pressure and boiling

In a liquid, molecules have a range of energies. The fastest ones near the surface escape into the gas phase; in a closed container, some return, and soon the rates of evaporation and condensation balance. The pressure of the vapour at that balance is the liquid's vapour pressure. It depends only on the substance and the temperature, not on how much liquid there is, and it rises steeply with temperature because more molecules have enough energy to escape. Liquids with weak intermolecular forces, such as gasoline components or acetone, have high vapour pressures and evaporate readily; they are called volatile. Water, held together by hydrogen bonds, has a fairly low vapour pressure at room temperature.

A liquid boils when its vapour pressure equals the surrounding pressure: bubbles of vapour can then form inside the liquid and grow. At 101.3 kPa water boils at 100 °C, its normal boiling point. At lower pressure, as on a mountain or in a vacuum evaporator, it boils at a lower temperature; at higher pressure, as in a pressure cooker, an autoclave or a power-plant boiler, at a higher one.

The Clausius–Clapeyron equation

The vapour pressure curve follows from the energy needed to vaporize the liquid, its molar enthalpy of vaporization ΔH_vap (40.7 kJ/mol for water at its boiling point). Treating the vapour as an ideal gas and ΔH_vap as constant gives the Clausius–Clapeyron equation:

with temperatures in kelvin and R = 8.314 J/(mol·K). It lets you find the vapour pressure at one temperature from another, or the boiling point at a given pressure.

Humidity and dew point

Air always contains some water vapour. Its partial pressure (Lesson 3) cannot exceed the vapour pressure of water at the air's temperature; air at that limit is saturated. The relative humidity is the ratio of the actual partial pressure of water vapour to the saturation value:

If moist air is cooled, its water vapour partial pressure stays the same while the saturation pressure falls. At the dew point, the two are equal and water begins to condense. This is why cold-water pipes and windows "sweat", why fog forms on clear nights, why compressed-air systems need dryers and drains, and why building scientists worry about moisture condensing inside walls, where it rots wood, corrodes fasteners and grows mould.

Phase diagrams

A phase diagram maps which phase of a substance is stable at each combination of temperature and pressure. Lines separate the solid, liquid and gas regions; along each line two phases coexist. The liquid–gas line is the vapour pressure curve. It ends at the critical point, beyond which liquid and gas can no longer be told apart and the substance is a supercritical fluid. The three lines meet at the triple point, the single temperature and pressure where all three phases coexist.

• Water: triple point 0.01 °C and 0.611 kPa; critical point 374 °C and 22.1 MPa. Unusually, its solid–liquid line slopes backward, because ice is less dense than liquid water (Lesson 2): pressure favours the denser liquid, so it slightly lowers the melting point.
• Carbon dioxide: triple point −56.6 °C and 518 kPa; critical point 31.0 °C and 7.38 MPa. Because its triple point lies above atmospheric pressure, solid CO₂ (dry ice) does not melt at 1 atm but sublimes directly to gas at −78.5 °C. Liquid CO₂ exists only under pressure, as in fire extinguishers and pipelines for carbon capture.

Supercritical fluids combine a gas's ability to penetrate porous solids with a liquid's ability to dissolve things. Supercritical CO₂ decaffeinates coffee and extracts oils without toxic solvent residues, and supercritical water and CO₂ are the working fluids of advanced power cycles that are more efficient than conventional steam plants.

Solutions and concentration

A solution is a uniform mixture of a solute dissolved in a solvent. Lesson 1 introduced molarity (mol/L), the most common unit in the laboratory. Other units suit other purposes:

• Molality, m = moles of solute per kilogram of solvent, does not change with temperature (volumes do), so it is used for colligative properties.
• Mole fraction, x = moles of a component / total moles, is used for vapour pressure and gas mixtures.
• Mass percent and parts per million (ppm, mg/kg, or about mg/L for dilute water solutions) are used in water treatment, environmental limits and alloy compositions.

Whether a substance dissolves depends on the intermolecular forces of Lesson 2 ("like dissolves like") and on temperature. Most solids dissolve better in hot water; most gases dissolve less, as the next sections show. A solution holding the maximum dissolved amount is saturated; cooling it, or evaporating solvent, makes the excess crystallize. This is how salt is refined, how scale forms in kettles and heat exchangers when hard water is heated (Lesson 8), and how sugar is purified.

Vapour pressure lowering and Raoult's law

A dissolved non-volatile solute takes up part of the liquid surface and lowers the solvent's tendency to escape. For ideal solutions, Raoult's law gives the solvent's vapour pressure as its mole fraction times the pure solvent's vapour pressure:

For a mixture of two volatile liquids, each contributes its own term, and the vapour is richer in the more volatile component. That difference is the basis of distillation, which separates crude oil into gasoline, kerosene and diesel fractions, purifies ethanol, and recovers solvents for reuse.

Freezing point depression and boiling point elevation

Because a solute lowers the vapour pressure, a solution boils at a higher temperature and freezes at a lower temperature than the pure solvent. For dilute solutions the changes are proportional to the molality of dissolved particles:

For water, K_f = 1.86 K·kg/mol and K_b = 0.512 K·kg/mol. The van 't Hoff factor i counts the particles each formula unit produces: about 1 for sugar or glycol, 2 for NaCl (Na⁺ and Cl⁻), 3 for CaCl₂. These properties depend only on the number of dissolved particles, not their identity, and are called colligative properties.

Engine coolant uses the same effect in both directions: a 50/50 mixture of ethylene glycol and water freezes near −37 °C and, under the radiator cap's pressure, boils well above 120 °C. At such high concentrations the simple formula is only a rough guide, and engineers use measured data.

Osmosis and reverse osmosis

If a solution and pure solvent are separated by a semipermeable membrane, which passes solvent molecules but not solute, solvent flows into the solution. This flow, osmosis, stops when the solution side is pressurized by the osmotic pressure:

with M the molarity. Osmotic pressures are large. Applying more than the osmotic pressure to the solution side reverses the flow and pushes nearly pure water out through the membrane: reverse osmosis, the leading technology for desalination and for making ultrapure water for boilers and semiconductor plants.

Gases in liquids: Henry's law

The amount of a gas that dissolves in a liquid is proportional to the partial pressure of that gas above it:

where k_H is Henry's law constant, which depends on the gas, the solvent and the temperature. For oxygen in water at 25 °C, k_H ≈ 1.3 × 10⁻³ mol/(L·atm).

Henry's law has many other consequences. Carbonated drinks are bottled under CO₂ pressure and fizz when opened. Divers breathing compressed air dissolve extra nitrogen in their blood and must ascend slowly to avoid decompression sickness. Boiler feedwater is heated and stripped in a deaerator to drive out dissolved oxygen and CO₂, which would otherwise corrode the boiler tubes.

Lesson 5 quantifies the heat involved in warming, melting and boiling, and Lesson 8 returns to dissolved substances through acid–base and solubility equilibria.