Phase Changes and Vapor Pressure (Lecture Notes)

Intermolecular forces and phase properties

When thinking about liquids, solids, and gases, the key question is: what forces act between the constituent atoms, ions, or molecules?
Bonding, melting points, surface tension, viscosity, and related properties are governed by the terminal lateral (intermolecular) forces between constituent particles.
Vaporization is the process of a liquid changing to a gas; it is endothermic (requires energy input) because molecules must overcome intermolecular forces to escape the liquid.
Condensation is the reverse process: gas molecules must lose energy to be pulled back into the liquid by intermolecular forces.

Dynamic equilibrium and vapor pressure

Vapor pressure describes the pressure exerted by the vapor in dynamic equilibrium with its liquid at a given temperature.
In a closed container, some molecules have enough energy to escape the liquid and enter the gas phase, establishing a vapor pressure at that temperature.
As gas molecules form, they collide and may re-enter the liquid (condensation); the rate of vaporization and condensation becomes equal at equilibrium.
Dynamic equilibrium means that for every molecule escaping, one returns; the vapor pressure is constant at a given temperature.
The rate of vaporization is temperature-dependent: at higher temperatures, a larger fraction of molecules have enough energy to escape.
Example: vapor pressure of pentane at 25°C is about 510 torr; at 36°C it rises to about 764 torr. Higher temperature → higher vapor pressure.
This equilibrium system responds to disturbances (Le Châtelier-like behavior): changing temperature, volume, or pressure shifts the system to re-establish the new equilibrium vapor pressure at the new temperature.

Temperature, volume, and pressure effects in a closed system

Temperature increases: both vaporization and condensation rates increase, and a new equilibrium vapor pressure is established at the higher temperature.
Increasing volume (constant temperature): the pressure above the liquid drops, more liquid vaporizes, and equilibrium re-establishes at the same vapor pressure as before, but with more liquid vaporized to maintain the same pressure.
Decreasing volume (constant temperature): the gas above the liquid becomes more crowded, condensation increases, and the pressure rises until equilibrium is re-established at the same vapor pressure.
Key point: vapor pressure is a function of temperature alone (in equilibrium); changing volume or external pressure at a fixed temperature does not change the intrinsic vapor pressure, only the equilibrium amount of vapor required to maintain that pressure.

Humidity and evaporative cooling in real life

Why humid days feel hotter: cooling primarily occurs via evaporation of sweat. In high humidity, the ambient air already contains a lot of water vapor, so sweat evaporates less efficiently, reducing cooling and making you feel hotter.
This is analogous to vapor pressure dynamics: higher external water vapor makes it harder for additional water (evaporated from skin) to escape, reducing cooling.

Evaporation vs boiling

Evaporation: surface phenomenon; occurs at temperatures below the boiling point; rate increases with surface area.
Boiling: occurs when the liquid’s vapor pressure equals the external pressure; interior molecules gain enough energy to escape, forming bubbles throughout the liquid.
In evaporation, increasing surface area increases the rate because more molecules at the surface can escape.
In boiling, energy input continues until the liquid reaches the boiling temperature where vapor pressure matches external pressure; bubbles form inside the liquid.

Normal boiling point and atmospheric pressure

Normal boiling point is the temperature at which a liquid’s vapor pressure equals 1 atmosphere (standard pressure).
Water's normal boiling point is 100°C at 1 atm.
Boiling point depends on external pressure: at higher elevations (lower external pressure), water boils at lower temperatures (e.g., on Mount Everest, around 70°C). At Denver (~0.8 atm), boiling occurs at a bit above 90°C; in a typical high-elevation cooking example, eggs boiled at altitude have different textures due to lower boiling temperatures.
As atmospheric pressure drops, the boiling point drops; as pressure increases, the boiling point rises (e.g., pressure cookers raise external pressure to raise the boiling point and cook foods faster).
For example, a pressure cooker with ~1.8 atm above the liquid raises the boiling point to about 117°C, enabling faster cooking because more energy can be transferred to the food before the liquid boils.

Pressure, external pressure, and cooking timing (examples)

At sea level (1 atm), water boils at 100°C.
At high altitude (lower external pressure), water boils at lower temperatures, affecting cooking times (e.g., eggs require longer cooking).
In a pressure cooker, higher external pressure raises the boiling point, enabling higher cooking temperatures and shorter cooking times.

Intermolecular forces and vapor pressure (qualitative rankings)

There is an inverse relationship between vapor pressure at a given temperature and the strength of intermolecular forces: stronger internal forces yield lower vapor pressures.
Molecules with more hydrogen bonding (strong intermolecular interactions) generally have lower vapor pressures at the same temperature than molecules with weaker interactions.
In a series of liquids, the one with weaker intermolecular forces will show a higher vapor pressure at the same temperature.

Phase changes and energetics (latent heats)

Melting (fusion): solid to liquid; endpoint is the fusion point. Heat of fusion ΔHfus is positive (endothermic) and represents energy to overcome some of the organized solid structure.
Freezing: liquid to solid; reverse of melting; energy is released (exothermic); ΔHfus is the same magnitude but negative when reversed.
Vaporization: liquid to gas; energy required to overcome all intermolecular forces in a liquid; latent heat of vaporization ΔHvap is positive (endothermic) and typically much larger than ΔHfus.
Condensation: gas to liquid; reverse of vaporization; energy is released (exothermic).
Sublimation: solid to gas; bypasses the liquid phase; enthalpy of sublimation ΔHsublim is roughly the sum of ΔHfus and ΔHvap (the total energy required to go from solid to gas in one step).
Deposition: gas to solid; reverse of sublimation; energy is released.
Summary relation: ΔHvap > ΔHfus because vaporization requires breaking all intermolecular interactions in the liquid phase, whereas fusion only partially overcomes them.

Energetics in a single heat-and-phase-change diagram

To transform a solid to a gas (viaHeating and phase changes):
- q = m c_solid ΔT (heating solid to its melting point)
- q += n ΔHfus (melting at the melting point)
- q += m c_liquid ΔT (heating liquid from 0°C to boiling temperature)
- q += n ΔHvap (vaporization at the boiling point)
- q += m c_gas ΔT (heating gas to final temperature, if needed)
Important practical note: you cannot change phase and temperature at the same time; phase changes occur at fixed temperatures while the phase is changing.
For water as an example (outline): heat ice from a low temperature up to 0°C, melt at 0°C, heat liquid water to 100°C, vaporize at 100°C, then heat steam if a final temperature is required.
Key takeaway: in problem solving you must break the path into distinct steps with the appropriate heat terms and keep units consistent (convert all heats to the same unit, e.g., joules or kilojoules). Latent heats are typically given in kilojoules per mole, while specific heats are given per gram or per mole.

Worked approach: a representative example (ice to steam, qualitative steps)

Step 1: heat solid ice from initial temperature to 0°C using q = m c_ice ΔT.
Step 2: melt all ice at 0°C using q = n ΔHfus.
Step 3: heat liquid water from 0°C to 100°C using q = m c_liquid ΔT.
Step 4: vaporize all water at 100°C using q = n ΔHvap.
Step 5: (optional) heat the resulting steam to a final temperature using q = m c_gas ΔT.
Note: ΔHfus and ΔHvap are material-specific; for water, ΔHvap ≈ 40.7 kJ/mol and ΔHfus ≈ 6.02 kJ/mol at the standard points.

Worked example: heat to vaporize 25 g of water at 100°C (approximate)

Given: density of water ≈ 1.0 g/mL, so 25 mL ≈ 25 g of water; molar mass of water ≈ 18.015 g/mol.
Moles of water: $$n = rac{25 ext{ g}}{18.015 ext{ g/mol}} \