2.1 Phase changes and phase diagrams

Phase changes and phase diagrams are crucial for understanding how substances behave under different conditions. They show us when matter shifts between solid, liquid, and gas states, and how temperature and pressure affect these transitions.

Knowing about phase changes helps us predict and control material behavior in various applications. From cooking to industrial processes, this knowledge is essential for manipulating substances and optimizing their properties for specific uses.

Phases of Matter and Their Characteristics

Solid, Liquid, and Gas Phases

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• Matter exists in three main phases: solid, liquid, and gas, each with distinct properties related to the arrangement and motion of particles
• In the solid phase, particles are tightly packed in a fixed arrangement, vibrating in fixed positions, resulting in a definite shape and volume (ice cube)
• In the liquid phase, particles are close together but can move relative to one another, giving liquids a definite volume but allowing them to take the shape of their container (water in a glass)
• In the gas phase, particles are widely separated and move randomly, causing gases to have no fixed shape or volume and expand to fill their container (helium in a balloon)

Plasma and Other Exotic Phases

• Plasma is sometimes considered a fourth state of matter, consisting of ionized particles with high energy (stars, lightning)
• Other exotic phases of matter include Bose-Einstein condensates, supercritical fluids, and quark-gluon plasmas, each with unique properties and requiring specific conditions to form

Interpretation of Phase Diagrams

Key Features and Boundaries

• A phase diagram is a graphical representation of the equilibrium conditions between different phases of matter, typically plotting pressure versus temperature
• The critical point represents the highest temperature and pressure at which the liquid and gas phases can coexist in equilibrium; beyond this point, the distinction between liquid and gas phases disappears (carbon dioxide at 31.1°C and 7.38 MPa)
• The triple point is the unique combination of temperature and pressure at which all three phases (solid, liquid, and gas) can coexist in equilibrium (water at 0.01°C and 611.73 Pa)
• Phase boundaries on the diagram represent the conditions under which two phases can coexist in equilibrium, including the sublimation curve (solid-gas), melting curve (solid-liquid), and vaporization curve (liquid-gas)

Supercritical Fluids and Applications

• The supercritical fluid region exists at temperatures and pressures above the critical point, where the substance exhibits properties of both a liquid and a gas (supercritical carbon dioxide used for decaffeination)
• Supercritical fluids have unique properties, such as high density, low viscosity, and high diffusivity, making them useful for various applications, including extraction processes, chemical reactions, and materials processing

Phase Transitions and Energy Changes

Types of Phase Transitions

• Phase transitions occur when a substance changes from one phase to another due to changes in temperature, pressure, or both
• Melting is the transition from solid to liquid, which occurs when the thermal energy overcomes the attractive forces between particles; the melting point is the temperature at which this transition occurs at a given pressure (ice melting at 0°C and 1 atm)
• Vaporization is the transition from liquid to gas, which can occur through evaporation (at the surface) or boiling (throughout the bulk); the boiling point is the temperature at which the vapor pressure equals the external pressure (water boiling at 100°C and 1 atm)
• Sublimation is the direct transition from solid to gas, bypassing the liquid phase, and occurs when the vapor pressure of the solid equals the external pressure (dry ice sublimating at room temperature and pressure)
• Condensation is the transition from gas to liquid, which occurs when the thermal energy is insufficient to overcome the attractive forces between particles (water vapor condensing on a cold surface)
• Freezing is the transition from liquid to solid, which occurs when the thermal energy is reduced to the point where attractive forces between particles dominate (water freezing at 0°C and 1 atm)

Enthalpy Changes and Latent Heats

• Phase transitions involve changes in enthalpy (heat energy); melting, vaporization, and sublimation are endothermic processes (require heat input), while freezing and condensation are exothermic processes (release heat)
• The heat of fusion is the amount of energy required to melt one mole or unit mass of a substance at its melting point (water: 6.01 kJ/mol or 333.55 kJ/kg)
• The heat of vaporization is the amount of energy required to vaporize one mole or unit mass of a substance at its boiling point (water: 40.65 kJ/mol or 2257 kJ/kg)
• Latent heat is the energy absorbed or released during a phase transition without a change in temperature, as the energy is used to overcome intermolecular forces rather than increase kinetic energy

Vapor Pressure Calculations with Clausius-Clapeyron

The Clausius-Clapeyron Equation

• The Clausius-Clapeyron equation describes the relationship between vapor pressure and temperature for a substance undergoing a phase transition
• The equation is typically expressed as: $ln(P2/P1) = (ΔHvap/R) * (1/T1 - 1/T2)$, where P1 and P2 are the vapor pressures at temperatures T1 and T2, ΔHvap is the molar heat of vaporization, and R is the universal gas constant
• The equation assumes that the molar heat of vaporization is constant over the temperature range and that the vapor behaves as an ideal gas

Applications and Calculations

• The Clausius-Clapeyron equation can be used to calculate the vapor pressure at a given temperature, provided the vapor pressure at another temperature and the heat of vaporization are known (calculating the vapor pressure of water at 50°C given the vapor pressure at 100°C and the heat of vaporization)
• The equation can also be used to determine the heat of vaporization from vapor pressure data at different temperatures (using vapor pressure data for ethanol at various temperatures to calculate its heat of vaporization)
• The slope of a plot of $ln(P)$ versus $1/T$ yields the negative of the molar heat of vaporization divided by the gas constant $(-ΔHvap/R)$, providing a graphical method to determine the heat of vaporization from experimental data