5.2 Phase Equilibria and Phase Diagrams
4 min read•august 14, 2024
Phase equilibria and phase diagrams are crucial for understanding how substances behave under different conditions. They show us when materials change from solid to liquid to gas, and help predict what form a substance will take at specific temperatures and pressures.
These concepts are key to grasping chemical equilibrium and phase transitions. By learning to read phase diagrams, we can figure out how materials will behave in various situations, from everyday life to complex industrial processes.
Phase diagrams for single-component systems
Graphical representations of equilibrium relationships
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- Phase diagrams graphically represent the equilibrium relationships between different phases of a substance as a function of temperature and pressure
- The regions between the phase boundaries correspond to the stable phases of the substance under the given conditions of temperature and pressure (solid, liquid, gas)
- Interpreting a phase diagram allows for predicting the phase behavior of a substance under specific temperature and pressure conditions
Phase boundaries and their slopes
- The lines on a phase diagram, known as phase boundaries or coexistence curves, represent the conditions at which two phases can coexist in equilibrium
- The slope of the solid-liquid ( curve) is typically positive due to the increase in volume upon melting for most substances
- The solid-gas phase boundary ( curve) has a positive slope, indicating that higher temperatures and pressures favor the solid phase
- The liquid-gas phase boundary (vaporization curve) ends at the , beyond which the liquid and gas phases become indistinguishable
Triple points, critical points, and phase boundaries
Triple points
- A is a unique condition of temperature and pressure at which three phases of a substance (solid, liquid, and gas) can coexist in equilibrium
- At the triple point, the solid, liquid, and gas phases have equal vapor pressures and Gibbs free energies
- The triple point of water occurs at 273.16 K (0.01°C) and 611.73 Pa (0.006 atm)
Critical points
- A critical point represents the highest temperature and pressure at which a substance can exist as a liquid and a gas simultaneously
- Above the critical point, the liquid and gas phases become indistinguishable, forming a single supercritical fluid phase
- The critical point of water occurs at 647.10 K (373.95°C) and 22.06 MPa (218 atm)
Phase boundaries
- Phase boundaries, or coexistence curves, represent the conditions at which two phases can coexist in equilibrium
- The phase boundaries intersect at the triple point and terminate at the critical point
- Examples of phase boundaries include the melting curve (solid-liquid), vaporization curve (liquid-gas), and sublimation curve (solid-gas)
Degrees of freedom using the Gibbs phase rule
Gibbs phase rule equation
- The Gibbs phase rule relates the number of components (C), phases (P), and degrees of freedom (F) in a system at equilibrium:
- For a single-component system, C = 1, and the Gibbs phase rule simplifies to
- The degrees of freedom represent the number of intensive variables (e.g., temperature and pressure) that can be independently varied without changing the number of phases in equilibrium
Degrees of freedom at different points and regions
- At the triple point, where three phases coexist, the number of degrees of freedom is zero (), meaning that both temperature and pressure are fixed
- Along a phase boundary, where two phases coexist, the number of degrees of freedom is one (), allowing either temperature or pressure to be varied independently
- In a single-phase region, the number of degrees of freedom is two (), permitting both temperature and pressure to be varied independently without changing the phase
Phase behavior under varying conditions
Predicting phase behavior using phase diagrams
- The phase behavior of a substance can be predicted by locating the corresponding point on the phase diagram based on the given temperature and pressure conditions
- If the point lies within a single-phase region, the substance will exist in that particular phase (solid, liquid, or gas) under the specified conditions
- If the point lies on a phase boundary, the substance will exist in equilibrium between the two phases represented by the boundary
Phase transitions and their direction
- Crossing a phase boundary by changing temperature or pressure will result in a phase transition, such as melting, vaporization, or sublimation
- The direction of a phase transition can be determined by the slope of the phase boundary and the direction of the temperature or pressure change
- Increasing temperature at constant pressure or decreasing pressure at constant temperature generally favors the phase with higher entropy (gas > liquid > solid)
- Decreasing temperature at constant pressure or increasing pressure at constant temperature generally favors the phase with lower entropy (solid > liquid > gas)
- For example, heating ice at atmospheric pressure will cause it to melt into liquid water, while further heating will result in vaporization to form water vapor
Key Terms to Review (18)
Azeotropic mixture: An azeotropic mixture is a combination of two or more liquids that has a constant boiling point and composition throughout the distillation process. This unique characteristic occurs because the vapor phase has the same composition as the liquid phase at the azeotropic point, preventing separation through simple distillation. Azeotropes are significant in understanding phase equilibria and are depicted in phase diagrams as specific curves or points that represent the behavior of mixtures under varying temperatures and pressures.
Boiling: Boiling is the process where a liquid turns into vapor when it reaches its boiling point, which is the temperature at which the vapor pressure of the liquid equals the external pressure surrounding it. This phase change is marked by the formation of bubbles within the liquid, and it plays a critical role in understanding phase equilibria and phase diagrams as it relates to the balance of energy and molecular interactions between different states of matter.
Boiling point elevation: Boiling point elevation is the phenomenon where the boiling point of a solvent increases when a non-volatile solute is added to it. This change occurs because the presence of solute particles disrupts the ability of solvent molecules to escape into the vapor phase, requiring a higher temperature to achieve boiling. This concept relates to how mixtures behave in phase equilibria, connects with the Clausius-Clapeyron equation for understanding vapor pressures, and highlights the importance of colligative properties which depend on the number of solute particles rather than their identity.
Composition diagram: A composition diagram is a graphical representation that shows the relationships between the different phases present in a mixture based on their composition and temperature. It provides critical information on how components interact at various concentrations and is essential for understanding phase equilibria, particularly in binary systems.
Critical point: The critical point is a specific condition at which the properties of a substance change dramatically, particularly at the end of the liquid-gas phase equilibrium line in a phase diagram. At this point, the distinction between liquid and gas phases disappears, leading to a state known as a supercritical fluid, where the substance exhibits unique properties distinct from both phases. Understanding the critical point is essential for grasping phase transitions and behaviors of substances under varying conditions.
Enthalpy of fusion: Enthalpy of fusion is the heat energy required to change a substance from solid to liquid at constant pressure and temperature. This thermodynamic property is crucial in understanding phase changes and is represented as a positive value, reflecting the energy needed to overcome intermolecular forces holding the solid structure together.
Entropy of vaporization: The entropy of vaporization is the measure of the change in disorder or randomness when a substance transitions from a liquid state to a gaseous state. This change is significant in understanding phase equilibria, as it reflects how the energy disperses when molecules escape from the liquid into the vapor phase, influencing the equilibrium position and the overall thermodynamic stability of phases.
Freezing point depression: Freezing point depression is the phenomenon where the freezing point of a solvent is lowered when a solute is added. This occurs due to the disruption of the solvent's ability to form a solid structure, which in turn affects phase equilibria and the colligative properties of solutions, demonstrating how solute particles influence the freezing behavior of solvents.
Gibbs Free Energy: Gibbs free energy is a thermodynamic potential that measures the maximum reversible work obtainable from a closed system at constant temperature and pressure. It connects the concepts of enthalpy and entropy, serving as a crucial indicator for determining the spontaneity of processes and phase transitions in various systems, including chemical reactions and phase equilibria.
Ideal solution: An ideal solution is a mixture where the interactions between different components are similar to the interactions within each component. In this case, the properties of the solution, such as vapor pressure and boiling point, behave according to Raoult's Law and show linear behavior. Ideal solutions are important in understanding phase equilibria and colligative properties because they serve as a baseline for comparing real solutions, which often deviate from this ideal behavior due to differences in molecular interactions.
Le Chatelier's Principle: Le Chatelier's Principle states that if a system at equilibrium is subjected to a change in concentration, temperature, or pressure, the equilibrium will shift in a direction that counteracts the change. This principle is fundamental in understanding how systems respond to perturbations and is deeply connected to the concepts of chemical potential and Gibbs free energy as well as the behavior of phases in phase equilibria.
Melting: Melting is the process by which a solid turns into a liquid when it absorbs enough heat energy to overcome the forces holding its particles in a fixed structure. This transformation occurs at a specific temperature known as the melting point, where the solid and liquid phases coexist in equilibrium. Understanding melting is crucial for analyzing phase equilibria and the stability of various phases represented in phase diagrams.
P-t diagram: A p-t diagram, or pressure-temperature diagram, is a graphical representation that shows the relationship between the pressure and temperature of a substance, illustrating its different phases and phase transitions. This diagram helps in understanding how a substance behaves under varying conditions of temperature and pressure, providing crucial insights into phase equilibria and the stability of different states of matter.
Phase boundary: A phase boundary is a distinct interface that separates different phases of matter within a system, such as solid, liquid, and gas. This boundary represents the conditions under which two phases coexist in equilibrium and is crucial for understanding phase transitions and the behavior of substances at varying temperatures and pressures.
Raoult's Law: Raoult's Law states that the vapor pressure of a solvent in a solution is directly proportional to the mole fraction of the solvent present. This law highlights how the presence of a solute lowers the vapor pressure of the solvent, playing a critical role in understanding solutions and their behaviors, particularly in phase equilibria and colligative properties.
Sublimation: Sublimation is the process where a substance transitions directly from a solid to a gas without passing through the liquid phase. This phenomenon occurs under specific conditions of temperature and pressure and is significant in understanding phase equilibria, as it illustrates the dynamic behavior of substances in different states.
Tie line: A tie line is a horizontal line in a phase diagram that connects the compositions of two coexisting phases at equilibrium. It helps visualize the relationship between the phases and their compositions, particularly in multi-component systems, allowing for an understanding of how different phases interact and coexist at specific conditions.
Triple point: The triple point of a substance is the specific temperature and pressure at which three phases (gas, liquid, and solid) coexist in thermodynamic equilibrium. This unique point is crucial in understanding phase equilibria and phase diagrams, as it provides a reference for the behavior of materials under varying conditions.