Graduate
  1. Physical Chemistry  1.1. Thermodynamics  1.1.1. Laws of Thermodynamics  1.1.2. Enthalpy and heat capacity  1.1.3. Entropy and free energy  1.1.4. Phase Equilibrium  1.1.5. Statistical thermodynamics  1.1.6. Thermodynamic cycle  1.1.7. Fugacity and activity  1.2. Quantum Chemistry  1.2.1. Principles of quantum mechanics  1.2.2. Schrödinger Equation  1.2.3. Particle in a box  1.2.4. Operators and eigenvalues  1.2.5. Atomic orbitals  1.2.6. Molecular orbital theory  1.2.7. Perturbation theory  1.2.8. Valence bond theory  1.2.9. Hybridization and chemical bonding  1.3. Chemical kinetics  1.3.1. Rate laws and reaction mechanisms  1.3.2. Collision theory  1.3.3. Transition state theory  1.3.4. Enzyme Kinetics  1.3.5. Chain Reactions and Polymerization  1.3.6. Photochemical reactions  1.4. Statistical mechanics  1.4.1. Partitioning functions  1.4.2. Molecular distribution functions  1.4.3. Boltzmann Distribution  1.4.4. Bose–Einstein and Fermi–Dirac statistics  1.5. Spectroscopy  1.5.1. Rotational Spectroscopy  1.5.2. Vibrational Spectroscopy  1.5.3. Electronic Spectroscopy  1.5.4. Nuclear magnetic resonance spectroscopy  1.5.5. Mass Spectrometry  1.5.6. Raman Spectroscopy  1.5.7. Electron paramagnetic resonance spectroscopy  1.6. Surface and colloidal chemistry  1.6.1. Absorption isotherm  1.6.2. Surface tension and wetting  1.6.3. Colloidal Stability  1.6.4. Catalysis  1.6.5. Emulsions and micelles  1.7. Electrochemistry  1.7.1. Nernst equation  1.7.2. Electrochemical cells  1.7.3. Conductivity and mobility  1.7.4. War  1.7.5. Fuel cells  1.7.6. Electrolysis
  2. Organic chemistry  2.1. Reaction mechanism  2.1.1. Nucleophilic substitution reactions  2.1.2. Electrophilic addition reactions  2.1.3. Elimination reactions  2.1.4. Rearrangement reactions  2.1.5. Radical reactions  2.1.6. Pericyclic reactions  2.2. Spectroscopy and structural determination  2.2.1. UV-Vis Spectroscopy  2.2.2. IR Spectroscopy  2.2.3. NMR Spectroscopy  2.2.4. Mass Spectrometry  2.2.5. X-ray crystallography  2.3. Stereoscopic  2.3.1. Chirality and optical activity  2.3.2. Structural analysis  2.3.3. Geometrical isomerism  2.3.4. Dynamic Stereochemistry  2.4. Organometallic Chemistry  2.4.1. Organolithium and organomagnesium reagents  2.4.2. Palladium-catalyzed cross-coupling reactions  2.4.3. Transition Metal Complexes  2.4.4. Metal–carbon bond  2.5. Polymer chemistry  2.5.1. Polymerization mechanism  2.5.2. Polymer Characteristics  2.5.3. Biodegradable Polymer  2.5.4. Conducting polymer  2.5.5. Supramolecular polymers  2.6. Medicinal chemistry  2.6.1. Drug design and development  2.6.2. Pharmacokinetics and pharmacodynamics  2.6.3. Structure-activity relationships  2.6.4. Molecular docking and drug screening
  3. Inorganic chemistry  3.1. Coordination chemistry  3.1.1. Crystal field theory  3.1.2. Ligand field theory  3.1.3. Spectrochemical Series  3.1.4. Chelation and stability  3.2. Organometallic Chemistry  3.2.1. Metal Carbonyls  3.2.2. Catalysis by organometallic complexes  3.2.3. Metallocenes  3.3. Bio-inorganic chemistry  3.3.1. Metalloproteins and enzymes  3.3.2. The role of metals in biological systems  3.3.3. Metal ion transport and storage  3.4. Solid state chemistry  3.4.1. Crystal Structures  3.4.2. Band theory of solids  3.4.3. Superconductors  3.4.4. Defects in the crystal  3.5. Lanthanides and Actinides  3.5.1. Electronic configuration in lanthanides and actinides  3.5.2. Coordination chemistry of the lanthanides  3.5.3. Magnetic Properties of Lanthanides
  4. Analytical chemistry  4.1. Chromatography  4.1.1. Gas Chromatography  4.1.2. High Performance Liquid Chromatography  4.1.3. Thin Layer Chromatography  4.2. Spectroscopic Techniques  4.2.1. Atomic absorption spectroscopy  4.2.2. X-ray diffraction  4.2.3. Inductively coupled plasma spectroscopy  4.3. Electroanalytical methods  4.3.1. Potentiometry  4.3.2. Voltammetry  4.3.3. Colometry  4.4. Mass Spectrometry  4.4.1. Ionization Technique  4.4.2. Fragmentation Pattern  4.5. Chemometrics  4.5.1. Multidisciplinary analysis  4.5.2. Machine Learning in Chemistry
  5. Theoretical and Computational Chemistry  5.1. Molecular dynamics simulation  5.1.1. Force fields and energy minimization  5.1.2. Monte Carlo simulation in molecular dynamics simulations  5.2. Quantum chemical methods  5.2.1. Hartree–Fock theory  5.2.2. Density functional theory  5.2.3. Semi-empirical methods  5.3. Computational drug design  5.3.1. Molecular Docking  5.3.2. QSAR Modeling  5.3.3. Virtual Screening
  6. Biochemistry  6.1. Enzyme Kinetics  6.1.1. Michaelis-Menten kinetics  6.1.2. Inhibition mechanism  6.2. Metabolism and Bioenergetics  6.2.1. Glycolysis  6.2.2. Citric acid cycle  6.2.3. Electron transport chain  6.3. molecular Biology  6.3.1. DNA replication and repair  6.3.2. Protein synthesis  6.3.3. Gene Regulation  6.4. Structural Biochemistry  6.4.1. Protein Folding  6.4.2. Membrane Biophysics
  7. Environmental Chemistry  7.1. Atmospheric Chemistry  7.1.1. Greenhouse gases  7.1.2. Ozone depletion  7.1.3. Air pollutants and smoke  7.2. Water Chemistry  7.2.1. pH and water hardness  7.2.2. Wastewater treatment  7.2.3. Aquatic Chemistry  7.3. Soil Chemistry  7.3.1. Heavy metal contamination  7.3.2. Soil pH and Buffering  7.3.3. Nutrient cycling  7.4. Toxicology and Chemical Safety  7.4.1. Toxicokinetics  7.4.2. Risk Assessment in Toxicology and Chemical Safety in Environmental Chemistry  7.4.3. Effects of pollutants on the environment

Graduate → Physical Chemistry → Thermodynamics ↓


Phase Equilibrium


Phase equilibrium is an important concept in thermodynamics and physical chemistry, describing the balance between different phases of matter in a chemical system at equilibrium. Understanding phase equilibrium helps scientists and engineers predict the conditions under which substances will exist as solids, liquids or gases, or in mixtures of these phases. Such understanding is important when designing industrial processes, materials synthesis and even environmental science applications.

Basic concepts of states of matter

Before delving into phase equilibria, it is important to understand the basic states of matter: solid, liquid and gas. In solids, the particles are closely packed in a fixed, ordered lattice structure, forming a definite shape and volume. Liquids have a definite volume, but they can take the shape of their container, as their particles are not in a fixed position but close to each other. Gases, on the other hand, have neither a definite shape nor volume, the particles move around freely and remain in the container they are in.

Phase transition

Phase transitions refer to changes from one state of matter to another, such as solid to liquid (melting), liquid to gas (evaporation), or solid to gas (sublimation). There are also opposite transitions: liquid to solid (solidification), gas to liquid (condensation), and gas to solid (deposition).

Phase changes occur due to changes in temperature or pressure. For example:

Ice (solid) → Water (liquid) at 0°C (melting)
Water (liquid) → Steam (gas) at 100°C (boiling at 1 atm)

Phase diagram

A phase diagram is a graphical representation of the equilibrium between different states of matter as affected by variables such as temperature and pressure. In these diagrams, lines or curves known as phase boundaries divide regions representing different phases and indicate the conditions of temperature and pressure where the phases coexist in equilibrium.

Solid liquid Gas Pressure(atm) Temperature (°C)

In the figure above, different lines represent phase boundaries: the line between the solid and liquid is the melting line, the line between the liquid and gas is the boiling line, and the line between the solid and gas is the sublimation line.

Triple point and critical point

The triple point is a unique position in the phase diagram where all three phases of a substance coexist in equilibrium. For water, this point occurs at a temperature of 0.01°C and a pressure of 0.00604 atm.

Triple Point: T = 0.01°C, P = 0.00604 atm

The critical point represents the highest temperature and pressure at which a substance can exist simultaneously in both a liquid and a gas state. Above this point, the substance becomes a supercritical fluid, combining properties of both a liquid and a gas.

Critical Point (water): T ≈ 374°C, P ≈ 218 atm

Applications and implications

Phase equilibria have many applications in various scientific and industrial fields. Some prominent examples include:

  • Petrochemical industry: The design and optimization of distillation processes for the refining of crude oil depend largely on phase equilibrium principles.
  • Pharmaceuticals: Understanding the solubility and crystallization processes helps in creating drugs with desired properties.
  • Environmental science: Phase equilibrium knowledge is needed to predict pollutant behaviour in the atmosphere, especially for compounds that condense or sublimate under different environmental conditions.

Gibbs phase rule

The Gibbs phase rule provides a simple way to determine the number of degrees of freedom, or independent variables that can change without affecting the number of phases in a system. The rule is expressed as:

F = C - P + 2

Where:

  • F is the number of degrees of freedom.
  • C is the number of components.
  • P is the number of steps present.

For example, water in a system exists as a solid, liquid, and gas at the triple point:

F = 1 - 3 + 2 = 0

This means that there are no degrees of freedom available; the temperature and pressure of the system are fixed.

Real-world example: Water

Consider the water system as a ubiquitous example of phase equilibrium. The phase behavior of water is well described and plays an important role in Earth's climate, biology, and even human technology. For example, when water freezes, it expands due to its unique crystalline structure, affecting everything from weather patterns to biological cells.

Furthermore, understanding the vapor pressure of water is important for many applications. The vapor pressure of water is the pressure exerted by water vapor in equilibrium with the liquid or solid form. At the boiling point, this pressure is equal to atmospheric pressure, causing water to convert into vapor.

The equilibrium states of water can vary widely from normal to extreme environmental conditions:

  • At higher altitudes: Atmospheric pressure is lower, which causes water to boil at a lower temperature; this affects cooking times and processes.
  • Deep ocean conditions: Under extreme pressures, water can remain liquid even at temperatures well above its normal boiling point.

Conceptual visualization with SVG

To further understand phase equilibria, let's imagine an example where a simplified phase diagram helps predict specific states under different conditions.

Solid liquid Gas

In this conceptual diagram, overlapping regions illustrate situations where multiple phases may exist simultaneously. Such diagrams are simplifications but are powerful tools for understanding and predicting phase behavior in different environmental contexts.

Conclusion

Phase equilibria encompass fascinating aspects of physical chemistry, forming the backbone of many scientific endeavours and industrial applications. Whether considering complex organic mixtures or simple binary systems such as water, understanding phase behaviour through diagrams, equations and the Gibbs phase rule enriches our ability to predict the behaviour of substances in diverse environments.

The concepts discussed here only scratch the surface and invite further exploration into the depth of phase transitions, critical phenomena, and multi-component systems essential to innovation and problem solving in the chemistry and engineering disciplines.


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Phase Equilibrium

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