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 ↓


Fugacity and activity


In the vast field of thermodynamics within physical chemistry, the concepts of fugacity and activity play a vital role in helping scientists understand how substances behave under various conditions. With a focus on equilibrium processes, fugacity and activity are particularly essential when analyzing real gases and solutions, where ideal behavior does not always apply. This detailed exploration provides a simple yet comprehensive understanding of fugacity and activity, strengthening our understanding of these fundamental concepts in undergraduate-level chemistry.

Understanding fugacity

Fugacity arises from the realization that real gases do not strictly obey the ideal gas law under all conditions. The ideal gas law is represented as follows:

PV = nRT

The suggestion is that pressure (P) and volume (V) should be proportional to the product of the amount of substance in moles (n), the universal gas constant (R) and the temperature (T). However, real gases deviate from this ideal behavior due to molecular interactions and volume occupancy.

The concept of fugacity, represented as f, was introduced to overcome the shortcomings of the ideal gas law in describing real gas behavior. Fugacity acts as a correcting pressure, which balances the discrepancies to ensure the consistency of the thermodynamic equations.

Defining fugacity mathematically

To correct for non-ideal behaviour, the fugacity of a gas is defined by the following relation:

f = φP

where f is the fugacity, φ is the fugacity coefficient, and P is the gas pressure. The fugacity coefficient provides a measure of the deviation from ideal behavior.

For an ideal gas, φ = 1, thus fugacity is equal to the actual pressure. In contrast, for real gases, the fugacity coefficient deviates from unity when temperature and pressure conditions change.

Graphical interpretation of fugacity

ideal gas Real gas P V

In the graph above, the blue dashed line represents the expected relationship for an ideal gas, while the red curve represents the actual gas path due to the effect of molecular interactions. The red curve shows the fugacity adjustment against pressure deviation.

Fugacity in practice

In practical terms, fugacity is extremely important for accurately describing the behavior of gases in many chemical processes, including reactions occurring at high pressure or involving compressed gases.

Understanding the activity

Activity captures the actual behavior of substances in solutions or mixtures, just as fugacity works for gases. While the concentrations of substances may be innocuous, non-ideal interactions mandate a more accurate idea of the substance's effectiveness; activity accomplishes this.

Activity for solute in solution

Activity helps to improve the ideal model assumption where interactions are negligible. The activity (a) of a substance in a solution can be described as:

a = γc

where γ is the activity coefficient and c is the concentration. The activity coefficient represents the extent to which the interactions deviate from ideality.

Visualization of activity coefficients

The Ideal Solution Real Solutions A C

The graph shows how the activities depart from the linearity representing ideal solutions as real interactions become more important.

General importance in chemical equilibrium

In reactions and processes, the effective concentrations of reactants and products determine the progress and extent of the reactions. Therefore, activity is an important metric in calculating the equilibrium constant within the framework of the law of mass action:

K = (a_C)^c (a_D)^d / (a_A)^a (a_B)^b

where K is the equilibrium constant, and the sub-digits represent the stoichiometric coefficients.

Linking fugacity and activity

Although fugacity and activism address different states of matter and scenarios, they have a common goal: to correct modeling assumptions in order to provide a clearer, more accurate thermodynamic picture.

Fugacity in relation to the equilibrium constant

For reactions involving gases, fugacity replaces pressure in the equilibrium constant for accuracy:

K = (f_C)^c (f_D)^d / (f_A)^a (f_B)^b

Conclusion

Fugacity and activity are indispensable concepts in thermodynamics to accurately reflect the true nature of physical systems. They take into account the non-idealities arising from real-world interactions, providing chemists and engineers with tools to model and predict system behaviors.

In graduate-level chemistry, understanding and applying these concepts helps to understand complex chemical processes, guide further research, and improve experimental and industrial practices. As scientists advance, mastering fugacity and activity becomes part of creating detailed models that connect theoretical assumptions to practical realities.


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Fugacity and activity

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