Chemical_thermodynamics

# Chemical thermodynamics **Chemical thermodynamics** is the study of the relations between heat, work and chemical change: the application of the [[Laws_of_thermodynamics|laws of thermodynamics]] to [[Chemical_reaction|chemical reactions]], [[Phase_transition|phase changes]] and [[Solution_(chemistry)|solutions]]. Its central question is not how fast a reaction runs, which belongs to [[Chemical_kinetics|kinetics]], but whether it can run at all in a given direction under given conditions, how far it will go before reaching [[Chemical_equilibrium|equilibrium]], and how much of the energy released can be turned into work. For a system held at constant temperature and pressure the answer is carried by the [[Gibbs_free_energy|Gibbs energy]] G = H − T·S: a change is spontaneous when ΔG < 0, at equilibrium when ΔG = 0, and must be driven when ΔG > 0. In the microsim below the reader slides the temperature and picks one of four reaction presets, one for each combination of the signs of ΔH and ΔS: ice melting (+, +), the decomposition of calcium carbonate (+, +), the synthesis of [[Ammonia|ammonia]] from nitrogen and hydrogen (−, −), and the [[Combustion|combustion]] of propane (−, +). The line ΔG = ΔH − T·ΔS is drawn against T; where it crosses zero, at T = ΔH/ΔS, the verdict flips, and the readouts give ΔG at the chosen temperature and the [[Equilibrium_constant|equilibrium constant]] from ΔG° = −R·T·ln K. On the [[Chemistry]] flagship this article is the child of Part V — Energy, section *Energy* (row K24), a section shared with the [[Energy]] and [[Materials_science]] flagships, where the same spontaneity dial is the C10 embed. ## History Chemical thermodynamics grew out of the thermochemistry of the eighteenth and nineteenth centuries. [[Antoine_Lavoisier|Lavoisier]] and Laplace measured the heat of combustion and of respiration with an ice calorimeter and reported the results to the Académie in 1783; Germain Hess showed in 1840 that the heat of a reaction is the same whether it runs in one step or several, which is now [[Hess's_law|Hess's law]] and the first statement that reaction heat is a property of the states and not of the path.[^lavoisier-laplace][^hess1840] [[Rudolf_Clausius|Clausius]] gave the second law its modern form and coined the word [[Entropy|entropy]] in 1865.[^clausius1865] The thermochemists Thomsen and Berthelot then proposed that a reaction runs in the direction that releases the most heat — Berthelot's "principle of maximum work", set out in his *Essai de mécanique chimique* of 1879 — which is true for many reactions at room temperature and false in general, because it ignores entropy.[^berthelot1879] The general theory came from [[Josiah_Willard_Gibbs|Josiah Willard Gibbs]], whose "On the Equilibrium of Heterogeneous Substances", published in the Transactions of the Connecticut Academy in 1875–1878, introduced the [[Chemical_potential|chemical potential]] and the [[Phase_rule|phase rule]] and gave the criterion that a system at constant temperature and pressure is at equilibrium when the function now called the Gibbs energy is a minimum.[^gibbs1878] [[Hermann_von_Helmholtz|Helmholtz]] independently defined the free energy at constant volume in 1882 and showed that it, not the heat of reaction, measures the work a reaction can deliver in a cell.[^helmholtz1882] Van 't Hoff connected the equilibrium constant to temperature in his *Études de dynamique chimique* of 1884, and Nernst's heat theorem of 1906, the [[Third_law_of_thermodynamics|third law]], made it possible to compute equilibrium constants from thermal measurements alone.[^vanthoff1884][^nernst1906] Lewis and Randall's textbook of 1923 taught chemists to work with free energies, activities and fugacities and fixed the tabular form — ΔH_f°, S°, ΔG_f° — that every general-chemistry appendix still uses.[^lewis-randall] [[Ilya_Prigogine|Ilya Prigogine]] received the 1977 Nobel Prize in Chemistry for extending the subject to systems far from equilibrium.[^prigogine-nobel] ## Overview A chemical system is described by a small set of [[State_function|state functions]] whose changes depend only on the initial and final states: the [[Internal_energy|internal energy]] U, the [[Enthalpy|enthalpy]] H = U + P·V, the entropy S, and the two free energies, the Helmholtz energy A = U − T·S and the Gibbs energy G = H − T·S. The [[First_law_of_thermodynamics|first law]] is the accounting rule ΔU = q + w, heat absorbed plus work done on the system; at constant pressure the work of expansion is −P·ΔV and the heat absorbed equals ΔH, which is why enthalpy, not internal energy, is what [[Calorimetry|calorimetry]] at atmospheric pressure delivers. The [[Second_law_of_thermodynamics|second law]] says that the entropy of an isolated system never decreases and so picks the direction of change; the third law fixes the zero of entropy at a perfect crystal at 0 K and lets absolute entropies S° be tabulated.[^likharev-thermo][^af2e-ch12] For a closed system of fixed composition the two laws combine into the fundamental relation dU = T·dS − P·dV, and Gibbs's addition of a term Σ μᵢ·dnᵢ for every species that can enter, leave or be created by reaction turns it into the equation of chemical thermodynamics.[^likharev-thermo][^gibbs1878] Everything else in the subject — equilibrium constants, cell voltages, solubilities, [[Phase_diagram|phase diagrams]] — is that one relation evaluated under the constraints a chemist can actually impose, most often constant temperature and pressure. ## Chemical energy [[Chemical_energy|Chemical energy]] is the part of a substance's internal energy stored in its bonds and in the arrangement of its electrons. When bonds are broken and re-formed, the difference between the energy needed to break the old bonds and the energy released by forming the new ones appears as heat or work: breaking the H–H bond costs 436 kJ/mol, while forming a mole of liquid water from its elements releases 285.8 kJ.[^cboc-h2][^af2e-appg] The bookkeeping uses the standard [[Standard_enthalpy_of_reaction|enthalpy of reaction]], computed by Hess's law from tabulated enthalpies of formation as ΔH° = Σ ΔH_f°(products) − Σ ΔH_f°(reactants), and the same additivity lets a [[Born–Haber_cycle|Born–Haber cycle]] assemble the lattice energy of a salt from steps that can each be measured.[^af2e-ch9][^cboc-nacl] The scale of chemical energy is set by the electron. Burning a hydrocarbon releases about 650 kJ per mole of CH₂ units, whereas the fission of a mole of uranium-235 releases about 1.65×10¹⁰ kJ, some 2.5×10⁷ times more (derived), because nuclear binding involves the strong force rather than valence electrons.[^ball-nuclear] Within chemistry the energy content of [[Fuel|fuels]], [[Electric_battery|batteries]] and [[Food_energy|foods]] reduces to the same enthalpy accounting, but the conversion of that energy into work, in an engine, a [[Fuel_cell|fuel cell]] or a muscle, is bounded by the free-energy change rather than the enthalpy change, which is the subject of the next section. ## Chemical reactions For a reaction at constant temperature and pressure the second law takes the form ΔG = ΔH − T·ΔS ≤ 0 for any spontaneous change, where ΔH is the heat the reaction exchanges with its surroundings and T·ΔS is the part of that heat accounted for by the system's own entropy change.[^af2e-ch12] A reaction with ΔH < 0 and ΔS > 0 is [[Spontaneous_process|spontaneous]] at every temperature; one with ΔH > 0 and ΔS < 0 at none; the two mixed cases flip at a crossover temperature T = ΔH/ΔS, below which the enthalpy term decides and above which the entropy term does. That is the whole content of the microsim, and it is also why the old principle of maximum work failed: it kept ΔH and dropped T·ΔS. ### Gibbs function or Gibbs Energy The microsim's four presets are chosen so that each sign case appears once. The reader slides T from 200 K to 1,500 K and reads ΔG off the line ΔG = ΔH − T·ΔS, drawn with ΔH and ΔS held at their standard 298 K values (an ILLUSTRATIVE simplification: both vary slowly with temperature, so the true crossover shifts by a few kelvin). The readouts give ΔG at the chosen temperature and the equilibrium constant from ΔG° = −R·T·ln K, with R = 8.3145 J/(mol·K).[^averill-R] | Preset | Reaction | ΔH° (kJ/mol) | ΔS° (J/(mol·K)) | Crossover T = ΔH/ΔS | Spontaneous | |---|---|---|---|---|---| | Ice melting | H₂O(s) → H₂O(l) | +6.0 | +22.0 | 273 K | above 0 °C | | Limestone | CaCO₃(s) → CaO(s) + CO₂(g) | ≈ +179 | ≈ +160 | ≈ 1,120 K | above ≈ 840 °C | | Ammonia synthesis | N₂(g) + 3 H₂(g) → 2 NH₃(g) | ≈ −92 | ≈ −198 | ≈ 460 K | below ≈ 190 °C | | Propane combustion | C₃H₈(g) + 5 O₂(g) → 3 CO₂(g) + 4 H₂O(g) | ≈ −2,044 | ≈ +100 | none | at every T | *The sim's preset table. The ice row uses the enthalpy of fusion of water and the entropy of fusion ΔH/T_m derived from it; the other three rows are computed from the Appendix G standard enthalpies of formation and absolute entropies in the Portal Book and rounded (derived).*[^nist-webbook-water][^af2e-appg] The [[Enthalpy_of_fusion|melting of ice]] is the everyday case: the solid has the lower enthalpy, the liquid the higher entropy, and the line crosses zero at 273 K, where the two terms are equal and [[Ice|ice]] and water coexist. The limestone preset is the same sign case with the crossover pushed to about 1,120 K because the enthalpy cost of breaking up the carbonate is large; a lime kiln under one atmosphere of CO₂ therefore has to run above roughly 840 °C (derived), and the sim shows ΔG falling through zero as the slider passes that point. The [[Haber_process|ammonia]] preset is the opposite case: four moles of gas become two, so ΔS° is strongly negative and the synthesis is favoured only below about 460 K — yet the industrial process runs hotter and at high pressure, because at low temperature the reaction is far too slow and the equilibrium yield lost to heat is bought back with pressure. Kinetics, not thermodynamics, sets that compromise; the sim's ΔG line says only what is possible.[^af2e-ch13] The propane preset never crosses: seven moles of gas form from six, so ΔS° is positive while ΔH° is large and negative, and at 298 K the equilibrium constant K = exp(−ΔG°/R·T) is about 10³⁶³ (derived) — combustion is complete for every practical purpose, and only its rate, which waits for a spark, is in question. Because ΔG° = −R·T·ln K, a reaction with ΔG° = 0 has K = 1, and every 5.7 kJ/mol of ΔG° at 298 K moves K by a factor of ten (derived from R·T·ln 10). The same quantity sets the maximum electrical work of a [[Galvanic_cell|cell]] through ΔG = −n·F·E: for [[Electrolysis_of_water|water electrolysis]] ΔG° = 237 kJ/mol gives an equilibrium voltage of 1.23 V, while the enthalpy, 286 kJ/mol, corresponds to the thermoneutral voltage of 1.48 V, and between the two the cell runs while drawing heat from its surroundings.[^haverkort-6-1] [[Exergonic_reaction|Exergonic]] and [[Endergonic_reaction|endergonic]] are the names for the two signs of ΔG, and the coupling of an endergonic step to an exergonic one, as [[Adenosine_triphosphate|ATP]] hydrolysis drives biosynthesis, is the same accounting applied inside a cell. ### Chemical affinity Before Gibbs, the tendency of substances to react was called affinity and was pictured as a force; Berthelot equated it with the heat evolved.[^berthelot1879] Théophile De Donder gave the word its modern definition: the affinity A of a reaction is the negative slope of the Gibbs energy with respect to the extent of reaction ξ at constant T and P, A = −(∂G/∂ξ) = −Σ νᵢ·μᵢ, where the νᵢ are the stoichiometric coefficients and the μᵢ the chemical potentials.[^dedonder1936] A reaction advances while A > 0, stops when A = 0, and its rate of [[Entropy_production|entropy production]] is A·(dξ/dt)/T, which is never negative. The affinity is the same quantity as −ΔG per mole of reaction, so the sim's crossover is the temperature at which A changes sign. ### Solutions In a solution each component has its own chemical potential, μᵢ = μᵢ° + R·T·ln aᵢ, where the activity aᵢ reduces to the mole fraction in an ideal solution and to the concentration in a dilute one.[^af2e-ch11] The logarithm is what makes mixing spontaneous even when there is no heat effect: the entropy of mixing is positive, so ΔG_mix < 0. The same expression yields [[Raoult's_law|Raoult's law]] for the vapour pressure above a solution, the [[Colligative_properties|colligative properties]] that depend on the number of solute particles and not their nature, the [[Solubility_equilibrium|solubility product]] of a sparingly soluble salt, and the [[Nernst_equation|Nernst equation]] for a cell voltage away from standard conditions.[^af2e-ch11] Real solutions depart from ideality through the same [[Intermolecular_force|intermolecular forces]] that make real gases non-ideal, and the activity coefficient that corrects for them is measured rather than predicted for all but the most dilute [[Electrolyte|electrolytes]]. ## Non-equilibrium Classical chemical thermodynamics compares equilibrium states and says nothing about the path or the time between them. Non-equilibrium thermodynamics, begun by Onsager in 1931 and developed by the Brussels school around Prigogine, treats the entropy production inside a system as a sum of products of fluxes — reaction rate, [[Diffusion|diffusion]], [[Heat_transfer|heat flow]] — and the forces that drive them: affinity over T, a concentration gradient, a temperature gradient.[^onsager1931][^prigogine-nobel] Near equilibrium each flux is linear in the forces and the cross-coefficients are symmetric, which are Onsager's reciprocal relations, and they are why a temperature gradient can drive a diffusion flux and a concentration gradient a heat flux.[^onsager1931] Far from equilibrium, when a reacting system is held open by a steady supply of reactants, the linear laws fail and the system can organise itself into oscillations or spatial patterns; Prigogine called these [[Dissipative_system|dissipative structures]], and they are the thermodynamic setting of a living cell, which is never at equilibrium and is kept alive by its throughput of free energy.[^prigogine-nobel] ### System constraints Which function is minimised depends on what is held fixed. An isolated system maximises its entropy; a system at constant temperature and volume minimises the Helmholtz energy A; one at constant temperature and pressure — the chemist's usual case — minimises G.[^likharev-thermo] Holding the composition away from equilibrium by removing a product or supplying a reactant, as an open reactor or a cell does, is another constraint, and it is the one that lets a reaction with a positive ΔG° be driven forward indefinitely: the [[Reaction_quotient|reaction quotient]] Q is kept away from K, so ΔG = ΔG° + R·T·ln Q stays negative. [[Le_Chatelier's_principle|Le Chatelier's principle]] is the qualitative version of the same statement. What no constraint can do is change K itself at a given temperature: a [[Catalysis|catalyst]] raises the forward and reverse rate constants by the same factor, so their ratio, which is K, is untouched, and the [[Steady_state_(chemistry)|steady state]] of an open system is a kinetic balance, not an equilibrium.[^af2e-catalysis] ## See also - [[Gibbs_free_energy]] - [[Thermodynamic_free_energy]] - [[Exergonic_reaction]] - [[Endergonic_reaction]] - [[Spontaneous_process]] - [[Thermochemistry]] - [[Chemical_equilibrium]] - [[Entropy]] - [[Calorimetry]] ## References [^lavoisier-laplace]: Lavoisier, A. L.; Laplace, P. S. (1783). "Mémoire sur la chaleur." *Mémoires de l'Académie royale des sciences*, année 1780 (Paris, 1784). [^hess1840]: Hess, H. (1840). "Thermochemische Untersuchungen." *Annalen der Physik und Chemie* 126 (3): 385–404. [^clausius1865]: Clausius, R. (1865). "Ueber verschiedene für die Anwendung bequeme Formen der Hauptgleichungen der mechanischen Wärmetheorie." *Annalen der Physik und Chemie* 125 (7): 353–400. [^berthelot1879]: Berthelot, M. (1879). *Essai de mécanique chimique fondée sur la thermochimie*. 2 vols. Paris: Dunod. [^gibbs1878]: Gibbs, J. W. (1875–1878). "On the Equilibrium of Heterogeneous Substances." *Transactions of the Connecticut Academy of Arts and Sciences* 3: 108–248, 343–524. [^helmholtz1882]: Helmholtz, H. von (1882). "Die Thermodynamik chemischer Vorgänge." *Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften zu Berlin*, 1882. [^vanthoff1884]: van 't Hoff, J. H. (1884). *Études de dynamique chimique*. Amsterdam: Frederik Muller & Co. [^nernst1906]: Nernst, W. (1906). "Ueber die Berechnung chemischer Gleichgewichte aus thermischen Messungen." *Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-physikalische Klasse*, 1906: 1–40. [^lewis-randall]: Lewis, G. N.; Randall, M. (1923). *Thermodynamics and the Free Energy of Chemical Substances*. New York: McGraw-Hill. [^prigogine-nobel]: Nobel Prize Outreach. "The Nobel Prize in Chemistry 1977 — Ilya Prigogine." https://www.nobelprize.org/prizes/chemistry/1977/summary/ [^onsager1931]: Onsager, L. (1931). "Reciprocal Relations in Irreversible Processes. I." *Physical Review* 37 (4): 405–426. https://doi.org/10.1103/PhysRev.37.405 [^dedonder1936]: De Donder, Th.; Van Rysselberghe, P. (1936). *Thermodynamic Theory of Affinity: A Book of Principles*. Stanford: Stanford University Press. [^likharev-thermo]: Likharev, Konstantin (2013). *Essential Graduate Physics, Part SM: Statistical Mechanics*. Chapter 1 "Review of Thermodynamics", pp. 10–12 (dE = T dS − P dV) and pp. 22–26 (thermodynamic potentials and the Carnot cycle; the constrained-minimum statements, page to pin). Portal Book 075. [^af2e-ch12]: Flowers, Paul; Neth, Edward; Robinson, William; et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. Chapter 12 "Thermodynamics", §12.4 "Free Energy" (chapter pp. 597–622; page to pin). https://openstax.org/books/chemistry-atoms-first-2e/pages/12-4-free-energy — Portal Book 051, https://open.umn.edu/opentextbooks/textbooks/chemistry-atoms-first [^af2e-ch9]: Flowers et al. (2019), *Chemistry: Atoms First 2e*, Chapter 9 "Thermochemistry", §9.3 "Enthalpy" (chapter pp. 421–474; page to pin). Portal Book 051. [^af2e-ch11]: Flowers et al. (2019), *Chemistry: Atoms First 2e*, Chapter 11 "Solutions and Colloids" (chapter pp. 545–596; page to pin). Portal Book 051. [^af2e-ch13]: Flowers et al. (2019), *Chemistry: Atoms First 2e*, Chapter 13 "Fundamental Equilibrium Concepts", the Haber-process discussion under Le Chatelier's principle (chapter pp. 623–664; page to pin). Portal Book 051. [^af2e-appg]: Flowers et al. (2019), *Chemistry: Atoms First 2e*, Appendix G "Standard Thermodynamic Properties for Selected Substances", pp. 1093–1110 (ΔH_f°, ΔG_f°, S° for H₂O, CaCO₃, CaO, CO₂, N₂, H₂, NH₃, C₃H₈, O₂). Portal Book 051. [^af2e-catalysis]: Flowers et al. (2019), *Chemistry: Atoms First 2e*, Chapter 17 "Kinetics", pp. 834–835 (K = k_f/k_r; a catalyst changes both rate constants equally). Portal Book 051. [^averill-R]: Averill, Bruce; Eldredge, Patricia (2011). *General Chemistry: Principles, Patterns, and Applications*. Chapter 10 "Gases", p. 904 (R = 8.3145 J/(K·mol)). Portal Book 050, https://open.umn.edu/opentextbooks/textbooks/general-chemistry-principles-patterns-and-applications [^cboc-h2]: Blackstock, Lindsay; Brewer, Sharon; Cinel, Bruno (2022). *Chemical Bonding and Organic Chemistry*. Chapter 4 "Chemical Bonding I", p. 231 (H₂ → 2H, +436 kJ/mol). Portal Book 054, https://open.umn.edu/opentextbooks/textbooks/chemical-bonding-and-organic-chemistry [^cboc-nacl]: Blackstock, Brewer and Cinel (2022), *Chemical Bonding and Organic Chemistry*, Chapter 4, pp. 224–225 (Born–Haber cycle for NaCl). Portal Book 054. [^ball-nuclear]: Ball, David W. (2011). *Introductory Chemistry*. Chapter 15 "Nuclear Chemistry", p. 753 (U-235 fission ≈ 1.65×10¹⁰ kJ/mol against ≈ 650 kJ/mol per CH₂ of hydrocarbon combustion). Portal Book 056, https://open.umn.edu/opentextbooks/textbooks/introductory-chemistry [^haverkort-6-1]: Haverkort, Willem (2024). *Electrolysers, Fuel Cells and Batteries: Analytical Modelling*. Chapter 1 "Electrochemistry", pp. 25–27 (ΔG = −nF·V_eq; 237 kJ/mol → 1.23 V; 286 kJ/mol → 1.48 V; heat uptake between them). Portal Book 053, https://open.umn.edu/opentextbooks/textbooks/electrolysers-fuel-cells-and-batteries-analytical-modelling [^nist-webbook-water]: NIST Chemistry WebBook, SRD 69. Water (CAS 7732-18-5), phase-change data: enthalpy of fusion 6.01 kJ/mol at 273.15 K. https://webbook.nist.gov/chemistry/ ## Further reading - Flowers, Neth, Robinson et al., *Chemistry: Atoms First 2e* (OpenStax, 2019), Chapter 12 "Thermodynamics" and Appendix G — Portal Book 051. - Ball, *Introductory Chemistry* (2011), Chapter 7 "Energy and Chemistry", pp. 317–368 — Portal Book 056. - Yan, *Introduction to Engineering Thermodynamics* (2022), Chapter 6 "Entropy and the Second Law of Thermodynamics", pp. 239–348 — Portal Book 115, https://open.umn.edu/opentextbooks/textbooks/introduction-to-engineering-thermodynamics - Likharev, *Essential Graduate Physics, Part SM* (2013), Chapter 1 "Review of Thermodynamics" — Portal Book 075. - Lewis and Randall, *Thermodynamics and the Free Energy of Chemical Substances* (1923), the book that fixed the modern tables. ## External links - [NIST Chemistry WebBook](https://webbook.nist.gov/chemistry/), thermochemical data by species - [Chemistry: Atoms First 2e](https://openstax.org/details/books/chemistry-atoms-first-2e) at OpenStax - The Wikipedia pair's external links list further open resources  **Microsim — three.js (Wikitube framework):** *Chemical thermodynamics* <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/matter/Chemical_thermodynamics.html" data-title="Chemical thermodynamics"></div> *Built from `MICROSIM_GUIDE/specs/sims/Chemical_thermodynamics.json`; part of the [[PORTAL_Matter|Matter portal]] spine (section sims and See-also variants).*  ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Chemical_thermodynamics) : [Wikitube](https://en.wikitube.io/wiki/Chemical_thermodynamics) · pinned revision [1353862826](https://en.wikipedia.org/w/index.php?oldid=1353862826) · 2026-09-11 ## Previous hub tags Hubs: `Life_Physics`. Portals: [[PORTAL_Chemistry]], [[PORTAL_Energy]], [[PORTAL_Materials_science]]. --- *Matter & Energy Cluster child articles, wave 1 · 2026-09-11 · drafted · Chemistry row K24 · sim pending (matter/Chemical_thermodynamics).*