# Le Chatelier's principle **Le Chatelier's principle** is the rule that a system at [[Chemical_equilibrium|chemical equilibrium]], when disturbed by a change in concentration, [[Temperature|temperature]], [[Pressure|pressure]] or volume, shifts its composition in the direction that partly undoes the disturbance. It is named for the French chemist Henry Louis Le Chatelier, who stated it in a note to the Académie des sciences in 1884 and developed it in a memoir of 1888; the German physicist Karl Ferdinand Braun reached a similar statement independently in 1887, so the rule is also called the Le Chatelier–Braun principle.[^lechatelier1884][^lechatelier1888][^braun1887] The principle predicts the direction of a shift, never its size; the size comes from the [[Equilibrium_constant|equilibrium constant]] and the [[Van_'t_Hoff_equation|van 't Hoff equation]], published by Jacobus van 't Hoff the same year as Le Chatelier's note.[^vanthoff1884] On the [[Chemistry]] flagship the principle is the working tool of Part X, *Equilibrium*, where it sits beside the equilibrium constant and the [[Reaction_quotient|reaction quotient]] and opens the industrial case treated on [[Haber_process]]; [[Contact_process]] is the sulfur-spine variant of the same trade-off. In the microsim below the reader runs the Haber balance, `N2 + 3H2 <=> 2NH3`, and pushes three things: the temperature, the total pressure, and the amount of [[Ammonia|ammonia]] drawn off. The ammonia fraction answers to each push. Pressure helps, because the reaction consumes four moles of gas and makes two (Δn = −2); heat hurts, because the reaction is exothermic (ΔH° ≈ −92 kJ per mole of reaction), so `d ln K/dT = ΔH°/(R·T²)` is negative and the constant falls as the temperature rises; and removal pulls, because the reaction quotient drops below the constant and the mixture reacts forward to close the gap. A yield map over temperature and pressure marks the industrial corner at about 450 °C and 200 atm.[^openstax-ch13] ## Thermodynamic statement For a closed system held at constant temperature and pressure the [[Gibbs_free_energy|Gibbs free energy]] *G* is a minimum at equilibrium, and any spontaneous change lowers it.[^openstax-ch13] A reacting mixture has a driving force ΔG = ΔG° + R·T·ln Q, where *Q* is the reaction quotient built from the instantaneous concentrations or [[Partial_pressure|partial pressures]]. At equilibrium ΔG = 0 and Q = K, so `ΔG° = −R·T·ln K`.[^openstax-ch13] A disturbance is anything that makes *Q* differ from *K* again, or that changes *K* itself. If Q < K the forward reaction is spontaneous and the mixture moves toward products; if Q > K it moves toward reactants. Everything the principle says about concentration and pressure follows from the sign of ln(Q/K) after the disturbance; everything it says about temperature follows from how *K* moves with *T*. The temperature dependence is the van 't Hoff relation, `d ln K/dT = ΔH°/(R·T²)`.[^vanthoff1884] For an [[Exothermic_reaction|exothermic reaction]] (ΔH° < 0) the constant falls with rising temperature, so the equilibrium composition drifts toward reactants when heat is added; for an [[Endothermic_process|endothermic]] reaction it drifts toward products. The pressure dependence at constant temperature comes from the volume change of reaction: compressing a gas mixture favours the side with fewer moles of gas. ### Explicit statement The explicit form treats a perturbation of one intensive variable and asks how the conjugate extensive variable responds. Raise the temperature of an equilibrium mixture at constant pressure, and the reaction runs in the endothermic direction, absorbing heat and so moderating the temperature rise that a non-reacting mixture would have shown. Raise the pressure at constant temperature, and the reaction runs toward the side of smaller volume, moderating the pressure rise. Add a reactant at constant volume, and the reaction consumes part of it. In each case the response opposes the perturbation but never cancels it: the new equilibrium lies between the old one and the state a frozen mixture would have reached.[^openstax-ch13] This is the statement the [[Chemical_thermodynamics|thermodynamic]] stability conditions guarantee, and it is the one the microsim computes. ## Other statements Le Chatelier's own 1888 wording was that a system at equilibrium subjected to a change in one of the factors governing the equilibrium undergoes a transformation in the direction that tends to produce the opposite change in that factor.[^lechatelier1888] Braun's 1887 version, drawn from the solubility of salts, said that the solubility of a solid changes with temperature in the direction that makes dissolving absorb heat.[^braun1887] The textbook form used in the Portal Books, "a stress applied to a system at equilibrium is relieved by a shift in the direction that reduces the stress", works for concentration, pressure and temperature but must be handled with care for volume and inert-gas changes, where the "stress" is not the quantity that moves the reaction quotient.[^ball-ch13][^openstax-ch13] The loose form can fail. For the ammonia synthesis at constant temperature and total pressure, adding [[Nitrogen|nitrogen]] to a mixture in which nitrogen is already more than half the gas shifts the equilibrium toward *reactants*, because the added nitrogen dilutes the hydrogen, which enters the quotient as a cube, faster than it raises the nitrogen term.[^deheer1957] The reversal begins where the mole fraction of the added reactant exceeds the ratio of its stoichiometric coefficient to the net change in moles of gas, 1/2 for nitrogen here (derived; ILLUSTRATIVE, ideal gas). The thermodynamic statement never fails; the verbal one is a shortcut that usually points the right way. ## Chemistry Chemists use the principle to move a reversible reaction toward the product they want. The archetype is the synthesis of ammonia from [[Hydrogen|hydrogen]] and nitrogen, `N2(g) + 3H2(g) <=> 2NH3(g)`, which is exothermic and reduces the number of gas molecules.[^openstax-ch13] From the standard enthalpies of formation in Appendix G of the Portal Book *Chemistry: Atoms First*, ΔHf°(NH3, g) = −45.9 kJ/mol, so ΔH° for the reaction as written is 2 × (−45.9) = −91.8 kJ, and from the standard entropies (192.8 J/(mol·K) for NH3, 191.6 for N2 and 130.7 for H2) ΔS° = 385.6 − 191.6 − 392.1 = −198.1 J/K.[^openstax-appg] At 298.15 K that gives ΔG° = −91.8 + 59.1 = −32.7 kJ and `K = exp(32,700/(8.314 × 298.15)) ≈ 5 × 10⁵` (derived). The reaction is strongly favoured at room temperature and does not happen there at any useful rate. The principle explains why the plant runs hot and high, and the microsim puts numbers on the trade. ### Effect of change in concentration Adding a reactant or removing a product at fixed volume makes Q < K, and the forward reaction runs until Q returns to K; adding a product or removing a reactant does the reverse.[^openstax-ch13] The amount that reacts is always less than the amount added, so the disturbance is moderated, not cancelled. The microsim's "draw off NH₃" control is this case: each unit of ammonia removed lowers the numerator of `Q = P_NH3² / (P_N2 · P_H2³)`, and the mixture reacts forward until the quotient climbs back to *K*. In the plant the removal is done by cooling the loop gas until ammonia condenses and recycling the unreacted nitrogen and hydrogen, so the reactor never sees an equilibrium mixture at all; the principle gives the direction, the loop gives the throughput.[^openstax-ch13] Concentration changes never alter *K*; they alter *Q*. ### Effect of change in temperature Temperature is the one disturbance that changes *K* itself, which is why heat behaves differently from every other control in the microsim. The van 't Hoff equation, integrated with ΔH° held constant, gives `ln(K₂/K₁) = −(ΔH°/R)·(1/T₂ − 1/T₁)`.[^vanthoff1884][^openstax-ch13] Taking K₁ ≈ 5 × 10⁵ at 298 K and ΔH° = −91.8 kJ, the constant at 723 K (450 °C) is `K₂ ≈ 5 × 10⁵ × exp(−21.8) ≈ 2 × 10⁻⁴` (derived; ILLUSTRATIVE, since the real ΔH° drifts with temperature and the true constant is somewhat smaller). Nine orders of magnitude vanish between the bench and the furnace. In the microsim the temperature slider tilts the whole yield map: at 400 °C and 200 atm the ideal-gas equilibrium holds about 46 % ammonia, at 450 °C about 36 %, and at 500 °C about 28 % (derived; ILLUSTRATIVE). The industrial corner sits where the [[Reaction_rate|rate]] over the [[Catalysis|catalyst]] is fast enough to matter but the equilibrium has not yet run away. ### Effect of change in pressure For a gas-phase equilibrium written with partial pressures, `K_p = P_NH3² / (P_N2 · P_H2³)`, raising the total pressure at fixed temperature multiplies every partial pressure by the same factor, so *Q* changes by that factor raised to the power Δn, the net change in moles of gas. For the ammonia reaction Δn = 2 − 4 = −2, so compression drops *Q* below *K* and the reaction runs forward until the quotient recovers; expansion does the opposite.[^openstax-ch13] The microsim's pressure slider is this computation. With a stoichiometric feed and the ammonia mole fraction *x*, the [[Mole_fraction|mole fractions]] of nitrogen and hydrogen are (1 − *x*)/4 and 3(1 − *x*)/4, and the equilibrium condition becomes `x² / (1 − x)⁴ = 27·K_p·P² / 256` (derived). At 450 °C with K_p ≈ 2 × 10⁻⁴ atm⁻², the ideal-gas equilibrium at 1 atm holds under half a percent ammonia, while at 200 atm it holds a little over a third of the gas as ammonia (derived; ILLUSTRATIVE). That two-hundredfold pressure rise is why Fritz Haber's bench apparatus needed Carl Bosch's high-pressure engineering: Haber received the 1918 Nobel Prize in Chemistry for the synthesis and Bosch shared the 1931 prize for high-pressure methods.[^nobel1918][^nobel1931] Reactions with Δn = 0, such as `H2 + I2 <=> 2HI`, do not respond to pressure at all. ### Effect of change in volume A change in the volume of a gas mixture at fixed temperature is a change in pressure by the [[Ideal_gas_law|ideal gas law]], and the principle reads the same way: halving the volume doubles every partial pressure, and the equilibrium shifts toward the side with fewer moles of gas.[^openstax-ch13] The Portal Books teach the volume case separately because students meet it as the piston problem, but the microsim treats it through the pressure slider, since the two disturbances change *Q* identically for an ideal gas. Equilibria in solution or between condensed phases have negligible volume changes and barely respond. ### Effect of adding an inert gas Adding an [[Inert_gas|inert gas]] such as argon at constant volume raises the total pressure but leaves every reacting partial pressure unchanged, so *Q* is unchanged and nothing shifts.[^openstax-ch13] Adding the same gas at constant total pressure expands the mixture, lowers every reacting partial pressure, and shifts the equilibrium toward the side with more moles of gas, which for ammonia is the reactants. This is the case where the verbal rule misleads: the "stress" of a higher total pressure is present in the first case and absent in the second, yet only the second case moves. The reaction quotient, not the gauge reading, decides. ### Effect of a catalyst A catalyst lowers the [[Activation_energy|activation energy]] of the forward and reverse reactions by the same amount, so it raises both rates and leaves *K* and the equilibrium composition untouched.[^openstax-ch13] What it changes is the time to reach equilibrium, and in the ammonia plant that is decisive: with the iron catalyst the operators can afford a temperature at which the equilibrium yield is modest but the approach to it is fast.[^openstax-ch13] The microsim has no catalyst control because the catalyst is invisible to equilibrium; it belongs to [[Chemical_kinetics|kinetics]], one part earlier on the flagship spine. ## General statements The principle is not special to chemistry. It is a statement about stable equilibrium in any system that has a thermodynamic potential to minimize, and it can be derived from the conditions that make the equilibrium stable rather than merely stationary. Two cases have to be kept apart: systems that are at a true equilibrium, where the derivation holds, and systems that are merely steady, where it does not. ### Thermodynamic equilibrium processes For a system in [[Thermodynamic_equilibrium|thermodynamic equilibrium]] the second derivatives of the relevant potential must be positive, which is the content of the [[Second_law_of_thermodynamics|second law]] applied to small displacements.[^callen1985] A perturbation that changes an intensive variable induces a response in the conjugate extensive variable, and the stability conditions fix the sign of that response so that the induced change in the intensive variable opposes the original perturbation. Heating a mixture at constant pressure raises its temperature by less than the heat capacity of a frozen mixture would predict, because part of the heat is absorbed by the endothermic shift; compressing it raises the pressure by less, because part of the volume change is absorbed by the reaction. Le Chatelier's principle is the qualitative reading of those inequalities. ### Non-equilibrium processes The principle applies to the equilibrium state and says nothing reliable about systems far from it. A reactor with continuous feed and removal sits at a steady state, not an equilibrium, and its composition is set by rates and flows. For small departures from equilibrium in an open system, [[Ilya_Prigogine|Prigogine]] showed that the steady state minimizes the rate of [[Entropy_production|entropy production]], which gives a weak analogue of the principle in the linear regime; the analogy breaks in the nonlinear regime, where [[Dissipative_system|dissipative structures]] can amplify a disturbance instead of moderating it.[^prigogine1947] The ammonia loop in the microsim is treated as a sequence of equilibria, an idealization the article labels ILLUSTRATIVE. ## Related system concepts Several other rules describe systems that respond so as to oppose a change. [[Lenz's_law|Lenz's law]] states that the current induced by a changing magnetic flux flows in the direction that opposes the change in flux; it is the electromagnetic member of the family. [[Negative_feedback|Negative feedback]] in [[Control_theory|control theory]] describes any loop in which the output is fed back to reduce the error that produced it, and [[Homeostasis|homeostasis]] is Walter Cannon's name for the physiological version, in which body temperature, blood pH and glucose are held near set points by opposing responses.[^cannon1932] A [[Buffer_solution|buffer solution]] is the chemical case in miniature: added acid is consumed by the conjugate base, so the pH moves less than it would in water, and the [[Bicarbonate_buffer_system|bicarbonate system]] in blood does this with an equilibrium that Le Chatelier's principle describes exactly. Feedback loops need an active controller; the chemical shift needs nothing but the equilibrium itself. ## Economics Paul Samuelson carried the principle into [[Economics|economics]] in *Foundations of Economic Analysis* (1947), where it appears as a theorem of comparative statics: when a system at an optimum is disturbed by a change in one parameter, the response of the corresponding variable is larger the fewer constraints are imposed on the other variables.[^samuelson1947] The familiar consequence is that long-run demand and supply curves are more elastic than short-run ones, because in the long run more inputs are free to adjust, just as an equilibrium mixture that can change temperature and volume responds more to a pressure change than one held at fixed volume. The chemical and the economic versions share a mathematical root, the second-order conditions for a minimum, which is why the same inequality appears in both. Samuelson named the result explicitly for Le Chatelier, and the name has stuck in the theory of the firm and in the analysis of constrained optimization generally.[^samuelson1947] ## See also - [[Van_'t_Hoff_equation]] - [[Haber_process]] - [[Contact_process]] - [[Chemical_equilibrium]] - [[Equilibrium_constant]] - [[Reaction_quotient]] - [[Dalton's_law]] ## References [^lechatelier1884]: Le Chatelier, H. (1884). "Sur un énoncé général des lois des équilibres chimiques." *Comptes rendus hebdomadaires des séances de l'Académie des sciences*, vol. 99. [^lechatelier1888]: Le Chatelier, H. (1888). "Recherches expérimentales et théoriques sur les équilibres chimiques." *Annales des mines*, 8th series, vol. 13. [^braun1887]: Braun, F. (1887). "Untersuchungen über die Löslichkeit fester Körper und die den Vorgang der Lösung begleitenden Volum- und Energieänderungen." *Zeitschrift für physikalische Chemie*, vol. 1. [^vanthoff1884]: van 't Hoff, J. H. (1884). *Études de dynamique chimique*. Amsterdam: Frederik Muller. [^openstax-ch13]: Flowers, P.; Neth, E.; Robinson, W.; et al. (2019). *Chemistry: Atoms First*, 2nd ed. OpenStax. Chapter 13, "Fundamental Equilibrium Concepts", pp. 623–664; §13.3 "Shifting Equilibria: Le Châtelier's Principle" (page to pin). https://open.umn.edu/opentextbooks/textbooks/chemistry-atoms-first [^openstax-appg]: Flowers, P.; Neth, E.; Robinson, W.; et al. (2019). *Chemistry: Atoms First*, 2nd ed. OpenStax. Appendix G, "Standard Thermodynamic Properties for Selected Substances", pp. 1093–1110 (entries for NH₃(g), N₂(g) and H₂(g); page to pin). https://open.umn.edu/opentextbooks/textbooks/chemistry-atoms-first [^ball-ch13]: Ball, D. W. (2011). *Introductory Chemistry*. Chapter 13, "Chemical Equilibrium", pp. 623–672 (page to pin). https://open.umn.edu/opentextbooks/textbooks/introductory-chemistry [^deheer1957]: de Heer, J. (1957). "The principle of Le Chatelier and Braun." *Journal of Chemical Education*, vol. 34. [^nobel1918]: The Nobel Prize in Chemistry 1918 (Fritz Haber). NobelPrize.org. https://www.nobelprize.org/prizes/chemistry/1918/summary/ [^nobel1931]: The Nobel Prize in Chemistry 1931 (Carl Bosch and Friedrich Bergius). NobelPrize.org. https://www.nobelprize.org/prizes/chemistry/1931/summary/ [^callen1985]: Callen, H. B. (1985). *Thermodynamics and an Introduction to Thermostatistics*, 2nd ed. New York: Wiley. Chapter 8, "Stability of thermodynamic systems". [^prigogine1947]: Prigogine, I. (1947). *Étude thermodynamique des phénomènes irréversibles*. Liège: Desoer. [^cannon1932]: Cannon, W. B. (1932). *The Wisdom of the Body*. New York: W. W. Norton. [^samuelson1947]: Samuelson, P. A. (1947). *Foundations of Economic Analysis*. Cambridge, Massachusetts: Harvard University Press. ## Bibliography of cited sources - Flowers, Neth, Robinson et al., *Chemistry: Atoms First*, 2nd ed. (OpenStax, 2019) — Portal Book 051; Chapter 13 and Appendix G. - Ball, *Introductory Chemistry* (2011) — Portal Book 056; Chapter 13. - van 't Hoff, *Études de dynamique chimique* (1884). - Callen, *Thermodynamics and an Introduction to Thermostatistics*, 2nd ed. (1985). - Samuelson, *Foundations of Economic Analysis* (1947). ## External links - [OpenStax](https://openstax.org/), publisher of *Chemistry: Atoms First* 2e, the Portal Book cited above - [Open Textbook Library record for *Chemistry: Atoms First*](https://open.umn.edu/opentextbooks/textbooks/chemistry-atoms-first) - The Wikipedia pair's external links section lists the remaining historical and teaching resources. <!-- MATTERSIM:BEGIN g24 — Matter & Energy Cluster microsim (framework build, specs/sims/Le_Chatelier's_principle.json); do not hand-edit inside --> **Microsim — three.js (Wikitube framework), pending deploy:** *Le Chatelier's principle* will play here once `https://wikitube-3d-microsims.netlify.app/matter/Le_Chatelier's_principle.html` is live. <!-- pending: <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/matter/Le_Chatelier's_principle.html" data-title="Le Chatelier's principle"></div> --> <!-- MATTERSIM:END --> ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Le_Chatelier's_principle) : [Wikitube](https://en.wikitube.io/wiki/Le_Chatelier's_principle) · pinned revision [1366339970](https://en.wikipedia.org/w/index.php?oldid=1366339970) · 2026-09-11 ## Previous hub tags Hubs: `Life_Physics`. Portals: [[PORTAL_Chemistry]]. --- *Matter & Energy Cluster child articles, wave 1 · 2026-09-11 · drafted · Chemistry row K49 · sim pending (matter/Le_Chatelier's_principle).*