In
chemistry
Chemistry is the scientific study of the properties and behavior of matter. It is a physical science within the natural sciences that studies the chemical elements that make up matter and chemical compound, compounds made of atoms, molecules a ...
, Le Chatelier's principle (pronounced or )
is a principle used to predict the effect of a change in conditions on
chemical equilibrium
In a chemical reaction, chemical equilibrium is the state in which both the Reagent, reactants and Product (chemistry), products are present in concentrations which have no further tendency to change with time, so that there is no observable chan ...
. Other names include Chatelier's principle, Braun–Le Chatelier principle, Le Chatelier–Braun principle or the equilibrium law.
The principle is named after French chemist
Henry Louis Le Chatelier who enunciated the principle in 1884 by extending the reasoning from the
Van 't Hoff relation of how temperature variations changes the equilibrium to the variations of pressure and what's now called
chemical potential
In thermodynamics, the chemical potential of a Chemical specie, species is the energy that can be absorbed or released due to a change of the particle number of the given species, e.g. in a chemical reaction or phase transition. The chemical potent ...
, and sometimes also credited to
Karl Ferdinand Braun
Karl Ferdinand Braun (; ; 6 June 1850 – 20 April 1918) was a German physicist, electrical engineer, and inventor. Braun contributed significantly to the development of radio with his 2 circuit system, which made long range radio transmiss ...
, who discovered it independently in 1887.
It can be defined as:
In scenarios outside thermodynamic equilibrium, there can arise phenomena in contradiction to an over-general statement of Le Chatelier's principle.
Le Chatelier's principle is sometimes alluded to in discussions of topics other than thermodynamics.
Thermodynamic statement
Le Chatelier–Braun principle analyzes the qualitative behaviour of a thermodynamic system when a particular one of its externally controlled state variables, say
changes by an amount
the 'driving change', causing a change
the 'response of prime interest', in its conjugate state variable
all other externally controlled state variables remaining constant. The response illustrates 'moderation' in ways evident in two related thermodynamic equilibria. Obviously, one of
has to be
intensive
In grammar, an intensive word form is one which denotes stronger, more forceful, or more concentrated action relative to the root on which the intensive is built. Intensives are usually lexical formations, but there may be a regular process for for ...
, the other
extensive. Also as a necessary part of the scenario, there is some particular auxiliary 'moderating' state variable
, with its conjugate state variable
For this to be of interest, the 'moderating' variable
must undergo a change
or
in some part of the experimental protocol; this can be either by imposition of a change
, or with the holding of
constant, written
For the principle to hold with full generality,
must be extensive or intensive accordingly as
is so. Obviously, to give this scenario physical meaning, the 'driving' variable and the 'moderating' variable must be subject to separate independent experimental controls and measurements.
Explicit statement
The principle can be stated in two ways, formally different, but substantially equivalent, and, in a sense, mutually 'reciprocal'. The two ways illustrate the Maxwell relations, and the stability of thermodynamic equilibrium according to the second law of thermodynamics, evident as the
spread of energy amongst the state variables of the system in response to an imposed change.
The two ways of statement differ in their experimental protocols. They share an ''index protocol'' (denoted
that may be described as 'changed driver, moderation permitted'. Along with the driver change
it imposes a constant
with
and allows the uncontrolled 'moderating' variable response
along with the 'index' response of interest
The two ways of statement differ in their respective ''compared protocols''. One form of ''compared protocol'' posits 'changed driver, no moderation' (denoted
The other form of ''compared protocol'' posits 'fixed driver, imposed moderation' (denoted
)
Forced 'driver' change, free or fixed 'moderation'
This way compares
with
to compare the effects of the imposed the change
with and without moderation. The protocol
prevents 'moderation' by enforcing that
through an adjustment
and it observes the 'no-moderation' response
Provided that the observed response is indeed that
then the principle states that
.
In other words, change in the 'moderating' state variable
moderates the effect of the driving change in
on the responding conjugate variable
Forcedly changed or fixed 'driver', respectively free or forced 'moderation'
This way also uses two experimental protocols,
and
, to compare the index effect
with the effect
of 'moderation' alone. The ''index protocol''
is executed first; the response of prime interest,
is observed, and the response
of the 'moderating' variable is also measured. With that knowledge, then the ''fixed driver, imposed moderation protocol''
enforces that
with the driving variable
held fixed; the protocol also, through an adjustment
imposes a change
(learnt from the just previous measurement) in the 'moderating' variable, and measures the change
Provided that the 'moderated' response is indeed that
then the principle states that the signs of
and
are opposite.
Again, in other words, change in the 'moderating' state variable
opposes the effect of the driving change in
on the responding conjugate variable
Other statements
The duration of adjustment depends on the strength of the
negative feedback
Negative feedback (or balancing feedback) occurs when some function (Mathematics), function of the output of a system, process, or mechanism is feedback, fed back in a manner that tends to reduce the fluctuations in the output, whether caused ...
to the initial
shock. The principle is typically used to describe closed negative-feedback systems, but applies, in general, to thermodynamically closed and isolated systems in nature, since the
second law of thermodynamics
The second law of thermodynamics is a physical law based on Universal (metaphysics), universal empirical observation concerning heat and Energy transformation, energy interconversions. A simple statement of the law is that heat always flows spont ...
ensures that the
disequilibrium caused by an instantaneous shock is eventually followed by a new equilibrium.
While well rooted in chemical equilibrium, Le Chatelier's principle can also be used in describing mechanical systems in that a system put under
stress will respond in such a way as to reduce or minimize that stress. Moreover, the response will generally be via the mechanism that most easily relieves that stress.
Shear pins and other such
sacrificial devices are design elements that protect systems against stress applied in undesired manners to relieve it so as to prevent more extensive damage to the entire system, a practical engineering application of Le Chatelier's principle.
Chemistry
Effect of change in concentration
Changing the concentration of a chemical will shift the equilibrium to the side that would counter that change in concentration. The chemical system will attempt to partly oppose the change that affected the original state of equilibrium. In turn, the rate of reaction, extent, and yield of products will be altered corresponding to the impact on the system.
This can be illustrated by the equilibrium of
carbon monoxide
Carbon monoxide (chemical formula CO) is a poisonous, flammable gas that is colorless, odorless, tasteless, and slightly less dense than air. Carbon monoxide consists of one carbon atom and one oxygen atom connected by a triple bond. It is the si ...
and
hydrogen
Hydrogen is a chemical element; it has chemical symbol, symbol H and atomic number 1. It is the lightest and abundance of the chemical elements, most abundant chemical element in the universe, constituting about 75% of all baryon, normal matter ...
gas, reacting to form
methanol
Methanol (also called methyl alcohol and wood spirit, amongst other names) is an organic chemical compound and the simplest aliphatic Alcohol (chemistry), alcohol, with the chemical formula (a methyl group linked to a hydroxyl group, often ab ...
.
:
C O + 2 H
2 ⇌ CH
3OH
Suppose we were to increase the concentration of CO in the system. Using Le Chatelier's principle, we can predict that the concentration of methanol will increase, decreasing the total change in CO. If we are to add a species to the overall reaction, the reaction will favor the side opposing the addition of the species. Likewise, the subtraction of a species would cause the reaction to "fill the gap" and favor the side where the species was reduced. This observation is supported by the
collision theory
Collision theory is a principle of chemistry used to predict the rates of chemical reactions. It states that when suitable particles of the Reagent, reactant hit each other with the correct orientation, only a certain amount of collisions result ...
. As the concentration of CO is increased, the frequency of successful collisions of that reactant would increase also, allowing for an increase in forward reaction, and generation of the product. Even if the desired product is not
thermodynamic
Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of th ...
ally favored, the end-product can be obtained if it is continuously removed from the
solution
Solution may refer to:
* Solution (chemistry), a mixture where one substance is dissolved in another
* Solution (equation), in mathematics
** Numerical solution, in numerical analysis, approximate solutions within specified error bounds
* Solu ...
.
The effect of a change in concentration is often exploited synthetically for
condensation reaction
In organic chemistry, a condensation reaction is a type of chemical reaction in which two molecules are combined to form a single molecule, usually with the loss of a small molecule such as water. If water is lost, the reaction is also known as a ...
s (i.e., reactions that extrude water) that are equilibrium processes (e.g., the formation of an
ester
In chemistry, an ester is a compound derived from an acid (either organic or inorganic) in which the hydrogen atom (H) of at least one acidic hydroxyl group () of that acid is replaced by an organyl group (R). These compounds contain a distin ...
from carboxylic acid and alcohol or an
imine
In organic chemistry, an imine ( or ) is a functional group or organic compound containing a carbon–nitrogen double bond (). The nitrogen atom can be attached to a hydrogen or an organic group (R). The carbon atom has two additional single bon ...
from an amine and aldehyde). This can be achieved by physically sequestering water, by adding desiccants like anhydrous magnesium sulfate or
molecular sieve
A molecular sieve is a material with pores of uniform size comparable to that of individual molecules, linking the interior of the solid to its exterior. These materials embody the molecular sieve effect, in which molecules larger than the pore ...
s, or by continuous removal of water by distillation, often facilitated by a
Dean-Stark apparatus.
Effect of change in temperature

The effect of changing the temperature in the equilibrium can be made clear by 1) incorporating heat as either a reactant or a product, and 2) assuming that an increase in temperature increases the heat content of a system. When the reaction is
exothermic
In thermodynamics, an exothermic process () is a thermodynamic process or reaction that releases energy from the system to its surroundings, usually in the form of heat, but also in a form of light (e.g. a spark, flame, or flash), electricity (e ...
(Δ''H'' is negative and energy is released), heat is included as a product, and when the reaction is
endothermic
An endothermic process is a chemical or physical process that absorbs heat from its surroundings. In terms of thermodynamics, it is a thermodynamic process with an increase in the enthalpy (or internal energy ) of the system.Oxtoby, D. W; Gillis, ...
(Δ''H'' is positive and energy is consumed), heat is included as a reactant. Hence, whether increasing or decreasing the temperature would favor the forward or the reverse reaction can be determined by applying the same principle as with concentration changes.
Take, for example, the
reversible reaction
A reversible reaction is a reaction in which the conversion of reactants to products and the conversion of products to reactants occur simultaneously.
: \mathit aA + \mathit bB \mathit cC + \mathit dD
A and B can react to form C and D or, in the ...
of
nitrogen
Nitrogen is a chemical element; it has Symbol (chemistry), symbol N and atomic number 7. Nitrogen is a Nonmetal (chemistry), nonmetal and the lightest member of pnictogen, group 15 of the periodic table, often called the Pnictogen, pnictogens. ...
gas with
hydrogen
Hydrogen is a chemical element; it has chemical symbol, symbol H and atomic number 1. It is the lightest and abundance of the chemical elements, most abundant chemical element in the universe, constituting about 75% of all baryon, normal matter ...
gas to form
ammonia
Ammonia is an inorganic chemical compound of nitrogen and hydrogen with the chemical formula, formula . A Binary compounds of hydrogen, stable binary hydride and the simplest pnictogen hydride, ammonia is a colourless gas with a distinctive pu ...
:
:N
2(g) + 3 H
2(g) ⇌ 2 NH
3(g) Δ''H'' = −92
kJ mol
−1
Because this reaction is exothermic, it produces heat:
:N
2(g) + 3 H
2(g) ⇌ 2 NH
3(g) + ''heat''
If the temperature were increased, the heat content of the system would increase, so the system would consume some of that heat by shifting the equilibrium to the left, thereby producing less ammonia. More ammonia would be produced if the reaction were run at a lower temperature, but a lower temperature also lowers the rate of the process, so, in practice (the
Haber process
The Haber process, also called the Haber–Bosch process, is the main industrial procedure for the ammonia production, production of ammonia. It converts atmospheric nitrogen (N2) to ammonia (NH3) by a reaction with hydrogen (H2) using finely di ...
) the temperature is set at a compromise value that allows
ammonia
Ammonia is an inorganic chemical compound of nitrogen and hydrogen with the chemical formula, formula . A Binary compounds of hydrogen, stable binary hydride and the simplest pnictogen hydride, ammonia is a colourless gas with a distinctive pu ...
to be made at a reasonable rate with an equilibrium concentration that is not too unfavorable.
In
exothermic reaction
In thermochemistry, an exothermic reaction is a "reaction for which the overall standard enthalpy change Δ''H''⚬ is negative." Exothermic reactions usually release heat. The term is often confused with exergonic reaction, which IUPAC define ...
s, an increase in temperature decreases the
equilibrium constant
The equilibrium constant of a chemical reaction is the value of its reaction quotient at chemical equilibrium, a state approached by a dynamic chemical system after sufficient time has elapsed at which its composition has no measurable tendency ...
, ''K'', whereas in
endothermic reaction
An endothermic process is a chemical or physical process that absorbs heat from its surroundings. In terms of thermodynamics, it is a thermodynamic process with an increase in the enthalpy (or internal energy ) of the system.Oxtoby, D. W; Gillis, ...
s, an increase in temperature increases ''K''.
Le Chatelier's principle applied to changes in concentration or pressure can be understood by giving ''K'' a constant value. The effect of temperature on equilibria, however, involves a change in the equilibrium constant. The dependence of ''K'' on temperature is determined by the sign of Δ''H''. The theoretical basis of this dependence is given by the
Van 't Hoff equation
The Van 't Hoff equation relates the change in the equilibrium constant, , of a chemical reaction to the change in temperature, ''T'', given the standard enthalpy change, , for the process. The subscript r means "reaction" and the superscript \om ...
.
Effect of change in pressure
The equilibrium concentrations of the products and reactants do not directly depend on the
total pressure of the system. They may depend on the
partial pressure
In a mixture of gases, each constituent gas has a partial pressure which is the notional pressure of that constituent gas as if it alone occupied the entire volume of the original mixture at the same temperature. The total pressure of an ideal g ...
of the products and reactants, but if the number of moles of gaseous reactants is equal to the number of moles of gaseous products, pressure has no effect on equilibrium.
Changing total pressure by adding an inert gas at constant volume does not affect the equilibrium concentrations (see ).
Changing total pressure by changing the volume of the system changes the partial pressures of the products and reactants and can affect the equilibrium concentrations (see below).
Effect of change in volume
Changing the volume of the system changes the partial pressures of the products and reactants and can affect the equilibrium concentrations. With a pressure increase due to a decrease in volume, the side of the equilibrium with fewer moles is more favorable
[.] and with a pressure decrease due to an increase in volume, the side with more moles is more favorable. There is no effect on a reaction where the number of moles of gas is the same on each side of the chemical equation.
Considering the reaction of nitrogen gas with hydrogen gas to form ammonia:
: ⇌ ΔH = −92kJ mol
−1
Note the number of
moles of gas on the left-hand side and the number of moles of gas on the right-hand side. When the volume of the system is changed, the partial pressures of the gases change. If we were to decrease pressure by increasing volume, the equilibrium of the above reaction will shift to the left, because the reactant side has a greater number of moles than does the product side. The system tries to counteract the decrease in partial pressure of gas molecules by shifting to the side that exerts greater pressure. Similarly, if we were to increase pressure by decreasing volume, the equilibrium shifts to the right, counteracting the pressure increase by shifting to the side with fewer moles of gas that exert less pressure. If the volume is increased because there are more moles of gas on the reactant side, this change is more significant in the denominator of the
equilibrium constant
The equilibrium constant of a chemical reaction is the value of its reaction quotient at chemical equilibrium, a state approached by a dynamic chemical system after sufficient time has elapsed at which its composition has no measurable tendency ...
expression, causing a shift in equilibrium.
Effect of adding an inert gas
An
inert gas
An inert gas is a gas that does not readily undergo chemical reactions with other chemical substances and therefore does not readily form chemical compounds. Though inert gases have a variety of applications, they are generally used to prevent u ...
(or
noble gas
The noble gases (historically the inert gases, sometimes referred to as aerogens) are the members of Group (periodic table), group 18 of the periodic table: helium (He), neon (Ne), argon (Ar), krypton (Kr), xenon (Xe), radon (Rn) and, in some ...
), such as
helium
Helium (from ) is a chemical element; it has chemical symbol, symbol He and atomic number 2. It is a colorless, odorless, non-toxic, inert gas, inert, monatomic gas and the first in the noble gas group in the periodic table. Its boiling point is ...
, is one that does not react with other elements or compounds. Adding an inert gas into a gas-phase equilibrium at constant volume does not result in a shift.
[ This is because the addition of a non-reactive gas does not change the equilibrium equation, as the inert gas appears on both sides of the chemical reaction equation. For example, if A and B react to form C and D, but X does not participate in the reaction: \mathitA + \mathitB + \mathitX <=> \mathitC + \mathitD + \mathitX. While it is true that the total pressure of the system increases, the total pressure does not have any effect on the equilibrium constant; rather, it is a change in partial pressures that will cause a shift in the equilibrium. If, however, the volume is allowed to increase in the process, the partial pressures of all gases would be decreased resulting in a shift towards the side with the greater number of moles of gas. The shift will never occur on the side with fewer moles of gas. It is also known as Le Chatelier's postulate.
]
Effect of a catalyst
A catalyst
Catalysis () is the increase in rate of a chemical reaction due to an added substance known as a catalyst (). Catalysts are not consumed by the reaction and remain unchanged after it. If the reaction is rapid and the catalyst recycles quick ...
increases the rate of a reaction without being consumed in the reaction. The use of a catalyst does not affect the position and composition of the equilibrium of a reaction, because both the forward and backward reactions are sped up by the same factor.
For example, consider the Haber process for the synthesis of ammonia (NH3):
:N2 + 3 H2 ⇌ 2 NH3
In the above reaction, iron (Fe) and molybdenum (Mo) will function as catalysts if present. They will accelerate any reactions, but they do not affect the state of the equilibrium.
General statements
Thermodynamic equilibrium processes
Le Chatelier's principle refers to states of thermodynamic equilibrium
Thermodynamic equilibrium is a notion of thermodynamics with axiomatic status referring to an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable ...
. The latter are stable
A stable is a building in which working animals are kept, especially horses or oxen. The building is usually divided into stalls, and may include storage for equipment and feed.
Styles
There are many different types of stables in use tod ...
against perturbations that satisfy certain criteria; this is essential to the definition of thermodynamic equilibrium.
OR
It states that changes in the temperature
Temperature is a physical quantity that quantitatively expresses the attribute of hotness or coldness. Temperature is measurement, measured with a thermometer. It reflects the average kinetic energy of the vibrating and colliding atoms making ...
, pressure
Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and eve ...
, volume
Volume is a measure of regions in three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch) ...
, or concentration
In chemistry, concentration is the abundance of a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished: '' mass concentration'', '' molar concentration'', '' number concentration'', ...
of a system will result in predictable and opposing changes in the system in order to achieve a new equilibrium state
Thermodynamic equilibrium is a notion of thermodynamics with axiomatic status referring to an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable ...
.
For this, a state of thermodynamic equilibrium is most conveniently described through a fundamental relation that specifies a cardinal function of state, of the energy kind, or of the entropy kind, as a function of state variables chosen to fit the thermodynamic operations through which a perturbation is to be applied.
In theory and, nearly, in some practical scenarios, a body can be in a stationary state with zero macroscopic flows and rates of chemical reaction (for example, when no suitable catalyst is present), yet not in thermodynamic equilibrium, because it is metastable or unstable; then Le Chatelier's principle does not necessarily apply.
Non-equilibrium processes
A simple body or a complex thermodynamic system can also be in a stationary state with non-zero rates of flow and chemical reaction; sometimes the word "equilibrium" is used in reference to such a state, though by definition it is not a thermodynamic equilibrium state. Sometimes, it is proposed to consider Le Chatelier's principle for such states. For this exercise, rates of flow and of chemical reaction must be considered. Such rates are not supplied by equilibrium thermodynamics. For such states, there are no simple statements that echo Le Chatelier's principle. Prigogine and Defay demonstrate that such a scenario may exhibit moderation, or may exhibit a measured amount of anti-moderation, though not a run-away anti-moderation that goes to completion. The example analysed by Prigogine and Defay is the Haber process
The Haber process, also called the Haber–Bosch process, is the main industrial procedure for the ammonia production, production of ammonia. It converts atmospheric nitrogen (N2) to ammonia (NH3) by a reaction with hydrogen (H2) using finely di ...
.
This situation is clarified by considering two basic methods of analysis of a process. One is the classical approach of Gibbs, the other uses the near- or local equilibrium approach of De Donder. The Gibbs approach requires thermodynamic equilibrium. The Gibbs approach is reliable within its proper scope, thermodynamic equilibrium, though of course it does not cover non-equilibrium scenarios. The De Donder approach can cover equilibrium scenarios, but also covers non-equilibrium scenarios in which there is only local thermodynamic equilibrium, and not thermodynamic equilibrium proper. The De Donder approach allows state variables called extents of reaction to be independent variables, though in the Gibbs approach, such variables are not independent. Thermodynamic non-equilibrium scenarios can contradict an over-general statement of Le Chatelier's Principle.
Related system concepts
It is common to treat the principle as a more general observation of system
A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its open system (systems theory), environment, is described by its boundaries, str ...
s, such as
or, "roughly stated":
The concept of systemic maintenance of a stable steady state despite perturbations has a variety of names, and has been studied in a variety of contexts, chiefly in the natural science
Natural science or empirical science is one of the branches of science concerned with the description, understanding and prediction of natural phenomena, based on empirical evidence from observation and experimentation. Mechanisms such as peer ...
s. In chemistry, the principle is used to manipulate the outcomes of reversible reaction
A reversible reaction is a reaction in which the conversion of reactants to products and the conversion of products to reactants occur simultaneously.
: \mathit aA + \mathit bB \mathit cC + \mathit dD
A and B can react to form C and D or, in the ...
s, often to increase their yield. In pharmacology
Pharmacology is the science of drugs and medications, including a substance's origin, composition, pharmacokinetics, pharmacodynamics, therapeutic use, and toxicology. More specifically, it is the study of the interactions that occur betwee ...
, the binding of ligands
In coordination chemistry, a ligand is an ion or molecule with a functional group that binds to a central metal atom to form a coordination complex. The bonding with the metal generally involves formal donation of one or more of the ligand's ...
to receptors may shift the equilibrium according to Le Chatelier's principle, thereby explaining the diverse phenomena of receptor activation and desensitization. In biology
Biology is the scientific study of life and living organisms. It is a broad natural science that encompasses a wide range of fields and unifying principles that explain the structure, function, growth, History of life, origin, evolution, and ...
, the concept of homeostasis
In biology, homeostasis (British English, British also homoeostasis; ) is the state of steady internal physics, physical and chemistry, chemical conditions maintained by organism, living systems. This is the condition of optimal functioning fo ...
is different from Le Chatelier's principle, in that homoeostasis is generally maintained by processes of active character, as distinct from the passive or dissipative character of the processes described by Le Chatelier's principle in thermodynamics. In economics
Economics () is a behavioral science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services.
Economics focuses on the behaviour and interac ...
, even further from thermodynamics, allusion to the principle is sometimes regarded as helping explain the price equilibrium of efficient economic systems. In some dynamic systems, the end-state cannot be determined from the shock or perturbation.
Economics
In economics, a similar concept also named after Le Chatelier was introduced by American economist Paul Samuelson
Paul Anthony Samuelson (May 15, 1915 – December 13, 2009) was an American economist who was the first American to win the Nobel Memorial Prize in Economic Sciences. When awarding the prize in 1970, the Swedish Royal Academies stated that he "h ...
in 1947. There the generalized Le Chatelier principle is for a maximum condition of economic equilibrium
In economics, economic equilibrium is a situation in which the economic forces of supply and demand are balanced, meaning that economic variables will no longer change.
Market equilibrium in this case is a condition where a market price is es ...
: Where all unknowns of a function are independently variable, auxiliary constraints—"just-binding" in leaving initial equilibrium unchanged—reduce the response to a parameter change. Thus, factor-demand and commodity-supply elasticities are hypothesized to be lower in the short run than in the long run because of the fixed-cost constraint in the short run.
Since the change of the value of an objective function in a neighbourhood
A neighbourhood (Commonwealth English) or neighborhood (American English) is a geographically localized community within a larger town, city, suburb or rural area, sometimes consisting of a single street and the buildings lining it. Neighbourh ...
of the maximum position is described by the envelope theorem, Le Chatelier's principle can be shown to be a corollary
In mathematics and logic, a corollary ( , ) is a theorem of less importance which can be readily deduced from a previous, more notable statement. A corollary could, for instance, be a proposition which is incidentally proved while proving another ...
thereof.
See also
*Homeostasis
In biology, homeostasis (British English, British also homoeostasis; ) is the state of steady internal physics, physical and chemistry, chemical conditions maintained by organism, living systems. This is the condition of optimal functioning fo ...
*Common-ion effect
In chemistry, the common-ion effect refers to the decrease in solubility of an ionic precipitate by the addition to the solution of a soluble compound with an ion in common with the precipitate. This behaviour is a consequence of Le Chatelier's ...
* Response reactions
References
Bibliography of cited sources
*
*Bailyn, M. (1994). ''A Survey of Thermodynamics'', American Institute of Physics Press, New York, .
* Callen, H.B. (1960/1985). ''Thermodynamics and an Introduction to Thermostatistics'', (1st edition 1960) 2nd edition 1985, Wiley, New York, .
*Münster, A. (1970), ''Classical Thermodynamics'', translated by E.S. Halberstadt, Wiley–Interscience, London, .
*Prigogine, I., Defay, R. (1950/1954). ''Chemical Thermodynamics'', translated by D.H. Everett, Longmans, Green & Co, London.
*{{cite book, last=Samuelson, first=Paul A, title=Foundations of Economic Analysis, publisher=Harvard University Press, year=1983, isbn=0-674-31301-1, url-access=registration, url=https://archive.org/details/foundationsofeco0000samu
External links
YouTube video of Le Chatelier's principle and pressure
Equilibrium chemistry
Homeostasis