Le Chatelier's principle
In chemistry, Le Châtelier's principle (pronounced /lə ˈʃɑːtlieɪ/), also called Chatelier's principle or "The Equilibrium Law", can be used to predict the effect of a change in conditions on a chemical equilibrium. The principle is named after Henry Louis Le Châtelier and sometimes Karl Ferdinand Braun who discovered it independently. It can be stated as:
- When any system at equilibrium is subjected to change in concentration, temperature, volume, or pressure, then the system readjusts itself to (partially) counteract the effect of the applied change and a new equilibrium is established.
or whenever a system in equilibrium is disturbed the system will adjust itself in such a way that the effect of the change will be nullified. (in short)
This principle has a variety of names, depending upon the discipline using it (see homeostasis, a term commonly used in biology). It is common to take Le Châtelier's principle to be a more general observation,[1] roughly stated:
- Any change in status quo prompts an opposing reaction in the responding system.
In chemistry, the principle is used to manipulate the outcomes of reversible reactions, often to increase the yield of reactions. In pharmacology, the binding of ligands to the receptor may shift the equilibrium according to Le Châtelier's principle, thereby explaining the diverse phenomena of receptor activation and desensitization.[2] In economics, the principle has been generalized to help explain the price equilibrium of efficient economic systems. In simultaneous equilibrium systems, phenomena that are in apparent contradiction to Le Châtelier's principle can occur; these can be resolved by the theory of response reactions.
Status as a physical law
Le Châtelier's principle describes the qualitative behavior of systems where there is an externally induced, instantaneous change in one parameter of a system; it states that a behavioural shift occurs in the system so as to oppose (partially cancel) the parameter change. The duration of adjustment depends on the strength of the negative feedback to the initial shock. Where a shock initially induces positive feedback (such as thermal runaway), the new equilibrium can be far from the old one, and can take a long time to reach. In some dynamic systems, the end-state cannot be determined from the 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 ensures that the disequilibrium caused by an instantaneous shock must have a finite half-life.[3] The principle has analogs throughout the entire physical world.
The principle while well rooted in chemical equilibrium and extended into economic theory, can also be used in describing mechanical systems in that the system put under stress will respond in a way such 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 reduce that change in concentration. The chemical system will attempt to partially oppose the change affected to 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 and hydrogen gas, reacting to form methanol.
Suppose we were to increase the concentration of CO in the system. Using Le Châtelier's principle, we can predict that the amount 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. 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 a desired product is not thermodynamically favored, the end-product can be obtained if it is continuously removed from the solution.
Effect of change in temperature
The effect of changing the temperature in the equilibrium can be made clear by a) incorporating heat as either a reactant or a product, and b) assuming that an increase in temperature increases the heat content of a system. When the reaction is exothermic (ΔH is negative, puts energy out), heat is included as a product, and, when the reaction is endothermic (ΔH is positive, takes energy in), 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 of nitrogen gas with hydrogen gas to form ammonia:
- N2(g) + 3 H2(g) ⇌ 2 NH3(g) ΔH = -92 kJ mol−1
Because this reaction is exothermic, it produces heat:
- N2(g) + 3 H2(g) ⇌ 2 NH3(g) + heat
If the temperature was 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 was run at a lower temperature, but a lower temperature also lowers the rate of the process, so, in practice (the Haber process) the temperature is set at a compromise value that allows ammonia to be made at a reasonable rate with an equilibrium concentration that is not too unfavorable.
In exothermic reactions, increase in temperature decreases the equilibrium constant, K, whereas, in endothermic reactions, increase in temperature increases the K value.
Le Chatelier's principle applied to changes in concentration or pressure can be understood by having K have 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 ΔH. The theoretical basis of this dependence is given by the Van 't Hoff equation.
Effect of change in pressure
Changes in pressure are attributable to changes in volume. The equilibrium concentrations of the products and reactants do not directly depend on the pressure subjected to the system. However, a change in pressure due to a change in volume of the system will shift the equilibrium.
Considering the reaction of nitrogen gas with hydrogen gas to form ammonia:
- N2 + 3 H2 ⇌ 2 NH3 ΔH = -92kJ mol−1
- 4 moles ⇌ 2 moles
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 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 expression, causing a shift in equilibrium.
The resulting shift from a change in pressure changes the amount of moles produced so that with a pressure increase, the side with fewer moles is more favorable and with a pressure decrease, the side with more moles is more favorable. Thus, an increase in system pressure due to decreasing volume causes the reaction to shift to the side with the fewer moles of gas.[4] A decrease in pressure due to increasing volume causes the reaction to shift to the side with more moles of gas. There is no effect on a reaction where the number of moles of gas is the same on each side of the chemical equation.
Effect of adding an inert gas
An inert gas (or noble gas), such as helium, 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.[4] 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: aA + bB + xX <--> cC + dD + xX. 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.
Effect of a catalyst
A catalyst has no effect on the position and composition of an equilibrium. It just speeds up both the forward and backward reactions equally, at the same time.
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. Since catalysts function as a means to increase reaction rate, the use of a catalyst cannot have an effect on the equilibrium of the reaction because both the forward and backward reactions are sped up by the same factor.
Applications in economics
In economics, a similar concept also named after Le Châtelier was introduced by U.S. economist Paul Samuelson in 1947. There the generalized Le Châtelier principle is for a maximum condition of economic equilibrium: 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.[5]
See also
References
- ↑ Gall, John (2002). The Systems Bible (3rd ed.). General Systemantics Press.
The System always kicks back
- ↑ "The Biophysical Basis for the Graphical Representations". Retrieved 2009-05-04.
- ↑ Kay, J. J. (February 2000) [1999]. "Application of the Second Law of Thermodynamics and Le Châtelier's Principle to the Developing Ecosystem". In Muller, F. Handbook of Ecosystem Theories and Management. Environmental & Ecological (Math) Modeling. CRC Press. ISBN 978-1-56670-253-9.
As systems are moved away from equilibrium, they will utilize all available avenues to counter the applied gradients... Le Châtelier's principle is an example of this equilibrium seeking principle.
For full details, see: "Ecosystems as Self-organizing Holarchic Open Systems: Narratives and the Second Law of Thermodynamics": 5. CiteSeerX: 10.1 ..1 .11 .856 - 1 2 Atkins1993, p. 114
- ↑ Samuelson, Paul A (1983). Foundations of Economic Analysis. Harvard University Press. ISBN 0-674-31301-1.
Bibliography
- Atkins, P.W. (1993). The Elements of Physical Chemistry (3rd ed.). Oxford University Press.
- Le Chatelier, H. and Boudouard O. (1898), "Limits of Flammability of Gaseous Mixtures", Bulletin de la Société Chimique de France (Paris), v. 19, pp. 483–488.
- Hatta, Tatsuo (1987), "Le Châtelier principle," The New Palgrave: A Dictionary of Economics, v. 3, pp. 155–57.
- Samuelson, Paul A. (1947, Enlarged ed. 1983). Foundations of Economic Analysis, Harvard University Press. ISBN 0-674-31301-1
- D.J. Evans, D.J. Searles and E. Mittag (2001), "Fluctuation theorem for Hamiltonian systems—Le Châtelier's principle", Physical Review E, 63, 051105(4).