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Le Chatelier's principle

In chemistry, Le Chatelier's Principle, also called the Le Chatelier-Braun principle, can be used to predict the effect of a change in conditions on a chemical equilibrium. The principle is named after Henry Louis Le Chatelier and Karl Ferdinand Braun who discovered it independently. It can be summarized as:

If a chemical system at equilibrium experiences a change in concentration, temperature, volume, or total pressure, then the equilibrium shifts to partially counter-act the imposed change.

It is common to take Le Chatelier's principle to be a more general observation, roughly stated: "Any change in status quo prompts an opposing reaction in the responding system." This principle also has a variety of names, depending upon the discipline using it. See for example Lenz's law and homeostasis.

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 Chatelier's principle thereby explaining the diverse phenomena of receptor activation and desensitization. And in economics, the principle has been generalized to help explain the price equilibrium of efficient economic systems.

In chemistry

Concentration

Changing the concentration of an ingredient 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.

C O + 2 H₂ ⇌ CH₃OH

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 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.

Temperature

Let us take for example the reaction of nitrogen gas with hydrogen gas. This is a reversible reaction, in which the two gases react to form ammonia:

N₂ + 3 H₂ ⇌ 2 NH₃ ΔH = −92kJ

This is an exothermic reaction when producing ammonia. If we were to lower the temperature, the equilibrium would shift in such a way as to produce heat. Since this reaction is exothermic to the right, it would favor the production of more ammonia. In practice, in the Haber process the temperature is instead increased to speed the reaction rate at the expense of producing less ammonia.

Changes in pressure owing 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.

Once again, let us refer to the reaction of nitrogen gas with hydrogen gas to form ammonia:

N₂ + 3 H₂ ⇌ 2 NH₃ ΔH = −92kJ

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. 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.

Thus, an increase in pressure due to decreasing volume causes the reaction to shift to the side with the fewer moles of gas. 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 system (or equation).

Effect of adding an inert gas

An inert gas (or noble gas) such as helium is one which 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 partial pressures of the other gases in the container. 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.

Applications in economics

In economics, a similar concept also named after Le Chatelier was introduced by US economist Paul Samuelson in 1947. There the generalized Le Chatelier 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 (1947, pp. 36, 38; Hatta, 1987, p. 155).

References

Hatta, Tatsuo (1987), "Le Chatelier 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 Chatelier's principle", Physical Review E, 63, 051105(4).

3. P.W. Atkins, The Elements of Physical Chemistry, 3rd edition, Oxford University Press, 1993, p. 114