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.

The principle is used by chemists in order 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. [1]

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Examples and generalization

Concentration

Changing the concentration of an ingredient will shift the equilibrium to the side that would reduce that change in concentration.

This can be illustrated by the equilibrium of carbon monoxide and hydrogen gas, reacting to form methanol.

CO + 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

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. We know that gases at the same temperature and pressure will occupy the same volume. We can use this fact to predict the change in equilibrium that will occur if we were to change the total pressure.

Suppose we increase total pressure on the system by decreasing the volume: now, by Le Châtelier's principle the equilibrium would move to decrease the pressure. Noting that 4 moles of gas occupy more volume than 2 moles of gas, we can deduce that the reaction will move towards the products if we were to increase the pressure.

Thus, an increase in pressure causes the reaction to shift to the side with the fewer moles. It has no impact on a reaction where the number of moles is the same on each side or when one of the reactants or products is not a gas.

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. To add an inert gas into a closed system at equilibrium may or may not result in a shift. For example, consider adding helium to a container with the following reaction:

N₂ + 3H₂ ⇌ 2NH₃

The main effect of adding an inert gas to a closed system is that it will increase the total pressure or increase the volume. An inert gas would not be directly involved in the reaction, but could result in a shift.

Volume held constant

If volume is held constant, as would be in case in any rigid sealed container, the added partial pressure of the inert gas will decrease the volume available for the gases in equilibrium, therefore, increasing the total pressure. This will, as a result, cause the reaction to shift to the side of the equation with the least amount of gas particles (least number of moles of gas particles).

Volume allowed to increase

If the volume is allowed to increase, the concentrations, as well as the partial pressures, all decrease. Because there are more stoichiometric moles on the lefthand side of the equation (4 moles vs. 2 moles), the decrease in concentration affects the lefthand side more than the righthand side. Therefore, the reaction would shift to the left until the system is at equilibrium again.

Applications in economics

In economics, a similar concept also named after Le Chatelier was introduced by American economist Paul Samuelson in 1947. There the generalized Le Chatelier principle is for a maximum condition of 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).