Le Châtelier’s Principle: Concentration and Pressure

Le Châtelier’s principle states that when a system at equilibrium is disturbed by a change in concentration, pressure or temperature, it shifts in the direction that partly counteracts the change. In brief: adding N₂ to the equilibrium N₂ + 3H₂ ⇌ 2NH₃ shifts it to the right, and compressing the mixture also shifts it to the right, because that side has fewer moles of gas (2 instead of 4).

The principle gives a quick qualitative way to predict how an equilibrium responds to a stress, and chemists use it to improve the yields of reactions. This article covers changes in concentration and pressure (volume), including the special cases of an inert gas and a reaction with no change in the number of gas moles; the effect of temperature and catalysts is treated in the following article. The explanation is backed up by calculations with the reaction quotient.

What does the principle say?

If a stress is applied to a system at equilibrium, the system adjusts itself to reduce the effect of the stress and reach a new equilibrium. A “stress” is a change in the concentration of a substance, the pressure or volume, or the temperature. After the shift, the equilibrium constant is unchanged if the temperature is the same, but the equilibrium concentrations are different. The principle is a rule of thumb that predicts the direction of the shift, but not its size; for that you need K and the reaction quotient.

How does a concentration change affect equilibrium?

• Adding a reactant: the system shifts toward the products, using up some of the added reactant.
• Removing a reactant: the system shifts toward the reactants to replace it.
• Adding a product: the system shifts toward the reactants.
• Removing a product: the system shifts toward the products. This is used to push reactions to completion, for example by removing ammonia from the reactor by condensation.

In terms of the reaction quotient, adding a reactant reduces Q below K, so the net reaction goes forward until Q = K again. Adding a product raises Q above K, so the net reaction goes in reverse. Adding a pure solid or liquid has no effect, because its concentration is constant.

How does pressure or volume affect equilibrium?

Pressure matters only for equilibria with gases in which the number of moles of gas changes.

• Higher pressure (smaller volume): the system shifts toward the side with fewer moles of gas, which reduces the pressure.
• Lower pressure (larger volume): the system shifts toward the side with more moles of gas.
• Equal moles of gas on both sides: a change in volume has no effect on the position, as in H₂ + I₂ ⇌ 2HI.

Adding an inert gas (such as argon) at constant volume increases the total pressure but not the partial pressures or concentrations of the reacting gases, so there is no shift. If an inert gas is added at constant pressure, the volume increases, the reacting gases are diluted and the system shifts toward the side with more moles of gas.

Summary of the shifts

Worked examples with Q

Example 1: adding a reactant

For N₂O₄ ⇌ 2NO₂, K_c = 0.0060. At equilibrium, [N₂O₄] = 0.0885 M and [NO₂] = 0.0230 M. Then 0.100 M of N₂O₄ is added at once, so that [N₂O₄] = 0.1885 M. Q = (0.0230)² / 0.1885 = 0.000529 / 0.1885 = 0.0028. Since Q < K, the reaction shifts to the right and more NO₂ forms, in agreement with the principle.

Example 2: compressing the mixture

The same system at equilibrium is compressed to half of its volume, so that the concentrations double: [N₂O₄] = 0.177 M and [NO₂] = 0.0460 M. Q = (0.0460)² / 0.177 = 0.002116 / 0.177 = 0.0120. This is twice K (0.0060), so Q > K and the reaction shifts to the left, toward N₂O₄, the side with fewer gas moles (1 instead of 2). The brown color of NO₂ first deepens as the concentration doubles, and then fades partly.

Example 3: no effect of pressure

For H₂ + I₂ ⇌ 2HI, K = 54.3. If the volume is halved, all concentrations double, and Q = (2[HI])² / ((2[H₂])(2[I₂])) = 4[HI]² / (4[H₂][I₂]) = K. Since Q = K, there is no shift.

Example 4: removing a product

In the esterification CH₃COOH + C₂H₅OH ⇌ CH₃COOC₂H₅ + H₂O, removing the water by distillation or with a drying agent, or using an excess of one reactant, shifts the equilibrium to the right and raises the yield of the ester.

Where is the principle applied?

• Haber process: a high pressure of 150–250 atm shifts the equilibrium toward ammonia, and the product is continuously liquefied and removed.
• Contact process for sulfuric acid: 2SO₂ + O₂ ⇌ 2SO₃ uses an excess of oxygen, and the SO₃ is removed between stages to give a high conversion.
• Carbonated drinks: opening a bottle lowers the pressure of CO₂, so the dissolved gas escapes.
• Blood chemistry: the equilibrium between hemoglobin and oxygen shifts with the oxygen pressure in the lungs and tissues.
• Diving and altitude: the body responds to a change in oxygen partial pressure.

Who formulated the principle?

Henri Louis Le Châtelier, a French chemist and engineer, stated the principle in 1884 for the effect of temperature and pressure on equilibria, and extended it in 1888. The German physicist Ferdinand Braun arrived at the same idea independently in 1887, so it is sometimes called the Le Châtelier–Braun principle. The more general statement, which relates changes in the intensive and extensive properties, is a consequence of the stability condition of thermodynamic equilibrium. The principle was important in the development of industrial processes, including the ammonia synthesis.

Which mistakes are common?

• Believing that K changes: concentration and pressure changes shift the equilibrium, but K remains the same.
• Saying that the shift completely undoes the stress: it only partly counteracts it.
• Applying pressure arguments to solids and liquids: they have little effect.
• Treating inert gas at constant volume as a stress: the partial pressures do not change.
• Counting all substances in the gas moles: only gases count.