14.8: Le Chatelier’s Principle: Changing Volume (Pressure)

For gas-phase equilibria, changes in the concentrations of reactants and products can occur with altered volume and pressure. The partial pressure, P, of an ideal gas is proportional to its molar concentration, M.

So changes in the partial pressures of any reactant or product are essentially changes in concentrations; therefore, these changes yield the same effects on equilibria. Aside from adding or removing reactants or products, the pressures (concentrations) of species in a gas-phase equilibrium can also be changed by changing the volume occupied by the system. Since all species of a gas-phase equilibrium occupy the same volume, a given change in volume will cause the same change in concentration for both reactants and products. In order to discern what shift, if any, this type of stress will induce, the stoichiometry of the reaction must be considered.

At equilibrium, the reaction N₂ (g) + O₂ (g) ⇌ 2 NO (g) is described by the reaction quotient

If the volume occupied by an equilibrium mixture of these species is decreased by a factor of 3, the partial pressures of all three species will be increased by a factor of 3:

And so, changing the volume of this gas-phase equilibrium mixture does not result in a shift of the equilibrium.

A similar treatment of a different system, 2 SO₂ (g) + O₂ (g) ⇌ 2 SO₃ (g), however, yields a different result:

In this case, the change in volume results in a reaction quotient smaller than the equilibrium constant, and so the equilibrium will shift right.

These results illustrate the relationship between the stoichiometry of a gas-phase equilibrium and the effect of a volume-induced pressure (concentration) change. If the total molar amounts of reactants and products are equal, as in the first example, a change in volume does not shift the equilibrium. If the molar amounts of reactants and products are different, a change in volume will shift the equilibrium in a direction that better “accommodates” the volume change. In the second example, three moles of reactant (SO₂ and O₂) yield two moles of product (SO₃), and so decreasing the system volume causes the equilibrium to shift right since the forward reaction produces less gas (2 mol) than the reverse reaction (3 mol). Conversely, increasing the volume of this equilibrium system would result in a shift towards reactants.

This text has been adapted from Openstax, Chemistry 2e, Section 13.3 Shifting Equilibria: LeChatelier’s Principle.

Le Châtelier’s principle can be used to predict how a system at equilibrium would respond to the stress of a change in volume or pressure.

The volume of a gas is inversely proportional to its pressure; therefore, for a system at equilibrium, a decrease in volume increases the pressure and disturbs the equilibrium. In response, the equilibrium position will shift in a direction to minimize the stress.

The ideal gas law states that the pressure of a gas is directly proportional to the number of moles. Thus, the direction of the shift needed to restore equilibrium is dependent on the number of moles of gas particles on either side of the reaction.

As more moles of gas results in a higher pressure, an increase in pressure shifts the equilibrium position to the side with fewer moles to lower the pressure. Likewise, a decrease in pressure shifts the equilibrium position to the side with more moles of gas.

Consider a chemical equilibrium, where one mole of gaseous phosphorus pentachloride decomposes into one mole of phosphorus trichloride and one mole of chlorine gas—two total moles of product.

If the piston is pushed down, the volume of the equilibrium system decreases, increasing the pressure. This disturbs the equilibrium and results in Q greater than K. Thus, the equilibrium position shifts towards the reactants, with fewer moles of gas particles, in order to lower the pressure and restore equilibrium.

Conversely, pulling the piston up increases the volume and decreases the pressure. In this case, Q becomes smaller than K. In order to raise the pressure, the equilibrium position shifts towards the products, the side with the most moles of gas, and restores equilibrium.

Increasing the pressure by adding an inert gas to an equilibrium mixture at constant volume, does not affect the equilibrium because the partial pressures of the gaseous reactants and products remain unchanged.

For equilibrium systems with equal numbers of moles of gaseous reactants and products, such as the reaction between iodine gas and chlorine gas to produce iodine monochloride, a change in the volume of the system will have no effect on the equilibrium.