# Pressure Dependence of Equilibria

The simplest way to predict qualitatively the response of a system at equilibrium to any change in the external conditions is to make use of Le Chatelier’s principle. This states that a system in equilibrium adjusts so as to minimise the effect of an applied alteration in conditions.

Thus, for example, compression of a gas that is in equilibrium with its condensed, liquid form may cause an increase in the proportion of  the liquid phase that is present, as this minimises the pressure increase in the system. (The conversion of gas to liquid reduces the amount of gas that is present, minimising the increase in pressure caused by confinement of the gas to a smaller volume.)

In a similar vein, we may consider the reaction between hydrogen and nitrogen to form ammonia, which is an equilibrium; 3H2 + N2 « 2NH3 . If hydrogen and nitrogen are reacted together, a reaction mixture containing hydrogen, nitrogen and ammonia results. If this mixture is compressed, the proportion of ammonia in the reaction mixture increases. This is because the reactant side of the equilibrium consists of four moles of gas, while the product side consists of only two moles of gas. Compression of the system reduces its volume and increases the pressure of the gases within it, but this pressure increase is minimised if the number of moles of gas in the system is reduced. This is achieved by a shift in the position of equilibrium to favour products. Note this is why high pressures are used in the Haber process; it increases the yield of ammonia.

The equilibrium constant for a reaction is directly related to the standard reaction Gibbs energy for the reaction, which is defined at one atmosphere pressure.

The value of ΔGrº , and hence the value of K, is thus independent of the pressure at which the equilibrium is established.

We may write this formally as:

However, the fact that K is pressure independent does not necessarily mean that the equilibrium composition is unaffected by pressure. Indeed, as illustrated by the above consideration of Le Chatelier’s principle, the equilibrium composition can be altered in dramatic and useful ways by compression of the system. Before exploring this apparent contradiction any further, it is necessary to distinguish between two different ways in which pressure may be applied to a system.

The pressure within a reaction system may be increased by adding an inert gas (commonly a noble gas or nitrogen) into the reaction vessel. If the gases behave perfectly, then addition of a pressurising gas does not alter the partial pressures of other gases that are present (remember the partial pressure is the pressure the gas would exert if it were alone in the container). Alternatively, we may consider that since the gases are still free to occupy the same volume, there has been no change in their molar concentrations.

Either way, it follows that pressurisation by means of the introduction of an inert gas does not alter the equilibrium composition of the reaction mixture (providing the gases behave perfectly – in practice small changes in the equilibrium composition may be observed).

Alternatively, the pressure of the system may be increased by compression (the reduction of the volume that the components of the system can occupy). This will alter the partial pressures (and molar concentrations) of the gases in the system.

Thus under pressurisation by compression, the composition of the equilibrium mixture can change.

Note that in either circumstance, the equilibrium constant for the reaction is unaltered. This means that the ratio of the activities or fugacities of reactants and products must not change with pressure, but this does not rule out a change in the absolute values of these quantities (which corresponds to a change in composition). For example, if we consider a simple reaction of two perfect gases, A and B;

where the partial pressures are given in bars. From Le Chatelier’s principle, we can state that an increase in pressure by compression will increase the proportion of A in the equilibrium mixture.

For K to remain constant, an increase in the partial pressure of A must cancel out the square of the increase in the partial pressure of B. This can only be achieved by a change in the equilibrium composition to one which is richer in A and less rich in B, which makes the partial pressure of A increase more rapidly than the simple effect of reducing the volume of the system (and reduces the increase in the partial pressure of B from the value that would be expected purely due to compression).