Equilibria and Partial Pressures

The following reaction between hydrogen and iodine is reversible:
H_2(g) + I_2(g) 2HI_(g)
If it is left for long enough, it will eventually reach dynamic equilibrium; this is where the forward and backward reactions are occurring at the same rate; therefore the concentrations of the reagents do not change.
The equilibrium constant, Kc, is given by the following expression:
In the equilibrium mixture, it is assumed that each gas behaves independently of the other gases present; the total pressure (P) of the mixture is therefore equal to the sum of the partial pressures of the gases present:
Total Pressure P = PH₂ + PI₂ + PHI
The partial pressure of each gas is proportional to its concentration; it is therefore possible to write an expression for the equilibrium constant in terms of partial pressures of the gases:
Similarly, it is also possible to write an equilibrium an expression for the equilibrium constant for the reaction between nitrogen and hydrogen to form ammonia:
N_2(g) + 3H_2(g) 2NH_3(g)
It is much more convenient to write the expression for the equilibrium constant in terms of the partial pressure of the gases.

Units

Pressure can be measured in Newtons per square metre (N m^-2); this can also be referred to as pascals: 1 Pa = 1 N m^-2.
However, atmospheres (atm) are generally the unit of pressure in equilibrium expressions: 1 atm = 1.01 x 10² kPa.
Therefore the units for the equilibrium constant for the reaction between iodine and hydrogen can be caluclated:
The units cancel out, so there are no units for the equilibrium constant for the reaction between hydrogen and iodine.
The units for the nitrogen/hydrogen/ammonia equilibrium constant are:
As for K_c, the units for each K_p expression must be worked out.

If the total pressure of a gas mixture at equilibrium is increased, then the reaction will respond by reducing the pressure again (Le Chatelier’s principle).
The pressure exerted by a gas is dependent on the number of gas molecules present; therefore the position of equilibrium will shift to the side with the fewest number of gas molecules if the pressure is increased.
In the reaction between nitrogen and hydrogen to form ammonia, there are four molecules of gas on the reactant side for every two molecules of gas on the product side:
1N_2(g) + 3H_2(g) 2NH_3(g)
Therefore, if the pressure is increased, the position of equilibrium will shift to the right to oppose the change made to the conditions of the reaction.
For example, at 1 atm total pressure, the equilibrium % of ammonia is equal to 24%. From this the equilibrium constant can be determined: The nitrogen and hydrogen react according to a 1:3 ratio, therefore the 99.76% is split into a 1:3 ratio: Converting these to partial pressures:

PN₂= 0.2494 * 1
PH₂ = 0.7482 * 1
PN₂= 0.0024 * 1

Substituting these into the equilibrium expression gives:
The graph below shows the percentage of ammonia at equilibrium at different pressures:
As the pressure increases, the percentage of ammonia at equilibrium also increases; this is why high pressures are used in the Haber process.
The K_p is constant for each reaction providing the temperature does not change.