Effect of change in Pressure (Le Chatelier’s Principle)

You Need to Know

Partial pressure of an ideal gas in a system having fixed volume depends on number of its particles present in it. Mathematically, (P = {nRT over V}). More number of moles of gases available, higher will be the pressure.

Pressure of a system can be changed in two ways. One, by changing volume of the system and second, by adding or removing gases that do not react with the mixture components of the reaction (such as inert gases).

Change in pressure by changing volume of the system

For a reaction (ce{N_2$(g)$ + 3H_2$(g)$<=>2NH_3$(g)$} ) in equilibrium condition,

Increase or decrease of pressure over a gaseous equilibrium mixture disturbs the equilibrium conditions and triggers a forward or backward reaction. The forward or backward reaction takes place as per the Le chatelier’s Principle.

When pressure is increased over the equilibrium mixture, the system tends to reduce this extra pressure. As number of total moles of products (here 2 for ammonia ) is less than the total moles of reactants (here 3 for Hydrogen and 1 for nitrogen) , the system tends to move in forward direction to reduce the number of particles in order to release some additional pressure. Similarly, when pressure is decreased over the equilibrium mixture, the system tends to increase pressure. As number of total moles of products (here 2 for ammonia ) is less than the total moles of reactants (here 3 for Hydrogen and 1 for nitrogen) , the system tends to move in backward direction to make more molecules and hence increase pressure.

Mathematically,

(ce{Q_$p$ = {(P_{NH_3})^2 over {(P_{H_2})^3.(P_{N_2)}}}}) = ((K_p))

Let the pressures of (N_2, H_2 and NH_3) are initially (n), (h), and (a ) respectively. (Q_p = {a^2 over {n times h^3}} = K_p). If volume of the system is halved, then partial pressure of each gas will be doubled, (P = {nRT over V}). Final pressures of (N_2, H_2 and NH_3) after compression of volume becomes (2n), (2h), and (2a ) respectively. New reaction quotient becomes (Q_p = {(2a)^2 over {(2n) times (2h)^3}} ) = ( {4a^2 over {2n times 8h^3}} ) = (ce {1/4{a^2 over {n times h^3}} = 1/4K_p}).

As (Q_p) has become lesser than (K_p), the reaction will move in forward direction.

Similarly, when partially pressures of gaseous reactants and products are decreased by increasing the volume of the system, value of (Q_p) increases that favours backward reaction.

Change in pressure by adding/removing non-reactive gases

The impact of change in pressure by adding/removing non-reactive gases are discussed in the topic Effect of Addition of Inert gases.

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