# Change in Pressure

If pressure of the system is increased, then according to Le Chatelier's principle, the equilibrium is adjusted to decrease the pressure of the system. Since pressure is directly proportional to number of molecules present in the system, it follows that the equilibrium will be shifted in a direction where there are a lesser number of gaseous substances. Taking the example of

N2(g) + 3H2(g) 2NH3(g)

we find that there are lesser number of gaseous species on the right-hand side as compared to the left-hand side. Thus, on increasing pressure, the equilibrium is shifted to the right-hand side. On the other hand, if we decrease pressure, the equilibrium will be shifted towards the left-hand side.

Since the equilibrium constant of a reaction is independent of pressure, the above shift is not due to the change in equilibrium constant but is due to the change in partial pressures (or mole fractions) of the constituents. Taking an example of the above reaction, we have

Writing partial pressures in terms of total pressure (p), we have

where x represents the mole fractions of the respective constituents. Since Kp has a constant value for a given temperature, it is obvious from the right-hand side that x depends on the pressure of the system. If pressure of the system is increased (say, by compressing the total volume), the denominator in the above expression is increased. Now in order to keep Kp constant, the value of the numerator will be increased. This means more ammonia will be formed, i.e. the equilibrium is shifted towards the lesser number of gaseous species. On the other side, if the pressure is decreased (say, by increasing the volume of the system), the value of xNH3 will also decrease to have the same value of equilibrium constant, i.e. the equilibrium is shifted towards larger number of gaseous species.

For a reaction in which there occurs no change in gaseous molecules, i.e.

= 0
there will be no effect of pressure on the equilibrium stage of the reaction. One of the examples of such reaction is H2(g) + I2(g) 2HI(g).