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Effect of an Inert Gas


The effects produced on the addition of an inert gas on the equilibrium of a reaction can be predicted qualitatively as follows.

Inert gas added keeping pressure of the system constant In this case, the addition of an inert gas increases the volume of the system, which in turn, causes the equilibrium position of the system to move in the direction of larger number of gaseous molecules. Thus, we will have

Reaction with

Direction of shift in equilibrium

Δng positive

right-hand side

Δng negative

left-hand side

Δng zero

remains unaffected

 

​Inert gas added keeping volume of the system constant. The effect of adding inert gas on equilibrium may be discussed by writing eq. (9.10) in terms of amount of substances, i.e.


 
Since pressure of the system is directly proportional to ntotal (p = nRT/V), the ration of ntotal/P will remain constant on the addition of inert gas. Since the value of Kp is independent of pressure, it follows that the amounts of substances at equilibrium remain unaffected by the addition of inert gas, i.e. the equilibrium position of the reaction remains unaffected.

Problem
For the exothermic formation of sulphur trioxide from sulphur dioxide and oxygen in the gas phase
2SO2(g) + O2(g) 2SO3(g)
Kp = 40.5 atm-1 at 900 K and H = -198 kJ mol-1.
  1. Write the expression for the equilibrium constant for the reaction.
  2. At room temperature ( 300K) will KP be greater than, less than or equal to Kp at 900 K.
  3. How will the equilibrium be affected if the volume of the vessel containing the three gases is reduced, keeping the temperature constant?
  4. What is the effect of adding 1 mol of helium gas to a flask containing SO2, O2 and SO3 at equilibrium, at constant pressure?
Solution
  1. The expression for equilibrium constant is
  2. For an exothermic reaction, on decreasing the temperature the equilibrium position of the reaction is shifted to the right-hand side. Hence in the expression for Kp, the value of numerator is increased. Thus, the value of Kp is increased, i.e. Kp at 300 K will be greater than Kp at 900 K.
  3. On reducing volume, the pressure of the system will be increased and it will affect the equilibrium by causing a shift towards the lesser number of molecules. Thus, the equilibrium will be shifted towards the right-hand side, i.e. more SO3 will be formed.
  4. The addition of inert gas at constant pressure will cause an increase in volume and this will shift the equilibrium towards the larger number of gaseous molecules. Thus, in the present case, the equilibrium will be shifted towards the left-hand side.




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