Question

What happens when an inert gas is added to an equilibrium keeping volume unchanged?
(a) more product will form
(b) less product will form
(c) more reactant will form
(d) equilibrium will remain unchanged

Answer 1

Hint: If we have a system that is at equilibrium, then it is affected by the following factors:(i) Change of concentration of any reactant or product, (ii) Change in temperature of the system, (iii) Change in pressure on the system, (iv) Addition of a catalyst and (v) Addition of an inert gas

Complete step by step solution:
If we have a system that is at equilibrium, then it is affected by the following factors:
(i) Change of concentration of any reactant or product.
(ii) Change in temperature of the system
(iii) Change in pressure on the system
(iv) Addition of a catalyst
(v) Addition of an inert gas
Let us understand the effect of addition of an inert gas on the equilibrium with the help of an example of the dissociation of phosphorus pentachloride:
${ PCl }_{ 5 }(g)\rightleftharpoons { PCl }_{ 3 }(g)+{ Cl }_{ 2 }(g)$
Applying the law of chemical equilibrium, the expression for the equilibrium constant will be:
${ K }_{ c }=\cfrac { \left[ { PCl }_{ 3 } \right] \left[ { Cl }_{ 2 } \right] }{ \left[ { PCl }_{ 5 } \right] } $
Now, if the reaction takes place at constant volume i.e. in a closed vessel then the addition of an inert gas will not change the molar concentration of the reactants and the products. Therefore there will not be any change in the state of the equilibrium of the system.
If the reaction takes place at constant pressure, then the addition of the inert gas will cause an increase in the total volume in order to keep the pressure constant since according to Boyle’s law, the volume and pressure for a given amount of a gas are inversely proportional at constant temperature i.e. PV=k (Where k is a constant). Since, the addition of gas to a system should cause an increase in its pressure but we want the pressure to be constant therefore the volume of the system must increase such that the addition of the inert gas will happen at constant pressure. Since the volume is increasing, hence the molar concentrations of the reactants and the products will decrease. In the expression for the equilibrium constant, there are two terms in the numerator and one in the denominator, therefore ${ K }_{ c }$ should decrease but we know that it remains constant at constant temperature. So, in order to keep ${ K }_{ c }$ constant, either $\left[ { PCl }_{ 5 } \right]$ should decrease or $\left[ { PCl }_{ 3 } \right]$ and $\left[ { Cl }_{ 2 } \right]$ should increase. This can take place if more ${ PCl }_{ 5 }$ dissociates in order to give ${ PCl }_{ 3 }$ and ${ Cl }_{ 2 }$. Hence the dissociation increases with the addition of an inert gas.

Hence the correct answer is (d) equilibrium will remain unchanged

Note: The effect of change in concentration, pressure and temperature on the equilibrium is predicted with the help of Le Chatelier’s principle which states that if a system is subjected to a change of concentration, temperature or pressure then the equilibrium shifts in a direction that tends to undo the effect of the change imposed.