Question

A change in the volume of the system does not alter the number of moles in which of the following equilibriums?
(A) $N_{2(g)}+ O_{2(g)}\rightleftharpoons 2NO_{(g)}$
(B) $PCl_{5(g)}\rightleftharpoons PCl_{3(g)}+Cl_{2(g)}$
(C) $N_{2(g)}+3H_{2(g)}\rightleftharpoons 2NH_{3(g)}$
(D) $SO_{2}Cl_{2(g)}\rightleftharpoons SO_{2(g)}+Cl_{2(g)}$

Answer 1

Hint: According to Le Chatelier’s principle, if a system at equilibrium is disturbed by an external stress, the system adjusts to partially offset the stress as the system attains a new equilibrium position. A change in volume, temperature, pressure, or concentration can affect the equilibrium of the system.

Formula Used: The change in volume will not affect the system if the change in the number of moles is zero. So, we have to check the change in the number of moles $\left( \Delta n \right)$.
$\Delta n={{n}_{P}}-{{n}_{R}}$

Complete Step by Step Answer:
We will check the change in the number of moles in each of the reactions. If there is no change in the number of moles between reactants and products, then the change in volume will not affect the system.
a. For the reaction: $N_{2(g)}+ O_{2(g)}\rightleftharpoons 2NO_{(g)}$
$\Delta n={{n}_{p}}-{{n}_{R}}$
$\Delta n=2-2=0$
Here, the change in the number of moles is zero. Hence, a change in volume will not affect the system.

b. For the reaction: $PCl_{5(g)}\rightleftharpoons PCl_{3(g)}+Cl_{2(g)}$
$\Delta n={{n}_{p}}-{{n}_{R}}$
 $\Delta n=2-1=1$
Here, the change in the number of moles is non-zero. Hence, a change in volume will affect the system.

c. For the reaction: $N_{2(g)}+3H_{2(g)}\rightleftharpoons 2NH_{3(g)}$
$\Delta n={{n}_{p}}-{{n}_{R}}$
$\Delta n=2-4=-2$
Here, the change in the number of moles is non-zero. Hence, a change in volume will affect the system.

d. For the reaction: $SO_{2}Cl_{2(g)}\rightleftharpoons SO_{2(g)}+Cl_{2(g)}$
$\Delta n={{n}_{p}}-{{n}_{R}}$
$\Delta n=2-1=1$
Here, the change in the number of moles is non-zero. Hence, a change in volume will affect the system.
Hence, the correct answer is Option (A).

Note: The change in the number of moles $\Delta n={{n}_{P}}-{{n}_{R}}$ is always calculated after balancing the reaction. The pressure of gases is related directly to their concentration. This means changing the pressure by increasing or decreasing the volume of a container will disturb an equilibrium system.