Question

In the reaction \[\text{2}{{\text{P}}_{\text{(g)}}}\text{ + }{{\text{Q}}_{\left( \text{g} \right)}}\text{ }\leftrightarrows\text{ 3}{{\text{R}}_{\text{(g)}}}\text{ + }{{\text{S}}_{\text{(g)}}}\]. If 2 moles each of P and Q taken initially in a 1 litre flask. At equilibrium which is true?
(A) \[\text{ }\!\![\!\!\text{ P }\!\!]\!\!\text{ }< \text{ }\!\![\!\!\text{ Q }\!\!]\!\!\text{ }\]
(B) \[\text{ }\!\![\!\!\text{ P }\!\!]\!\!\text{ =} \text{ }\!\![\!\!\text{ Q }\!\!]\!\!\text{ }\]
(C) \[\text{ }\!\![\!\!\text{ Q }\!\!]\!\!\text{ = }\!\![\!\!\text{ R }\!\!]\!\!\text{ }\]
(D) None of the above.

Answer 1

Hint: Chemical equilibrium refers to the state of a system in which the concentration of the reactant and the concentration of the products do not change with time and the system does not display any further change in properties.

Complete step by step answer: First we will write the moles of all reactants and products present initially.
\[\begin{matrix}
   {} \\
   \text{initial conc}\text{.} \\
\end{matrix}\text{ }\begin{matrix}
   2{{P}_{(g)}} \\
   2mol \\
\end{matrix}+\begin{matrix}
   {{Q}_{(g)}} \\
   2mol \\
\end{matrix}\begin{matrix}\leftrightarrows
   3{{R}_{(g)}} \\
   0 \\
\end{matrix}+\begin{matrix}
   {{S}_{(g)}} \\
   0 \\
\end{matrix}\]
Let ‘x’ be the concentration of R at equilibrium.
Since, we took 2 moles of each P and Q, at equilibrium we have,
\[\begin{matrix}
   {} \\
   \text{initial conc}\text{.} \\
   \text{At equilibrium} \\
\end{matrix}\text{ }\begin{matrix}
   2{{P}_{(g)}} \\
   2 \\
   (2-2\propto ) \\
\end{matrix}+\text{ }\begin{matrix}
   {{Q}_{(g)}} \\
   1 \\
   (2-\propto ) \\
\end{matrix}\begin{matrix}\leftrightarrows
   3{{R}_{(g)}} \\
   0 \\
   \propto \\
\end{matrix}+\begin{matrix}
   {{S}_{(g)}} \\
   0 \\
   \propto \\
\end{matrix}\]

So, at equilibrium we have concentration of Q more than concentration of P i.e. \[\left[ \text{P} \right]\text{ }<\text{ }\left[ \text{Q} \right]\].

Additional information: Several factors such as temperature, pressure, and concentration of the system are known to affect the equilibrium of a reaction.
Temperature: For an exothermic reaction, equilibrium constant decreases with increase in temperature and for an endothermic reaction equilibrium constant increases with increase in temperature.
Pressure: As the volume of reactant or product changes, pressure also changes. Change in pressure has more significance in gaseous reactions however in solid and liquid reactions change in pressure can be neglected if volume is independent of pressure.
Concentration: As the concentration of reactant or product changes, there is a change in the mixture of the chemical equilibrium. The concentration of the reactants or products added is relieved by the reaction which consumes the substance which is added. The concentration of reactants or products removed is relieved by the reaction which is in the direction that replenishes the substance which is removed.

Note: We have taken 2 moles of each P and Q and we know that 2 moles of P react with 1 mole of Q. That is why even at equilibrium we will have 1 mole of Q left unreacted. Hence, concentration of Q will be more.