Problem 100 - A Complete Resource Book in Chemistry for JEE Main

Question

In which of the following reactions, equilibrium is independent of pressure? (a) \(\mathrm{N}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g}) ; \Delta \mathrm{H}=+\mathrm{ve}\) (b) \(2 \mathrm{SO}_{2}+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{SO}_{3}(\mathrm{~g}) ; \Delta \mathrm{H}=-\mathrm{ve}\) (c) \(3 \mathrm{H}_{2}(\mathrm{~g})+\mathrm{N}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NH}_{3}(\mathrm{~g}) ; \Delta \mathrm{H}=-\mathrm{ve}\) (d) \(\mathrm{PCl}_{5}(\mathrm{~g}) \rightleftharpoons \mathrm{PCl}_{3}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g}) ; \Delta \mathrm{H}=+\mathrm{ve}\)

Step-by-Step Solution

Answer

Reaction (a) is independent of pressure.

Step 1: Understand the Effect of Pressure on Equilibrium

The equilibrium of a reaction involving gases is affected by pressure changes if there is a change in the number of moles of gas in the reaction. If the number of moles of gaseous reactants is equal to the number of moles of gaseous products, then the equilibrium will not be influenced by pressure changes.

Step 2: Analyze Reaction (a)

For reaction (a), \(\mathrm{N}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g})\), there are 2 moles of gaseous reactants and 2 moles of gaseous products. Since the moles are equal on both sides, the equilibrium is independent of pressure.

Step 3: Analyze Reaction (b)

In reaction (b), \(2 \mathrm{SO}_{2}+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{SO}_{3}(\mathrm{~g})\), there are 3 moles of gaseous reactants and 2 moles of gaseous products. Here, the change in moles implies that the equilibrium is dependent on pressure.

Step 4: Analyze Reaction (c)

Reaction (c) involves \(3 \mathrm{H}_{2}(\mathrm{~g})+\mathrm{N}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NH}_{3}(\mathrm{~g})\). There are 4 moles of gaseous reactants and 2 moles of gaseous products. The change in moles makes the equilibrium dependent on pressure.

Step 5: Analyze Reaction (d)

For reaction (d), \(\mathrm{PCl}_{5}(\mathrm{~g}) \rightleftharpoons \mathrm{PCl}_{3}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g})\), there is 1 mole of gaseous reactant and 2 moles of gaseous products. The equilibrium will thus be pressure-dependent.

Key Concepts

Pressure Dependency

Understanding how pressure impacts chemical equilibrium is crucial in gaseous reactions. The key aspect to consider is the number of moles of gaseous substances on the reactant and product sides. For a reaction where the moles of reactants equal the moles of products, the equilibrium is independent of pressure. This is because changes in pressure affect both sides equally, leading to no net change.

If there is a difference in the number of moles, pressure changes can shift the equilibrium position. Increasing pressure, for instance, tends to favor the formation of fewer moles of gas, thus shifting the equilibrium towards the side with fewer moles. Likewise, decreasing pressure favors the side with more moles.

In summary, analyzing pressure dependency involves identifying whether there is an equal amount of gaseous reactants and products:

• If yes, the equilibrium is pressure independent.
• If no, the equilibrium shifts upon pressure changes.

Mole Concept

The mole concept is foundational in understanding chemical equilibria, especially when dealing with reactions involving gases. It allows us to quantify the substances involved. One mole equals to Avogadro's number, approximately \(6.022 \ imes 10^{23}\), which equates to the number of atoms or molecules in one mole of a substance. This concept enables chemists to convert between number of particles and amount in moles, which simplifies calculations in chemical reactions.

In the context of pressure dependency, the mole concept helps identify changes in the number of moles during reactions. For example, in reaction (a), \(\mathrm{N}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g})\), there's an equal number of moles before and after the reaction (2 to 2), making it independent of pressure.

Understanding moles allows you to:

• Predict how a reaction will respond to pressure changes.
• Efficiently balance chemical equations.
• Calculate the quantities of reactants and products involved in a reaction.

Gaseous Reactions

Reactions involving gases have distinctive characteristics because gases are easily compressible and their volumes vary significantly with temperature and pressure. Equilibrium in gaseous reactions considers these traits, emphasizing the effects of pressure and volume according to Le Chatelier's Principle.

In a gaseous equilibrium system, an increase in pressure by reducing the volume will favor the side of the equation with fewer moles of gas. Conversely, a decrease in pressure by increasing volume will favor the side with more moles of gas. This dynamic allows us to predict how changes in external conditions affect the reaction.

When dealing with gaseous reactions, keep in mind:

• The ideal gas law (\(PV = nRT\), where \(P\) is pressure, \(V\) is volume, \(n\) is moles, \(R\) is the gas constant, and \(T\) is temperature) connects these properties and explains their relationships.
• Gaseous reactions can often reach equilibrium quicker due to the rapid motion and interaction of gas molecules.
• Environmental factors such as temperature and the presence of catalysts also heavily influence the direction and speed of these reactions.