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) \(\mathrm{PCl}_{5}(\mathrm{~g}) \rightleftharpoons \mathrm{PCl}_{3}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g}) ; \Delta \mathrm{H}=+\mathrm{ve}\)

Short answer

The equilibrium of reaction (a) is independent of pressure.

Step-by-step solution

Understanding Equilibrium Independence from Pressure

Equilibrium is independent of pressure when there is no change in the number of moles of gas during the reaction. In chemical reactions, the equilibrium constant (K) for reactions involving gases depends on the partial pressures of the reacting gases. However, if the number of gas molecules on each side of the reaction is the same, changes in pressure will not affect the equilibrium position.

Analyze Each Reaction for Moles of Gas

Examine each given reaction to determine if there is a change in the number of moles of gas between reactants and products:- (a) \( \mathrm{N}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g}) \): 1 + 1 moles \(\rightarrow\) 2 moles (No change, 2 \(\rightarrow\) 2)- (b) \(2 \mathrm{SO}_{2} + \mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{SO}_{3}(\mathrm{~g}) \): 2 + 1 moles \(\rightarrow\) 2 moles (Decrease, 3 \(\rightarrow\) 2)- (c) \(3 \mathrm{H}_{2}(\mathrm{~g})+\mathrm{N}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NH}_{3}(\mathrm{~g}) \): 3 + 1 moles \(\rightarrow\) 2 moles (Decrease, 4 \(\rightarrow\) 2)- (d) \(\mathrm{PCl}_{5}(\mathrm{~g}) \rightleftharpoons \mathrm{PCl}_{3}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g}) \): 1 mole \(\rightarrow\) 1 + 1 moles (Increase, 1 \(\rightarrow\) 2)

Determine Equilibrium Independence from Pressure

From Step 2, recognize that Reaction (a) maintains constant moles of gas - with no change from reactants to products (2 moles on each side). Therefore, it is the reaction where equilibrium is independent of pressure.

Key concepts

Mole Concept

The mole concept is a fundamental aspect of chemistry that helps us understand the amount of substance we have in any chemical reaction. A mole is essentially a quantity that stems from Avogadro's number, which is approximately \(6.022 \times 10^{23}\) entities, whether they be atoms, molecules, or ions. This concept is especially useful in balancing chemical equations and predicting the outcome of reactions. By using moles, chemists can precisely measure quantities of substances involved in chemical reactions.

When dealing with gaseous reactions, as in our original exercise, it's crucial to consider how many moles of gas are on each side of the chemical equation. This number directly influences whether a reaction's equilibrium is affected by changes in pressure. If the number of moles of gaseous reactants equals the number of moles of gaseous products, the system's equilibrium remains unchanged by pressure variations, as seen in exercise option (a).

Overall, understanding moles aids in conceptualizing how various factors like pressure can impact the balance of a chemical equation, especially for reactions occurring in a gaseous state.

Gaseous Reactions

Gaseous reactions are chemical reactions that involve substances in the gas phase. These reactions can be influenced by a variety of factors, including temperature, pressure, and concentration of reactants. Understanding how these factors affect gaseous reactions is critical for predicting how a reaction proceeds and reaches equilibrium.

In gaseous reactions, the ideal gas law \(PV=nRT\) can be a useful tool to relate pressure and volume. This relationship further explores the dynamics of how changes in pressure affect the behavior of gases involved in the reaction. Particularly, in the context of equilibrium, this relationship helps us understand why pressure changes influence some reactions but not others. If the number of moles of gas remains constant throughout the reaction, as demonstrated in reaction (a) of the exercise, then the equilibrium is not influenced by pressure variation.

An essential aspect of gaseous reactions is understanding how partial pressures of gases involved dictate the direction and extent of the reaction. Gaseous equilibrium can be shifted by altering conditions such as temperature and pressure, according to Le Chatelier's Principle. This leads us to the impact of Le Chatelier's Principle in understanding these equilibria in gaseous systems.

Le Chatelier's Principle

Le Chatelier's Principle is a key concept in understanding how systems at equilibrium respond to changes in conditions such as concentration, temperature, or pressure. The principle states that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium will shift to counteract the change, attempting to restore a new state of balance.

In the context of gaseous reactions, Le Chatelier's Principle helps to predict the direction in which the equilibrium will shift when pressure changes. When the number of moles of gases on one side differs from those on the other, increasing the pressure will shift the equilibrium towards the side with fewer moles of gas. Conversely, decreasing the pressure favors the side with more moles of gas. In reaction (a) of the exercise, since the number of moles on both sides of the reaction are equal, a change in pressure does not impact the position of equilibrium.

Understanding Le Chatelier’s Principle is crucial for predicting how reactions will behave under different conditions, which is particularly critical in industrial processes where controlling the equilibrium position can affect yield and efficiency.