Problem 6 - Chemistry in 30 days

Question

Which one of the following at equilibrium, with all reactants and products in the gaseous phase is unaffected by an increase in pressure? (a) \(\mathrm{PCl}_{5}=\mathrm{PCl}_{3}+\mathrm{Cl}_{2}\) (b) \(2 \mathrm{O}_{3} \rightleftharpoons 3 \mathrm{O}_{2}\) (c) \(\mathrm{H}_{2}+\mathrm{I}_{2} \rightleftharpoons 2 \mathrm{HI}\) (d) \(\mathrm{N}_{2} \mathrm{O}_{4} \rightleftharpoons 2 \mathrm{NO}_{3}\)

Step-by-Step Solution

Answer

Reaction (c) is unaffected by an increase in pressure.

Step 1: Understand Le Chatelier's Principle

Le Chatelier's Principle states that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium moves to counteract the change. In the case of pressure changes, the equilibrium will shift to favor the side with fewer moles of gas if pressure is increased.

Step 2: Analyze Reaction (a)

The reaction is \( \mathrm{PCl}_{5} \rightarrow \mathrm{PCl}_{3} + \mathrm{Cl}_{2} \). There is 1 mole of gas on the reactant side and 2 moles of gas on the product side. An increase in pressure will shift the equilibrium to the left, favoring fewer moles.

Step 3: Analyze Reaction (b)

The reaction is \( 2 \mathrm{O}_{3} \rightleftharpoons 3 \mathrm{O}_{2} \). There are 2 moles of gas on the reactant side and 3 moles on the product side. An increase in pressure will shift the equilibrium to the left, toward fewer moles of gas.

Step 4: Analyze Reaction (c)

The reaction is \( \mathrm{H}_{2} + \mathrm{I}_{2} \rightleftharpoons 2 \mathrm{HI} \). There are 2 moles of gas on the left and 2 moles of gas on the right. Since the moles of gas are equal on both sides, the equilibrium is unaffected by changes in pressure.

Step 5: Analyze Reaction (d)

The reaction is \( \mathrm{N}_{2} \mathrm{O}_{4} \rightleftharpoons 2 \mathrm{NO}_{3} \). There is 1 mole of gas on the reactant side and 2 moles of gas on the product side. An increase in pressure will shift the equilibrium to the left.

Key Concepts

Equilibrium

In chemistry, equilibrium refers to the state where the concentrations of reactants and products do not change over time. At this point, the rates of the forward and reverse reactions are equal. When a system is at equilibrium, it does not mean the amounts of reactants and products are equal, but rather that their ratios remain constant.

Equilibrium is dynamic, meaning that even though there appears to be no change, reactions are still occurring on a molecular level. This fine balance can be influenced by changes in temperature, concentration, and pressure, leading to a shift in the position of equilibrium according to Le Chatelier's Principle.

Knowing how to calculate and interpret the equilibrium constant (K_eq) can give insight into the position of the equilibrium. When we say a reaction "lies to the right," it indicates a higher concentration of products relative to reactants, and vice versa when it "lies to the left." This balance is crucial in processes like ammonia synthesis, the human respiratory system, and even oceans' buffering systems.

Pressure Change

Pressure changes in a gaseous system can have a profound effect on the position of equilibrium. According to Le Chatelier's Principle, increasing the pressure of a system at equilibrium will favor the side of the reaction with fewer moles of gas, while decreasing the pressure will favor the side with more moles of gas.

This principle can be understood by imagining gas molecules as tiny particles inside a container. Increasing pressure means the particles have less space to move, encouraging the reaction to proceed in the direction that reduces the number of gas molecules, thus alleviating some pressure.

For example:

• If in a reaction you have 1 mole of gas turning into 3 moles of gas, increasing pressure will favor the reverse reaction so the system can move towards 1 mole of gas.
• Similarly, if there are equal moles of gas on both sides, like \( ext{H}_2 + ext{I}_2 ightleftharpoons 2 ext{HI} \), pressure changes will not affect equilibrium since both sides are equally balanced.

Understanding how pressure influences equilibrium helps in industrial applications, where conditions are adjusted to maximize product yield.

Gaseous Reactions

Gaseous reactions are chemical reactions in which the reactants and products are in the gas phase. They are characterized by their dependence on conditions such as temperature, pressure, and volume due to the variable nature of gases.

These reactions often follow the ideal gas law, expressed as \( PV = nRT \), where \( P \) is pressure, \( V \) is volume, \( n \) is moles, \( R \) is the gas constant, and \( T \) is temperature. Changes in these conditions can significantly impact how a gaseous reaction progresses.

Considering gaseous reactions in equilibrium:

• The ratio of the moles of reactants to products can influence how these reactions react to changes in conditions such as pressure.
• The reaction \( ext{N}_2 ext{O}_4 ightleftharpoons 2 ext{NO}_3 \) is heavily influenced by pressure as changing it shifts equilibrium to reduce the overall \( n \), or moles of gas.

This aspect of gases means that understanding their properties can be crucial in both laboratory and industrial settings to control and optimize reactions.