Question

Does the value of the equilibrium constant increase or decrease when the temperature of each of the following equilibrium systems is decreased? (a) \(\mathrm{PCl}_{5}(g) \rightleftharpoons \mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g)\) endothermic (b) \(2 \mathrm{O}_{3}(g) \rightleftharpoons 3 \mathrm{O}_{2}(g)\) exothermic

Short answer

For the endothermic reaction, the equilibrium constant decreases when the temperature is decreased. For the exothermic reaction, the equilibrium constant increases when the temperature is decreased.

Step-by-step solution

Examine the Endothermic Reaction

Consider the endothermic reaction: \(\mathrm{PCl}_{5}(g) \rightleftharpoons \mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g)\). In this reaction, heat is absorbed, meaning we can rewrite this as \(\mathrm{PCl}_{5}(g) + heat \rightleftharpoons \mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g)\). If the temperature is decreased, according to Le Chatelier's Principle, the equilibrium will shift to the left to offset the change, meaning the reaction will favor the reactants. This will cause a decrease in the value of the equilibrium constant (K).

Examine the Exothermic Reaction

Consider the exothermic reaction: \(2 \mathrm{O}_{3}(g) \rightleftharpoons 3 \mathrm{O}_{2}(g)\). In this reaction, heat is released, so we can rewrite this as \(2 \mathrm{O}_{3}(g) \rightleftharpoons 3 \mathrm{O}_{2}(g) + heat\). If the temperature is decreased, that's equivalent to removing heat. According to Le Chatelier's Principle, the equilibrium will shift to the right in attempt to produce more heat, favoring the products. This will cause an increase in the value of the equilibrium constant (K).

Key concepts

Le Chatelier's Principle

Le Chatelier's Principle is a way to predict how a chemical equilibrium will shift to respond to changes. It states that if a dynamic equilibrium is disturbed, the system will adjust to minimize the disturbance and return to a state of equilibrium. This principle is useful in understanding how changes in concentration, pressure, and temperature affect equilibrium systems.

When we apply Le Chatelier's Principle to temperature changes:

• In an endothermic reaction, heat acts as a reactant. If you decrease the temperature, the system will try to produce more heat, shifting the equilibrium towards the reactants.
• In an exothermic reaction, heat is a product. If you lower the temperature, the system compensates by generating more heat, shifting the equilibrium towards the products.

It's like a balance scale of chemical reactions, adjusting to maintain a steady internal environment.

Endothermic and Exothermic Reactions

Chemical reactions are classified into two types based on heat changes: endothermic and exothermic reactions. These terms help us understand how reactions absorb or release heat during the process.

**Endothermic Reactions**:

• Endothermic reactions absorb heat from their surroundings.
• An example is the reaction \( \mathrm{PCl}_{5}(g) \rightleftharpoons \mathrm{PCl}_{3}(g) + \mathrm{Cl}_{2}(g) \).
• In this reaction, heat is absorbed to form the products, making heat a reactant.

**Exothermic Reactions**:

• Exothermic reactions release heat into their surroundings.
• For example, the reaction \( 2 \mathrm{O}_{3}(g) \rightleftharpoons 3 \mathrm{O}_{2}(g) \) releases heat.
• In this case, heat is considered a product of the reaction.

This heat exchange is crucial to understanding how equilibrium is affected by temperature changes.

Temperature Effect on Equilibrium

The effect of temperature on an equilibrium system is significant, as it can change the position of the equilibrium and alter the equilibrium constant, denoted as \( K \). When the temperature of a reaction is changed, it disrupts the equilibrium balance, prompting the system to readjust according to Le Chatelier's Principle.

**Decreasing Temperature**:

• For endothermic reactions, decreasing temperature shifts the equilibrium towards the reactants, lowering \( K \).
• For exothermic reactions, it shifts towards the products, increasing \( K \).

This means:

• For an endothermic reaction, lower heat makes the system respond by absorbing more heat, which often involves shifting back towards the reactants.
• For an exothermic reaction, reducing heat encourages the system to release more heat as compensation, shifting towards the products.

The interplay of temperature and equilibrium highlights why understanding reaction types is vital in predicting the effects of temperature changes.