Question

The reaction \(3 \mathrm{O}_{2}(g) \rightleftarrows 2 \mathrm{O}_{3}(g)\) has \(\Delta H=\) \(+285 \mathrm{~kJ} / \mathrm{mol}\). Does the equilibrium constant for the reaction increase or decrease when the temperature increases?

Short answer

The equilibrium constant increases when the temperature increases.

Step-by-step solution

Identify the Reaction Type

The reaction given is \(3 \mathrm{O}_2(g) \rightleftarrows 2 \mathrm{O}_3(g)\) with a \(\Delta H = +285\mathrm{~kJ/mol}\). A positive \(\Delta H\) indicates that the reaction is endothermic.

Understand Le Chatelier's Principle

According to Le Chatelier's Principle, if a reaction is endothermic (absorbs heat), increasing the temperature will favor the forward reaction. This is because the system will try to counteract the change by absorbing the additional heat.

Relate Temperature Change to Equilibrium Constant

For an endothermic reaction, increasing the temperature will shift the equilibrium position towards the products, which means more products are formed. As a result, the equilibrium constant \(K\), which depends on the ratio of product concentration to reactant concentration, increases.

Conclusion Based on Le Chatelier's Principle

Since increasing the temperature shifts the equilibrium towards more product formation, the equilibrium constant \(K\) increases for the reaction \(3 \mathrm{O}_2(g) \rightleftarrows 2 \mathrm{O}_3(g)\).

Key concepts

Endothermic Reaction

An endothermic reaction is characterized by its absorption of heat from the surrounding environment. This type of reaction requires energy input to proceed, resulting in a positive enthalpy change (\( \Delta H > 0 \)). A common example of this is the photochemical formation of ozone from oxygen, as indicated by the reaction:

• \(3\mathrm{O}_2(g) \rightleftarrows 2\mathrm{O}_3(g)\) with \( \Delta H = +285 \text{ kJ/mol} \).

This example illustrates that energy, in the form of heat, is a necessary component to drive the reaction forward, allowing further conversion of reactants into products. Through this absorption of energy, endothermic reactions are often sensitive to temperature changes, which can influence their direction and extent significantly.
Understanding these processes can help predict the behavior of such reactions under different conditions, making them crucial in fields like chemistry and environmental science.

Equilibrium Constant

The equilibrium constant, often denoted as \( K \), is a fundamental concept in chemical equilibrium, representing the ratio of the concentration of the products to the concentration of the reactants when a reaction has reached equilibrium. For a general reaction of the type:

• \( aA + bB \rightleftharpoons cC + dD \)

The equilibrium constant expression is \\[ K = \frac{{[C]^c[D]^d}}{{[A]^a[B]^b}} \]\This numeric value provides insight into the position of equilibrium; if \( K \) is large, the equilibrium lies to the right, favoring product formation. Conversely, a small \( K \) implies a reaction that favors reactants.
In the context of endothermic reactions, any shifts towards product formation, such as those caused by temperature changes, will result in an increase in the value of \( K \). Thus, understanding \( K \) offers predictive insights on how various conditions, such as temperature or pressure, might affect the extent to which a reaction proceeds.

Temperature Effect on Equilibrium

Temperature plays a pivotal role in shifting the equilibrium of a chemical reaction. According to Le Chatelier's Principle, if an external condition changes, such as temperature, the equilibrium will adjust to minimize that change. When temperature increases, an endothermic reaction will shift toward the formation of products to absorb the excess heat, as the equilibrium position remains dynamic. Therefore, you can expect the value of the equilibrium constant \( K \) to increase under such conditions.
For the specific reaction \( 3\mathrm{O}_2(g) \rightleftharrows 2\mathrm{O}_3(g) \), raising temperature favors the forward direction, thereby increasing the concentration of \( \mathrm{O}_3 \) compared to \( \mathrm{O}_2 \). As more \( \mathrm{O}_3 \) is formed, the equilibrium constant \( K \) rises, indicating a stronger preference for products over reactants. Thus, comprehending temperature's effect affords better control over chemical reactions, particularly in industrial applications where specific product yields need optimization.