Question

The equilibrium constant for the reaction \(\mathrm{Br}_{2} \rightleftharpoons\) \(2 \mathrm{Br}\) at \(500 \mathrm{~K}\) and \(700 \mathrm{~K}\) are \(1 \times 10^{\circ}\) and \(1 \times 10^{5}\), respectively. The reaction is (1) endothermic (2) exothermic (3) fast (4) slow

Short answer

Endothermic

Step-by-step solution

- Understanding Equilibrium Constant

The equilibrium constant, represented as Keq, indicates the ratio of the concentration of products to reactants at equilibrium. A large Keq means the reaction favors the formation of products, while a small Keq indicates the reactants are favored.

- Analyzing Keq at Different Temperatures

Compare the given equilibrium constants at the two temperatures: At 500 K, Keq = 1 (small value), while at 700 K, Keq = 10^5 (very large value). This means that as the temperature increases, the equilibrium shifts strongly towards the products.

- Determining Reaction Type with Temperature Change

For a reaction where the value of Keq increases with temperature, the reaction is endothermic. This is because adding heat to an endothermic reaction drives the equilibrium towards the product side, increasing Keq.

- Conclusion

Based on the changes in the equilibrium constant with temperature, the reaction must be endothermic. Therefore, the correct choice is (1) endothermic.

Key concepts

Endothermic Reactions

Endothermic reactions absorb heat from their surroundings. This means that heat is a reactant in these chemical processes. When an endothermic reaction occurs, you will notice a drop in temperature around the reaction area because the system is taking in heat.
Some common examples of endothermic reactions include:

• Photosynthesis: Plants absorb energy from sunlight to convert carbon dioxide and water into glucose and oxygen.
• Melting ice: Heat is absorbed from the surroundings to convert ice into water.

Understanding the concept of endothermic reactions is crucial for solving problems related to equilibrium and temperature changes, which we will discuss in the subsequent sections.

Temperature Effect on Equilibrium

The temperature influences the direction in which a chemical reaction proceeds. According to Le Chatelier's Principle, if you change the conditions of a system at equilibrium, the system will adjust to counteract that change.
For endothermic reactions:

• Increasing the temperature adds heat to the system, which shifts the equilibrium towards the products. This results in a higher equilibrium constant (Keq).
• Conversely, decreasing the temperature removes heat, shifting the equilibrium toward the reactants and resulting in a lower Keq.

In our example, the equilibrium constant for the reaction increases significantly from 1 at 500 K to 10^5 at 700 K. This tells us that the reaction absorbs heat as it goes from reactants to products, confirming it is an endothermic process.

Reaction Dynamics

Reaction dynamics explore how fast or slow a reaction occurs and how the conditions affect this rate. The dynamics cover crucial aspects like activation energy and the role of catalysts.
Factors affecting reaction dynamics include:

• Temperature: Higher temperatures generally increase reaction rates by providing the energy needed to overcome the activation barrier.
• Catalysts: These substances lower the activation energy, allowing the reaction to proceed faster without being consumed in the process.
• Concentration: Higher concentrations of reactants increase the frequency of collisions, leading to a faster reaction rate.

In the context of our equilibrium problem, while we haven't discussed the speed explicitly, the change in equilibrium constant with temperature gives insight into how endothermic reactions respond to thermal energy, which is a key part of reaction dynamics.