Question

Will \(K_{\text {eq }}\) for an endothermic reaction increase or decrease when the reaction mixture is (a) heated and (b) cooled? Explain your answer.

Short answer

For an endothermic reaction, the equilibrium constant (\(K_{eq}\)) will increase when the reaction mixture is heated and decrease when the reaction mixture is cooled. This occurs because of the Le Chatelier's principle, as the system tries to counteract the changes in temperature by shifting the equilibrium towards the direction that absorbs or releases heat, affecting the \(K_{eq}\) value accordingly.

Step-by-step solution

(a) Effect of Heating on \(K_{eq}\) for an Endothermic Reaction)

To understand the effect of increasing temperature on an endothermic reaction, we need to consider the Le Chatelier's principle. This principle states that if a system at equilibrium is subjected to a change in concentration, temperature, or pressure, the equilibrium will shift to counteract the change and establish a new equilibrium. For an endothermic reaction, heat is absorbed from the surroundings. Therefore, if we increase the temperature, the system will try to counteract this change by shifting the equilibrium in the direction that absorbs more heat, i.e., in the forward direction. This shift in the forward direction will lead to an increase in the equilibrium constant, \(K_{eq}\). Hence, for an endothermic reaction, the equilibrium constant \(K_{eq}\) increases when the reaction mixture is heated.

(b) Effect of Cooling on \(K_{eq}\) for an Endothermic Reaction)

Now, let's analyze the effect of decreasing temperature on an endothermic reaction. As per Le Chatelier's principle, the system will try to counteract the change in temperature by shifting the equilibrium in the direction that releases heat. In the case of an endothermic reaction, cooling the reaction mixture corresponds to removing heat from the system. The equilibrium will shift towards the direction that releases heat to restore the balance, i.e., it will favor the reverse reaction. Consequently, the equilibrium constant \(K_{eq}\) will decrease when the reaction mixture is cooled. In summary, for an endothermic reaction, the equilibrium constant \(K_{eq}\) decreases when the reaction mixture is cooled.

Key concepts

Le Chatelier's Principle

When studying how reactions reach a state of balance, Le Chatelier's principle is a foundational concept that helps us predict how a system at equilibrium responds to external changes. Imagine a seesaw perfectly balanced. If you place extra weight on one side, the other rises. In chemical terms, when a dynamic equilibrium is disturbed by altering conditions such as concentration, pressure, or temperature, the system adjusts to regain equilibrium by favoring the forward or reverse reaction accordingly.

Considering concentration, if we add more reactants, the system will shift towards producing more products, and vice versa. If pressure is increased by reducing the volume of a gaseous system, the equilibrium shifts towards the side with fewer gas molecules. As for temperature, the direction depends on whether the reaction is endothermic (absorbing heat) or exothermic (releasing heat). For endothermic reactions, an increase in temperature will shift the equilibrium to the right, producing more products, while a decrease in temperature will shift it left, towards the reactants.

Endothermic Reactions

Chemical reactions that absorb energy from their surroundings, particularly in the form of heat, are known as endothermic reactions. These reactions essentially 'pull in' heat during the process, therefore raising the energy of the products in comparison to the reactants. To understand endothermic processes, picture absorbing warmth from a room: as this 'warmth'—thermal energy—is absorbed, the temperature of the room decreases. Similarly, in endothermic reactions, absorbing heat is a critical component of the reaction mechanism.

Common examples include photosynthesis, where plants absorb sunlight, or the process of melting ice, which requires heat from the environment. These reactions require continuous energy input to progress, aligning with the concept that energy is absorbed to break bonds in the reactants and form new ones in the products.

Effect of Temperature on Equilibrium

Temperature can play a significant role in determining the position of equilibrium in a reaction. According to Le Chatelier's principle, if the temperature of a system at equilibrium is changed, the system will adjust to minimize the effect of that change.

For endothermic reactions, where heat is a reactant, raising the temperature drives the equilibrium towards the products, effectively increasing the equilibrium constant (\( K_{eq} \)). This is because the added heat is being used up by the reaction, so the system 'shifts' to use more heat and form more products. Conversely, when the temperature is lowered, the system will shift towards the reactants to produce more heat, thereby reducing the equilibrium constant. Essentially, temperature increases favor the direction which absorbs heat, and temperature decreases favor the direction which releases heat.

Understanding the impact of temperature on equilibrium is crucial in various applications, such as industrial chemical synthesis and enzyme activity in biology, where precise control of reaction conditions can lead to optimal yields or biological activity.