Question

How do the following changes affect the value of the equilibrium constant for a gas-phase exothermic reaction: (a) removal of a reactant (b) removal of a product, (c) decrease in the volume, (d) decrease in the temperature, (e) addition of a catalyst?

Short answer

In summary, for a gas-phase exothermic reaction, the value of the equilibrium constant (K) is affected only by changes in temperature. A decrease in temperature will result in a decrease of the equilibrium constant value. The removal or addition of reactants, products, or catalysts, and changes in volume do not affect the equilibrium constant value.

Step-by-step solution

1. Understanding the equilibrium constant

The equilibrium constant (K) is a value that is related to the rate constants for the forward and reverse reactions in a chemical system at equilibrium. It is calculated as the ratio of the product concentrations to the reactant concentrations, with each concentration raised to the power of its respective coefficient in the balanced chemical equation. For a general exothermic reaction, represented as: \(aA + bB \rightleftharpoons cC + dD \) The equilibrium constant is given by: \(K = \frac{[C]^c[D]^d}{[A]^a[B]^b}\) Now, let's see how the different changes in the system affect the equilibrium constant.

2. Effect of removal of a reactant (a)

Removing a reactant will decrease its concentration in the system. According to Le Chatelier's principle, the system will shift to counteract the disturbance and restore the equilibrium. In this case, the system will shift towards the reactants to increase the concentration of the removed reactant. However, the equilibrium constant value remains unaffected as it is only dependent on the temperature of the system.

3. Effect of removal of a product (b)

Similarly, removing a product will decrease its concentration in the system. Again, according to Le Chatelier's principle, the system will shift to counteract the disturbance. In this case, the system will shift towards the products to increase the concentration of the removed product. The equilibrium constant value remains unaffected as it depends only on the temperature.

4. Effect of decrease in volume (c)

A decrease in volume will increase the pressure of the system. According to Le Chatelier's principle, the system will respond by shifting in the direction that reduces pressure. In this case, it will shift towards the side with fewer moles of gas. However, the equilibrium constant value remains unaffected as it depends only on the temperature.

5. Effect of decrease in temperature (d)

Since the reaction is exothermic, a decrease in temperature will favor the forward reaction, as it releases heat to the surroundings. As a result, the equilibrium will shift towards the products. This change in temperature will affect the equilibrium constant value. In this case, decreasing the temperature will cause the equilibrium constant value to decrease as well.

6. Effect of addition of a catalyst (e)

Adding a catalyst to the system will increase the rate of both the forward and reverse reactions without affecting the equilibrium concentrations of the reactants or products. As a result, the system will reach equilibrium more quickly, but the equilibrium constant value will remain unaffected. In summary, the value of the equilibrium constant for a gas-phase exothermic reaction is only affected by changes in temperature (decreasing temperature will decrease the equilibrium constant). Removal or addition of reactants, products, or catalysts, and changes in volume do not affect the equilibrium constant value.

Key concepts

Le Chatelier's Principle

Le Chatelier's Principle is a fundamental concept in chemistry that helps us predict how a system at equilibrium will respond to external changes. When a system at equilibrium experiences a change in concentration, temperature, or pressure, it will adjust itself to counteract that change and restore a new equilibrium. This principle is essential for understanding the behavior of reactions under different conditions.

When the concentration of reactants or products changes, the system shifts to either produce or consume the substances that mitigate the change. For instance:

• If a reactant is removed, the equilibrium will shift to the left, favoring the formation of reactants.
• If a product is taken away, the equilibrium position shifts towards forming more products.
• Pressure changes often result in the system shifting towards the side with fewer gas moles.

Overall, Le Chatelier's Principle allows chemists to predict how a reaction will behave when subjected to different environmental changes, making it an invaluable tool in chemical synthesis and industrial applications.

Exothermic Reactions

Exothermic reactions are reactions that release energy to the surroundings, usually in the form of heat. A classic example is the combustion of fuel, which releases heat energy as it reacts with oxygen. Understanding exothermic reactions is crucial in predicting how temperature changes affect chemical equilibrium.

In the context of equilibrium:

• When heat is removed from an exothermic reaction (decreasing temperature), the system favors the forward reaction, shifting the equilibrium towards the formation of more products.
• Conversely, increasing the temperature will add heat to the system, often causing the equilibrium to shift towards the reactants to absorb the extra energy.

These responses align with Le Chatelier's Principle, further illustrating the dynamic nature of chemical equilibria and providing insight into the optimal conditions needed to maximize product yield in industrial processes.

Equilibrium Constant

The equilibrium constant (K) provides a quantitative measure of the position of equilibrium for a given reaction at a specific temperature. It is determined by the ratio of the concentrations of products to reactants, each raised to the power of their respective stoichiometric coefficients.

The formula for a generic reaction is:
\[ K = \frac{[C]^c[D]^d}{[A]^a[B]^b} \]
Here, K stays constant for a given reaction at a specific temperature and indicates the extent to which products are favored over reactants. It's vital to note that changes in reactant or product concentrations, volume, or the addition of a catalyst do not affect the value of K.

However, changes in temperature do affect K, particularly in exothermic and endothermic reactions. For an exothermic reaction, decreasing temperature decreases K, while increasing temperature results in a higher equilibrium constant, reflecting the system's shift in equilibrium.

Effect of Temperature on Equilibrium

Temperature has a significant impact on the equilibrium position and equilibrium constant of a reaction. This is closely related to whether a reaction is exothermic or endothermic.

For exothermic reactions:

• Lowering the temperature shifts the equilibrium towards the products, as the system releases heat.
• This shift results in a lower equilibrium constant since the forward reaction is favored.

For endothermic reactions:

• Raising the temperature favors the forward reaction because it absorbs heat, increasing the equilibrium constant.

Understanding the effect of temperature is crucial for controlling reaction outcomes, especially in chemical manufacturing, where maximizing efficiency and yield is essential.

Catalysts in Chemical Reactions

Catalysts are substances that speed up the rate of a chemical reaction without being consumed in the process. They work by lowering the activation energy, which allows the reaction to proceed faster. While catalysts can significantly enhance reaction rates, they do not affect the equilibrium concentrations of reactants or products.

Key points about catalysts include:

• They do not change the equilibrium position or the equilibrium constant of a reaction.
• Catalysts allow a system to reach equilibrium faster, which is beneficial in industrial reactions where time efficiency is critical.
• They provide alternative pathways for reactions, which can be crucial in processes requiring high specificity and efficiency.

In summary, while catalysts are invaluable for improving the speed and feasibility of reactions, they do not alter the fundamental characteristics of the equilibrium state of a chemical system.