Problem 70 - Chemistry The Central Science

Question

True or false: When the temperature of an exothermic reaction increases, the rate constant of the forward reaction decreases, which leads to a decrease in the equilibrium constant, \(K_{c} .\)

Step-by-Step Solution

Answer

False. When the temperature of an exothermic reaction increases, the rate constant of the forward reaction actually increases, not decreases, as described by the Arrhenius equation. However, the equilibrium constant, \(K_{c}\), does indeed decrease due to the shift in equilibrium towards reactants.

Step 1: Recall the Definitions

An exothermic reaction is one that releases heat. The forward reaction corresponds to the scenario where reactants are being converted into products. The rate constant of the forward reaction is a measure of how fast the reaction proceeds. The equilibrium constant, \(K_{c}\), is a measure of the relative concentration of products and reactants at equilibrium.

Step 2: Review Le Chatelier's Principle

Le Chatelier's principle states that if a system at equilibrium is subjected to a change in temperature, pressure, or concentration of reactants and products, the system will adjust its position to counteract the change and re-establish equilibrium. For an exothermic reaction, an increase in temperature shifts the equilibrium position to favor the reactants (backward reaction) since the reaction is generating heat. Conversely, a decrease in temperature will shift the equilibrium position to favor the products (forward reaction).

Step 3: Examine the Rate Constant

The dependence of the rate constant on temperature can be described by the Arrhenius equation: \(k = Ae^{-\frac{E_{a}}{RT}}\) Here, k is the rate constant, A is the pre-exponential factor, \(E_{a}\) is the activation energy, R is the gas constant, and T is the temperature in Kelvin. When the temperature increases, the value of \(\frac{E_{a}}{RT}\) decreases, and therefore the exponent becomes less negative. As the exponent becomes less negative, the rate constant (k) increases. For an exothermic reaction, an increase in temperature causes an increase in the rate constant of the forward reaction, contrary to what the statement claims.

Step 4: Evaluate the Equilibrium Constant

When the temperature of an exothermic reaction increases, the equilibrium shifts towards the reactants (reverse direction). The increase in the concentration of reactants and decrease in the concentration of products will ultimately result in a decrease in the equilibrium constant, \(K_{c}\). This part of the statement is correct.

Step 5: Final Verdict

Since the increase in temperature causes an increase, not a decrease, in the rate constant for the forward reaction, the statement is false in that regard. However, the temperature increase does indeed cause a decrease in the equilibrium constant, \(K_{c}\). Therefore, the statement as a whole is false.

Key Concepts

Exothermic Reaction

An exothermic reaction is a chemical process in which energy is released to the surroundings in the form of heat. This type of reaction is characterized by a net release of energy, meaning that the energy needed to break the bonds in the reactants is less than the energy released when new bonds form in the products. Common examples of exothermic reactions include combustion, such as a burning candle, or the reaction between quicklime and water.

Understanding the energy changes in exothermic reactions is crucial because they often influence how the reaction is carried out. For instance, in industrial processes, exothermic reactions can sometimes release enough heat to sustain the reaction without additional energy input. This can have implications for the safety and cost-efficiency of the process. Moreover, in the context of equilibrium, the heat released in an exothermic reaction is considered a product. Thus, according to Le Chatelier's principle, increasing the temperature will shift the equilibrium position towards the reactants, which is essential in predicting the behavior of these reactions under varying thermal conditions.

Le Chatelier's Principle

Le Chatelier's principle is a fundamental concept in chemistry, which shows how a system at equilibrium responds to disturbances. It can be used to predict the effect of changes in temperature, pressure, or concentration on the position of equilibrium. If a system at equilibrium experiences an increase in temperature, this principle suggests that the equilibrium position will shift in the direction that absorbs heat.

Implications for Temperature Changes in Reactions

For exothermic reactions, an increase in temperature will favor the formation of reactants, while a decrease will favor the formation of products. This response is the system's way of minimizing the disturbance, thereby adhering to Le Chatelier's principle. Consequently, this principle allows chemists to manipulate the conditions to favor the formation of desired products in both industrial applications and in the laboratory.

Arrhenius Equation

The Arrhenius equation mathematically describes the temperature dependence of reaction rates. It shows that the rate constant (k) increases exponentially with an increase in temperature. The equation incorporates the activation energy (\(E_{a}\)), which is the minimum amount of energy required for a reaction to occur.

The Arrhenius equation is stated as:
\[k = Ae^{-\frac{E_{a}}{RT}}\]
In this equation, A represents the frequency factor, which correlates with the frequency of collisions with proper orientation, and R is the universal gas constant.

When the temperature (T) rises, the factor \( -\frac{E_{a}}{RT} \) decreases, leading to an increase in the rate constant (k). This has a significant impact on the kinetics of chemical reactions and is pivotal for understanding why reactions speed up with higher temperatures. The implications of the Arrhenius equation on equilibria are profound, especially in the context of exothermic reactions, where the predicted increase in rate constant with temperature contradicts the false statement in the exercise under review.