CEFET-PR Question 14 Chemical Equilibrium Explained

Introduction to Chemical Equilibrium

In the realm of chemistry, chemical equilibrium holds a pivotal position, governing the extent to which reactions proceed and the composition of the final mixture. This concept is particularly crucial in various industrial processes, as it dictates the yield of desired products. To grasp the intricacies of chemical equilibrium, let's delve into a classic problem encountered in the CEFET-PR examination, question 14. This problem serves as an excellent springboard to explore the fundamental principles and calculations associated with equilibrium constants.

The CEFET-PR question 14 presents a scenario involving the reaction between carbon monoxide (CO) and nitrogen dioxide (NO₂), two gaseous pollutants, to form carbon dioxide (CO₂) and nitric oxide (NO). This reaction, represented by the equation CO(g) + NO₂(g) ⇌ CO₂(g) + NO(g), provides a tangible context to understand the dynamic nature of equilibrium. Equilibrium is not a static state where reactions cease; rather, it's a dynamic balance where the rates of the forward and reverse reactions are equal. This means that while CO and NO₂ are reacting to form CO₂ and NO, the reverse reaction is also occurring, converting CO₂ and NO back into CO and NO₂.

The question introduces a specific scenario: two moles of CO(g) react with two moles of NO₂(g) in a closed system. As the reaction progresses, the concentrations of reactants (CO and NO₂) decrease, while the concentrations of products (CO₂ and NO) increase. The system eventually reaches a state of equilibrium, where the rates of the forward and reverse reactions equalize. The problem states that at equilibrium, 3/4 of each of the reactants has been transformed into products. This information is critical for calculating the equilibrium constant, a numerical value that quantifies the relative amounts of reactants and products at equilibrium. The equilibrium constant (K) provides valuable insights into the extent to which a reaction proceeds to completion.

Determining the Equilibrium Constant (K)

The core of the CEFET-PR question 14 lies in determining the equilibrium constant (K) for the reaction. The equilibrium constant is a fundamental concept in chemistry that provides a quantitative measure of the relative amounts of reactants and products at equilibrium. It is defined as the ratio of the product of the equilibrium concentrations of the products to the product of the equilibrium concentrations of the reactants, each raised to the power of its stoichiometric coefficient in the balanced chemical equation. For the reaction CO(g) + NO₂(g) ⇌ CO₂(g) + NO(g), the equilibrium constant (K) is expressed as:

K = ([CO₂][NO]) / ([CO][NO₂])

Where the square brackets denote the molar concentrations of the respective species at equilibrium. To calculate K, we need to determine the equilibrium concentrations of all the reactants and products. The problem provides us with the initial amounts of reactants (2 moles each of CO and NO₂) and the fraction of reactants converted to products at equilibrium (3/4). We can use this information to construct an ICE (Initial, Change, Equilibrium) table, a common tool for solving equilibrium problems. The ICE table helps us track the changes in concentrations of reactants and products as the reaction reaches equilibrium.

Let's construct the ICE table for the reaction:

Here, 'x' represents the change in concentration of reactants and products as the reaction proceeds towards equilibrium. Since 3/4 of each reactant is transformed into products, the change in concentration (x) can be calculated as (3/4) * 2 moles = 1.5 moles. Therefore, at equilibrium, the concentrations are:

• [CO] = 2 - 1.5 = 0.5 moles
• [NO₂] = 2 - 1.5 = 0.5 moles
• [CO₂] = 1.5 moles
• [NO] = 1.5 moles

Now, we can substitute these equilibrium concentrations into the expression for K:

K = (1. 5 * 1.5) / (0.5 * 0.5) = 9

Thus, the equilibrium constant (K) for the reaction is 9. This value indicates that at equilibrium, the products (CO₂ and NO) are significantly favored over the reactants (CO and NO₂). A large value of K suggests that the reaction proceeds to a greater extent towards completion.

Implications of the Equilibrium Constant

The equilibrium constant (K) provides valuable insights into the extent to which a reaction proceeds to completion and the relative amounts of reactants and products present at equilibrium. A large value of K (K >> 1) indicates that the equilibrium lies to the right, favoring the formation of products. Conversely, a small value of K (K << 1) indicates that the equilibrium lies to the left, favoring the reactants. A value of K close to 1 suggests that the concentrations of reactants and products at equilibrium are comparable.

In the case of the CEFET-PR question 14, the calculated equilibrium constant (K) of 9 is significantly greater than 1. This implies that at equilibrium, the concentrations of the products (CO₂ and NO) are much higher than the concentrations of the reactants (CO and NO₂). In other words, the reaction proceeds extensively towards the formation of products. This information can be crucial in various applications, such as industrial processes where maximizing product yield is essential.

The equilibrium constant is also temperature-dependent. The value of K changes with temperature, reflecting the shift in equilibrium position as the temperature changes. Le Chatelier's principle provides a qualitative explanation for the effect of temperature on equilibrium. It states that if a change of condition (such as temperature, pressure, or concentration) is applied to a system in equilibrium, the system will shift in a direction that relieves the stress. For an endothermic reaction (heat is absorbed), increasing the temperature favors the forward reaction, leading to a higher K value. Conversely, for an exothermic reaction (heat is released), increasing the temperature favors the reverse reaction, resulting in a lower K value.

Le Chatelier's Principle and Equilibrium Shifts

Beyond the numerical value of the equilibrium constant, it's crucial to understand the factors that can influence the position of equilibrium. Le Chatelier's principle is a cornerstone concept that helps predict how a system at equilibrium will respond to changes in conditions. As mentioned earlier, Le Chatelier's principle states that if a change of condition is applied to a system in equilibrium, the system will shift in a direction that relieves the stress. These changes in conditions can include:

1. Changes in Concentration: Adding reactants or products will shift the equilibrium to consume the added substance. Removing reactants or products will shift the equilibrium to replenish the removed substance.
2. Changes in Pressure: For gaseous reactions, increasing the pressure will shift the equilibrium towards the side with fewer moles of gas. Decreasing the pressure will shift the equilibrium towards the side with more moles of gas.
3. Changes in Temperature: As discussed earlier, increasing the temperature will favor the endothermic reaction, while decreasing the temperature will favor the exothermic reaction.

In the context of the reaction CO(g) + NO₂(g) ⇌ CO₂(g) + NO(g), let's consider the effect of adding more CO(g) to the system at equilibrium. According to Le Chatelier's principle, the system will shift to relieve the stress of increased CO concentration. This means the equilibrium will shift to the right, favoring the forward reaction and consuming the added CO. As a result, more CO₂(g) and NO(g) will be formed, and the concentrations of NO₂(g) will decrease until a new equilibrium is established.

Similarly, if we were to remove CO₂(g) from the system, the equilibrium would shift to the right to replenish the removed CO₂(g). This would lead to a decrease in the concentrations of CO(g) and NO₂(g) and an increase in the concentration of NO(g).

Understanding Le Chatelier's principle allows us to manipulate reaction conditions to maximize the yield of desired products in chemical processes. For example, in the Haber-Bosch process, the industrial synthesis of ammonia (NH₃), high pressure and moderate temperature are used to favor the formation of ammonia from nitrogen and hydrogen gases. The reaction is exothermic, so lower temperatures favor product formation, but the reaction rate is slow at low temperatures. A moderate temperature is used to achieve a reasonable rate while still favoring product formation. High pressure favors the side with fewer moles of gas (the product side), further increasing the yield of ammonia.

Conclusion

The CEFET-PR question 14 provides a comprehensive illustration of the principles of chemical equilibrium. By understanding the concepts of equilibrium constant, ICE tables, and Le Chatelier's principle, we can analyze and predict the behavior of chemical reactions at equilibrium. The equilibrium constant (K) quantifies the relative amounts of reactants and products at equilibrium, while Le Chatelier's principle helps us understand how changes in conditions can shift the equilibrium position. These concepts are fundamental to various fields, including chemistry, chemical engineering, and environmental science. Mastery of these principles is essential for solving complex chemical problems and optimizing chemical processes.

The ability to calculate and interpret equilibrium constants is crucial in various applications, such as designing industrial processes, predicting reaction yields, and understanding environmental chemistry. For instance, in the design of a chemical reactor, engineers need to consider the equilibrium constant to determine the optimal conditions for maximizing product formation. In environmental chemistry, equilibrium principles are used to understand the distribution of pollutants in the environment and to design remediation strategies. By mastering the principles of chemical equilibrium, we gain a powerful tool for understanding and manipulating chemical reactions, ultimately contributing to advancements in various fields.