Question

If two equilibrium reactions are added together, what is the relationship between the equilibrium constants for the individual reactions and that for the overall reaction?

Short answer

The equilibrium constant for the overall reaction is the product of the equilibrium constants for the individual reactions: \( K_3 = K_1 \times K_2 \).

Step-by-step solution

Understanding Equilibrium Constants

In a chemical equilibrium, the equilibrium constant, denoted as \( K \), is a number that expresses the ratio of the concentrations of products to reactants at equilibrium. It is a measure of the extent of a reaction and depends on temperature.

Consider Two Equilibrium Reactions

Let's consider two equilibrium reactions: Reaction 1 with equilibrium constant \( K_1 \) and Reaction 2 with equilibrium constant \( K_2 \). If these reactions are: 1. \( A ightleftharpoons B \) with \( K_1 \)2. \( C ightleftharpoons D \) with \( K_2 \)

Adding the Reactions

When two equilibrium reactions are added, their net reaction will have reactants and products that are a combination of initial and added reactions. Let's denote the overall reaction as the sum of Reaction 1 and Reaction 2.

Relationship of Equilibrium Constants

The equilibrium constant for the overall reaction can be derived by multiplying the equilibrium constants of the individual reactions. Therefore, if \( K_3 \) is the equilibrium constant for the overall reaction, then:\[ K_3 = K_1 imes K_2 \]

Conclusion of the Calculation

Thus, the equilibrium constant for the overall reaction obtained by adding two equilibrium reactions is the product of the equilibrium constants of the two individual reactions.

Key concepts

Chemical Equilibrium

Chemical equilibrium is a state in a chemical reaction where the concentrations of reactants and products remain constant over time. This occurs when the forward and reverse reactions proceed at the same rate, effectively becoming balanced. It's important to understand that equilibrium doesn't mean the reactants and products are present in equal amounts; instead, it means their concentrations stop changing. In this balanced state, reactions still occur, but there is no net change because the rate of the forward reaction equals the rate of the backward reaction. This balance forms a vital part of understanding how equilibrium constants function.

Reaction Products

The products of a chemical reaction are the substances formed as a result of the reaction. When considering equilibrium reactions, the focus is on the concentrations of these products as they settle into a stable balance with the reactants. The progression of reaction products at equilibrium is crucial since it determines the value of the equilibrium constant, which reflects the ratio of product concentrations to reactant concentrations at equilibrium. In the context of the given chemical equations, understanding the nature and amount of reaction products involves recognizing their role in establishing the equilibrium state. Gathering this information is key, particularly when calculating the overall equilibrium constant for combined reactions.

Reactant Concentrations

Reactant concentrations are a critical aspect of chemical equilibrium. At equilibrium, the concentration of reactants stops changing, just like the products, creating a dynamic balance. To calculate the equilibrium constant, one must take the concentrations of reactants into account, along with the products. The ratio of these concentrations will define the equilibrium state as depicted by the equilibrium constant. Understanding how reactant concentrations affect and are affected by the chemical equilibrium gives insight into the behavior of a reaction under different conditions. When combining two reactions, these initial concentrations play a crucial role in determining the constant for the net reaction, especially as they influence each segment of the reaction mechanism.

Temperature Dependence

Temperature plays a significant role in chemical equilibrium. The equilibrium constant, represented as \( K \), is temperature-dependent, meaning it can change if the temperature varies. A temperature change can shift the position of equilibrium and alter the concentrations of reactants and products. For instance, increasing the temperature generally favors the endothermic direction of a reaction, whereas decreasing it favors the exothermic direction. This sensitivity to temperature is crucial when calculating or predicting the equilibrium constant for reactions under different conditions. It's essential for students to note that the interpretation of equilibrium constants needs adjusting if the reactions are studied at different temperatures.