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The concept of the equilibrium constant encapsulates the balance in reversible reactions. It describes the ratio of the concentrations of products to reactants at equilibrium, each raised to the power of their respective coefficients in the balanced equation. For a general reaction:\[aA + bB \rightleftharpoons cC + dD\]The equilibrium constant, denoted as \( K \), is defined as:\[K = \frac{[C]^c [D]^d}{[A]^a [B]^b}\]Understanding the equilibrium constant is essential because:

• It provides insight into the position of equilibrium—whether products or reactants are favored.
• The magnitude of \( K \) tells us about the extent of the reaction at equilibrium.

When \( K > 1 \), the products are predominant; when \( K < 1 \), reactants are predominant at equilibrium. In our specific problem, manipulating the equilibrium constants \( K_1 \) and \( K_2 \) helps derive the equilibrium constant for the desired reaction.

Manipulating reactions to obtain a desired reaction is a powerful tool in chemistry. By reversing or combining given reactions, we can derive new reactions and calculate the corresponding equilibrium constants. Key aspects of reaction manipulation include:- **Reversing a Reaction:** When a reaction is reversed, the equilibrium constant becomes its reciprocal. For instance, if a forward reaction has an equilibrium constant \( K \), reversing it results in: \[ \frac{1}{K} \]- **Combining Reactions:** When reactions are added together, their equilibrium constants are multiplied. This is crucial when you need to construct a new reaction from known ones, as seen in the exercise.In the exercise, two reactions are given. The manipulation involves reversing one reaction and keeping the other to find a new equilibrium constant.

Reversible reactions are chemical processes where the reactants form products, which can then react to form the original reactants. This back-and-forth nature means that these reactions can reach a state of equilibrium, where the rates of the forward and backward reactions are equal.- **Key Characteristics:**

• These reactions do not go to completion. Instead, they reach a state where the concentrations of reactants and products remain constant over time.
• The existence of a dynamic equilibrium where the forward reaction rate equals the backward reaction rate.

In our exercise, both reactions are reversible, each associated with an equilibrium constant \( K \). Understanding how to manipulate these to deduce the equilibrium expression for a desired reaction is critical in solving such problems.