The following equilibria were attained at 823 K:
CoO(s) + H₂(g) → Co(s) + H₂O(g) K_c = 67
CoO(s) + CO(g) → Co(s) + CO₂(g) K_c = 490
Based on these equilibria, calculate the value of 𝐾_𝑐 for H₂(𝑔)+ CO₂(𝑔) ⇌ CO(𝑔) + H₂O(𝑔) at 823 K.

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Identify the given reactions and their equilibrium constants: Reaction 1: CoO(s) + H_2(g) → Co(s) + H_2O(g) with K_{c1} = 67, Reaction 2: CoO(s) + CO(g) → Co(s) + CO_2(g) with K_{c2} = 490.

Write the target reaction: H_2(g) + CO_2(g) ⇌ CO(g) + H_2O(g).

Recognize that the target reaction can be derived by reversing Reaction 2 and adding it to Reaction 1.

Reverse Reaction 2: CO(s) + CO_2(g) → CoO(s) + CO(g), which changes the equilibrium constant to 1/K_{c2}.

Add the reversed Reaction 2 to Reaction 1 to obtain the target reaction, and calculate the equilibrium constant for the target reaction as K_{c} = K_{c1} * (1/K_{c2}).

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주요 개념

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Chemical Equilibrium

Chemical equilibrium occurs when the rates of the forward and reverse reactions are equal, resulting in constant concentrations of reactants and products. The equilibrium constant (Kc) quantifies the ratio of product concentrations to reactant concentrations at equilibrium, providing insight into the position of the equilibrium. Understanding this concept is crucial for manipulating and calculating Kc values in various reactions.

Equilibrium Constant (Kc)

The equilibrium constant (Kc) is a numerical value that expresses the relationship between the concentrations of products and reactants at equilibrium for a given reaction at a specific temperature. It is calculated using the formula Kc = [products]^[coefficients] / [reactants]^[coefficients]. The value of Kc indicates whether the products or reactants are favored in the equilibrium state, which is essential for solving equilibrium-related problems.

Manipulating Equilibrium Expressions

Manipulating equilibrium expressions involves using the properties of Kc to derive new equilibrium constants from known ones. For example, if a reaction is reversed, the new Kc is the reciprocal of the original. Additionally, if reactions are added together, the Kc for the overall reaction is the product of the individual Kc values. This concept is vital for calculating Kc for complex reactions based on simpler, known equilibria.

The following equilibria were attained at 823 K:CoO(s) + H2(g) → Co(s) + H2O(g) Kc = 67CoO(s) + CO(g) → Co(s) + CO2(g) Kc = 490Based on these equilibria, calculate the value of 𝐾𝑐 for H2(𝑔)+ CO2(𝑔) ⇌ CO(𝑔) + H2O(𝑔) at 823 K.