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 equilibrium constant for H₂(g) + CO₂(g) → CO(g) + H₂O(g) at 823 K.

검증된 단계별 안내

Identify the given reactions and their equilibrium constants: \( \text{CoO(s) + H}_2\text{(g) } \rightarrow \text{ Co(s) + H}_2\text{O(g) } \) with \( K_c = 67 \) and \( \text{CoO(s) + CO(g) } \rightarrow \text{ Co(s) + CO}_2\text{(g) } \) with \( K_c = 490 \).

Write the target reaction: \( \text{H}_2\text{(g) + CO}_2\text{(g) } \rightarrow \text{ CO(g) + H}_2\text{O(g) } \).

Recognize that the target reaction is the reverse of the sum of the given reactions. Therefore, reverse the first reaction and add it to the second reaction.

Calculate the equilibrium constant for the reverse of the first reaction: \( K_{c, \text{reverse}} = \frac{1}{67} \).

Use the relationship \( K_{c, \text{target}} = K_{c, \text{reverse}} \times K_{c, \text{second}} \) to find the equilibrium constant for the target reaction.

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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 extent of the reaction. Understanding this concept is crucial for manipulating and calculating equilibrium constants in various reactions.

Equilibrium Constant (Kc)

The equilibrium constant (Kc) is a dimensionless number that expresses the ratio of the concentrations of products to reactants at equilibrium, each raised to the power of their coefficients in the balanced equation. For reactions involving gases, Kc can be calculated using partial pressures. In this question, Kc values for two different reactions are provided, which can be used to derive the Kc for a third reaction through manipulation of the given equilibria.

Manipulating Equilibrium Expressions

To find the equilibrium constant for a new reaction based on known equilibria, one can manipulate the given reactions by reversing them or adding them together. When a reaction is reversed, the equilibrium constant is inverted, and when reactions are added, their equilibrium constants are multiplied. This principle allows for the calculation of Kc for complex reactions by using 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 equilibrium constant for H2(g) + CO2(g) → CO(g) + H2O(g) at 823 K.