The following equilibria were measured at 823 K: CoO(s) + H₂(g) ⇌ Co(s) + H₂O(g) K_c = 67 H₂(g) + CO₂(g) ⇌ CO(g) + H₂O(g) Kc = 0.14 (a) Use these equilibria to calculate the equilibrium constant, K_c, for the reaction CoO(s) + CO(g) ⇌ Co(s) + CO₂(g) at 823 K.

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Identify the given reactions and their equilibrium constants. The first reaction is CoO(s) + H2(g) ⇌ Co(s) + H2O(g) with Kc = 67. The second reaction is H2(g) + CO2(g) ⇌ CO(g) + H2O(g) with Kc = 0.14.

Write the target reaction: CoO(s) + CO(g) ⇌ Co(s) + CO2(g). Notice that this reaction can be obtained by reversing the first given reaction and adding it to the second given reaction.

Reverse the first reaction to get Co(s) + H2O(g) ⇌ CoO(s) + H2(g). The equilibrium constant for the reversed reaction will be the reciprocal of the original, which is 1/67.

Add the reversed first reaction to the second reaction. This involves adding Co(s) + H2O(g) ⇌ CoO(s) + H2(g) to H2(g) + CO2(g) ⇌ CO(g) + H2O(g). The H2(g) and H2O(g) will cancel out, resulting in CoO(s) + CO(g) ⇌ Co(s) + CO2(g).

Calculate the equilibrium constant for the target reaction by multiplying the constants of the individual reactions used. The equilibrium constant for the target reaction, Kc, is (1/67) * 0.14.

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주요 개념

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Equilibrium Constant (Kc)

The equilibrium constant, Kc, is a numerical value that expresses the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. It is calculated using the formula Kc = [products]^[coefficients] / [reactants]^[coefficients]. A Kc value greater than 1 indicates that products are favored at equilibrium, while a value less than 1 suggests that reactants are favored.

Le Chatelier's Principle

Le Chatelier's Principle states that if a dynamic equilibrium is disturbed by changing the conditions, the system will adjust itself to counteract the change and restore a new equilibrium. This principle is crucial for predicting how changes in concentration, pressure, or temperature will affect the position of equilibrium in a chemical reaction.

Manipulating Equilibrium Expressions

When dealing with multiple equilibria, it is essential to manipulate the equilibrium expressions correctly to derive the desired Kc for a new reaction. This involves using the relationships between the given reactions, such as reversing a reaction (which inverts Kc) or adding reactions (which multiplies Kc values). Understanding how to combine these expressions is key to solving complex equilibrium problems.

The following equilibria were measured at 823 K: CoO(s) + H2(g) ⇌ Co(s) + H2O(g) Kc = 67 H2(g) + CO2(g) ⇌ CO(g) + H2O(g) Kc = 0.14 (a) Use these equilibria to calculate the equilibrium constant, Kc, for the reaction CoO(s) + CO(g) ⇌ Co(s) + CO2(g) at 823 K.