The following equilibria were measured at 823 K: CoO1s2 + H21g2 ΔCo1s2 + H2O1g2 Kc = 67 H21g2 + CO21g2 ΔCO1g2 + H2O1g2 Kc = 0.14 (a) Use these equilibria to calculate the equilibrium constant, Kc, for the reaction CoO1s2 + CO1g2ΔCo1s2 + CO21g2 at 823 K.

Verified step by step guidance

1. 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.
2. 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.
3. 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.
4. 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).
5. 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.

Key Concepts

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.