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Ch.15 - Chemical Equilibrium
Brown - Chemistry: The Central Science 14th Edition
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232Not the one you use?Change textbook
All textbooksBrown 14th EditionCh.15 - Chemical EquilibriumProblem 96a
Chapter 15, Problem 96a

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.

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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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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.
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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.
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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.
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Related Practice
Textbook Question

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 (d) If the reaction vessel from part (c) is heated to 823 K and allowed to come to equilibrium, how much CoO(s) remains?

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Textbook Question

The phase diagram for SO2 is shown here. (d) At which of the three points marked in red does SO2(g) most closely approach ideal-gas behavior?

Textbook Question

At a temperature of 700 K, the forward and reverse rate constants for the reaction 2 HI(g) ⇌ H2(g) + I2(g) are kf = 1.8×10−30 M−1s−1 and kr = 0.063 M−1s−1.

(a) What is the value of the equilibrium constant Kc at 700 K?

(b) Is the forward reaction endothermic or exothermic if the rate constants for the same reaction have values of kf = 0.097M−1s−1 and kr = 2.6 M−1s−1 at 800 K?

Textbook Question

The phase diagram for SO2 is shown here. (e) At which of the three red points does SO2(g) behave least ideally?