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Chapter 15: Problem 27

The following equilibria were attained at \(823 \mathrm{K} :\) $$\operatorname{CoO}(s)+\mathrm{H}_{2}(g) \rightleftharpoons \mathrm{Co}(s)+\mathrm{H}_{2} \mathrm{O}(g) \quad K_{c}=67$$ $$\mathrm{CoO}(s)+\mathrm{CO}(g) \rightleftharpoons \mathrm{Co}(s)+\mathrm{CO}_{2}(g) \quad K_{c}=490$$ Based on these equilibria, calculate the equilibrium constant for \(\mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g) \rightleftharpoons \mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g)\) at 823 \(\mathrm{K}\) .

Short Answer

Expert verified
The equilibrium constant for the reaction H₂(g) + CO₂(g) ⇌ CO(g) + H₂O(g) at 823 K is approximately 7.31.

Step by step solution

01

Balanced equations for the given equilibria

The balanced equations for the given equilibria are already provided: 1. CoO(s) + H₂(g) ⇌ Co(s) + H₂O(g) (Kc = 67) 2. CoO(s) + CO(g) ⇌ Co(s) + CO₂(g) (Kc = 490)
02

Determine the relationship between the given reactions and the desired reaction

We want to find the equilibrium constant for the reaction: H₂(g) + CO₂(g) ⇌ CO(g) + H₂O(g) Notice that we can obtain the desired reaction by: 1. Reversing reaction 1: Co(s) + H₂O(g) ⇌ CoO(s) + H₂(g) 2. Adding the reversed reaction 1 and reaction 2: (Co(s) + H₂O(g) ⇌ CoO(s) + H₂(g)) + (CoO(s) + CO(g) ⇌ Co(s) + CO₂(g)) By doing this, the Co(s) and CoO(s) species cancel out, resulting in the desired reaction: H₂(g) + CO₂(g) ⇌ CO(g) + H₂O(g)
03

Calculate the equilibrium constant for the desired reaction

Since we want the equilibrium constant (Kc) for the desired reaction, we can make use of the fact that equilibrium constants multiply when reactions are combined: 1. Reversed reaction 1: Kc' = 1 / Kc₁ = 1 / 67 2. Reaction 2: Kc₂ = 490 Since we are combining these reactions to get the desired reaction, we can find the equilibrium constant Kc_desired by multiplying the constants for the individual reactions: Kc_desired = Kc' × Kc₂ = (1 / 67) × 490 = 490 / 67 ≈ 7.31 So, the equilibrium constant for the desired reaction H₂(g) + CO₂(g) ⇌ CO(g) + H₂O(g) at 823 K is approximately 7.31.

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Most popular questions from this chapter

Which of the following statements are true and which are false? (a) For the reaction \(2 \mathrm{A}(g)+\mathrm{B}(g) \rightleftharpoons \mathrm{A}_{2} \mathrm{B}(g) K_{c}\) and \(K_{p}\) are numerically the same. (b) It is possible to distinguish \(K_{c}\) from \(K_{p}\) by comparing the units used to express the equilibrium constant. (c) For the equilibrium in (a), the value of \(K_{c}\) increases with increasing pressure.

As shown in Table \(15.2,\) the equilibrium constant for the reaction \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)\) is \(K_{p}=4.34 \times 10^{-3} \mathrm{at} 300^{\circ} \mathrm{C}\) . Pure \(\mathrm{NH}_{3}\) is placed in a \(1.00-\mathrm{L}\) flask and allowed to reach equilibrium at this temperature. There are 1.05 \(\mathrm{g} \mathrm{NH}_{3}\) in the equilibrium mixture. (a) What are the masses of \(\mathrm{N}_{2}\) and \(\mathrm{H}_{2}\) in the equilibrium mixture? (b) What was the initial mass of ammonia placed in the vessel? (c) What is the total pressure in the vessel?

A mixture of 1.374 \(\mathrm{g}\) of \(\mathrm{H}_{2}\) and 70.31 \(\mathrm{g}\) of \(\mathrm{Br}_{2}\) is heated in a 2.00 -L vessel at 700 \(\mathrm{K}\) . These substances react according to $$\mathrm{H}_{2}(g)+\mathrm{Br}_{2}(g) \rightleftharpoons 2 \mathrm{HBr}(g)$$ At equilibrium, the vessel is found to contain 0.566 \(\mathrm{g}\) of \(\mathrm{H}_{2}\) (a) Calculate the equilibrium concentrations of \(\mathrm{H}_{2}, \mathrm{Br}_{2},\) and \(\mathrm{HBr}\) . (b ) Calculate \(K_{c} .\)

The equilibrium \(2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{NOCl}(g)\) is established at 500 \(\mathrm{K}\) . An equilibrium mixture of the three gases has partial pressures of 0.095 atm, 0.171 atm, and 0.28 atm for \(\mathrm{NO}, \mathrm{Cl}_{2},\) and \(\mathrm{NOCl}\) , respectively. (a) Calculate \(K_{p}\) for this reaction at 500.0 \(\mathrm{K}\) . (b) If the vessel has a volume of 5.00 \(\mathrm{L}\) , calculate \(K_{c}\) at this temperature.

At \(2000^{\circ} \mathrm{C},\) the equilibrium constant for the reaction $$2 \mathrm{NO}(g) \rightleftharpoons \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g)$$ is \(K_{c}=2.4 \times 10^{3} .\) If the initial concentration of \(\mathrm{NO}\) is \(0.175 \mathrm{M},\) what are the equilibrium concentrations of \(\mathrm{NO}\) \(\mathrm{N}_{2},\) and \(\mathrm{O}_{2} ?\)
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