Chemistry 2e · 13.4 Equilibrium Calculations

Equilibrium Calculations: practice problems

20 problems from the book, with its answers. Check your working, or have any of them explained to you on the whiteboard.

Exercises 50
A reaction is represented by this equation: $A (a q) + 2 B (a q) ⇌ 2 C (a q) K_{c} = 1 \times 10^{3}$
(a) Write the mathematical expression for the equilibrium constant.
(b) Using concentrations ≤1 M, identify two sets of concentrations that describe a mixture of A, B, and C at equilibrium.
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Exercises 52
What is the value of the equilibrium constant at 500 °C for the formation of NH₃ according to the following equation?
$N_{2} (g) + 3 H_{2} (g) ⇌ 2 NH_{3} (g)$
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Exercises 54
A 0.72-mol sample of PCl₅ is put into a 1.00-L vessel and heated. At equilibrium, the vessel contains 0.40 mol of PCl₃(g) and 0.40 mol of Cl₂(g). Calculate the value of the equilibrium constant for the decomposition of PCl₅ to PCl₃ and Cl₂ at this temperature.
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Exercises 56
Calculate the value of the equilibrium constant K $_{P}$ for the reaction $2 NO (g) + Cl_{2} (g) ⇌ 2 NOCl (g)$ from these equilibrium pressures: NO, 0.050 atm; Cl₂, 0.30 atm; NOCl, 1.2 atm.
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Exercises 58
A sample of ammonium chloride was heated in a closed container.
$NH_{4} Cl (s) ⇌ NH_{3} (g) + HCl (g)$
At equilibrium, the pressure of NH₃(g) was found to be 1.75 atm. What is the value of the equilibrium constant K $_{P}$ for the decomposition at this temperature?
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Exercises 60
Complete the following partial ICE tables.
(a)
$change 2 SO_{3} (g)___⇌ 2 SO_{2} (g) +___O_{2} (g) + x$
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Exercises 62
Why are there no changes specified for Ni in Exercise 13.60, part (f)? What property of Ni does change?
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Exercises 64
Analysis of the gases in a sealed reaction vessel containing NH₃, N₂, and H₂ at equilibrium at 400 °C established the concentration of N₂ to be 1.2 M and the concentration of H₂ to be 0.24 M.
$N_{2} (g) + 3 H_{2} (g) ⇌ 2 NH_{3} (g) K_{c} = 0.50 at 400 ° C$
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Exercises 66
What is the pressure of BrCl in an equilibrium mixture of Cl₂, Br₂, and BrCl if the pressure of Cl₂ in the mixture is 0.115 atm and the pressure of Br₂ in the mixture is 0.450 atm?
$Cl_{2} (g) + Br_{2} (g) ⇌ 2 BrCl (g) K_{P} = 4.7 \times 10^{- 2}$
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Exercises 68
Cobalt metal can be prepared by reducing cobalt(II) oxide with carbon monoxide.
$CoO (s) + CO (g) ⇌ Co (s) + CO_{2} (g) K_{c} = 4.90 \times 10^{2} at 550 °C$
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Exercises 70
Sodium sulfate 10−hydrate, Na₂SO₄·10H₂O, dehydrates according to the equation
$Na_{2} SO_{4} \cdot 10 H_{2} O (s) ⇌ Na_{2} SO_{4} (s) + 10 H_{2} O (g) K_{P} = 4.08 \times 10^{- 25} at 25 °C$
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Exercises 72
A student solved the following problem and found the equilibrium concentrations to be [SO₂] = 0.590 M, [O₂] = 0.0450 M, and [SO₃] = 0.260 M. How could this student check the work without reworking the problem? The problem was: For the following reaction at 600 °C:
$2 SO_{2} (g) + O_{2} (g) ⇌ 2 SO_{3} (g) K_{c} = 4.32$
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Exercises 74
Assume that the change in concentration of N₂O₄ is small enough to be neglected in the following problem.
(a) Calculate the equilibrium concentration of both species in 1.00 L of a solution prepared from 0.129 mol of N₂O₄ with chloroform as the solvent.
$N_{2} O_{4} (g) ⇌ 2 NO_{2} (g) K_{c} = 1.07 \times 10^{- 5}$ in chloroform
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Exercises 76
Assume that the change in pressure of H₂S is small enough to be neglected in the following problem.
(a) Calculate the equilibrium pressures of all species in an equilibrium mixture that results from the decomposition of H₂S with an initial pressure of 0.824 atm.
$2 H_{2} S (g) ⇌ 2 H_{2} (g) + S_{2} (g) K_{P} = 2.2 \times 10^{- 6}$
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Exercises 78
What are the concentrations of PCl₅, PCl₃, and Cl₂ in an equilibrium mixture produced by the decomposition of a sample of pure PCl₅ with [PCl₅] = 2.00 M?
$PCl_{5} (g) ⇌ PCl_{3} (g) + Cl_{2} (g) K_{c} = 0.0211$
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Exercises 79
Calculate the number of grams of HI that are at equilibrium with 1.25 mol of H₂ and 63.5 g of iodine at 448 °C.
$H_{2} + I_{2} ⇌ 2 HI K_{c} = 50.2 at 448 °C$
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Exercises 81
What is the minimum mass of CaCO₃ required to establish equilibrium at a certain temperature in a 6.50-L container if the equilibrium constant (K $_{c}$ ) is 0.50 for the decomposition reaction of CaCO₃ at that temperature?
$CaCO_{3} (s) ⇌ CaO (s) + CO_{2} (g)$
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Exercises 84
The equilibrium constant (K $_{c}$ ) for this reaction is 5.0 at a given temperature.
$CO (g) + H_{2} O (g) ⇌ CO_{2} (g) + H_{2} (g)$
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Exercises 86
Consider the equilibrium
$4 NO_{2} (g) + 6 H_{2} O (g) ⇌ 4 NH_{3} (g) + 7 O_{2} (g)$
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Exercises 88
Liquid N₂O₃ is dark blue at low temperatures, but the color fades and becomes greenish at higher temperatures as the compound decomposes to NO and NO₂. At 25 °C, a value of K $_{P}$ = 1.91 has been established for this decomposition. If 0.236 moles of N₂O₃ are placed in a 1.52-L vessel at 25 °C, calculate the equilibrium partial pressures of N₂O₃(g), NO₂(g), and NO(g).
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Equilibrium Calculations: practice problems

20 problems from the book, with its answers. Check your working, or have any of them explained to you on the whiteboard.

Exercises 50

A reaction is represented by this equation: $A (a q) + 2 B (a q) ⇌ 2 C (a q) K_{c} = 1 \times 10^{3}$

(a) Write the mathematical expression for the equilibrium constant.

(b) Using concentrations ≤1 M, identify two sets of concentrations that describe a mixture of A, B, and C at equilibrium.

Exercises 52

What is the value of the equilibrium constant at 500 °C for the formation of NH₃ according to the following equation?

$N_{2} (g) + 3 H_{2} (g) ⇌ 2 NH_{3} (g)$

Exercises 54

A 0.72-mol sample of PCl₅ is put into a 1.00-L vessel and heated. At equilibrium, the vessel contains 0.40 mol of PCl₃(g) and 0.40 mol of Cl₂(g). Calculate the value of the equilibrium constant for the decomposition of PCl₅ to PCl₃ and Cl₂ at this temperature.

Exercises 56

Calculate the value of the equilibrium constant K $_{P}$ for the reaction $2 NO (g) + Cl_{2} (g) ⇌ 2 NOCl (g)$ from these equilibrium pressures: NO, 0.050 atm; Cl₂, 0.30 atm; NOCl, 1.2 atm.

Exercises 58

A sample of ammonium chloride was heated in a closed container.

$NH_{4} Cl (s) ⇌ NH_{3} (g) + HCl (g)$

At equilibrium, the pressure of NH₃(g) was found to be 1.75 atm. What is the value of the equilibrium constant K $_{P}$ for the decomposition at this temperature?

Exercises 60

Complete the following partial ICE tables.

(a)

$change 2 SO_{3} (g)___⇌ 2 SO_{2} (g) +___O_{2} (g) + x$

Exercises 62

Why are there no changes specified for Ni in Exercise 13.60, part (f)? What property of Ni does change?

Exercises 64

Analysis of the gases in a sealed reaction vessel containing NH₃, N₂, and H₂ at equilibrium at 400 °C established the concentration of N₂ to be 1.2 M and the concentration of H₂ to be 0.24 M.

$N_{2} (g) + 3 H_{2} (g) ⇌ 2 NH_{3} (g) K_{c} = 0.50 at 400 ° C$

Exercises 66

What is the pressure of BrCl in an equilibrium mixture of Cl₂, Br₂, and BrCl if the pressure of Cl₂ in the mixture is 0.115 atm and the pressure of Br₂ in the mixture is 0.450 atm?

$Cl_{2} (g) + Br_{2} (g) ⇌ 2 BrCl (g) K_{P} = 4.7 \times 10^{- 2}$

Exercises 68

Cobalt metal can be prepared by reducing cobalt(II) oxide with carbon monoxide.

$CoO (s) + CO (g) ⇌ Co (s) + CO_{2} (g) K_{c} = 4.90 \times 10^{2} at 550 °C$

Exercises 70

Sodium sulfate 10−hydrate, Na₂SO₄·10H₂O, dehydrates according to the equation

$Na_{2} SO_{4} \cdot 10 H_{2} O (s) ⇌ Na_{2} SO_{4} (s) + 10 H_{2} O (g) K_{P} = 4.08 \times 10^{- 25} at 25 °C$

Exercises 72

A student solved the following problem and found the equilibrium concentrations to be [SO₂] = 0.590 M, [O₂] = 0.0450 M, and [SO₃] = 0.260 M. How could this student check the work without reworking the problem? The problem was: For the following reaction at 600 °C:

$2 SO_{2} (g) + O_{2} (g) ⇌ 2 SO_{3} (g) K_{c} = 4.32$

Exercises 74

Assume that the change in concentration of N₂O₄ is small enough to be neglected in the following problem.

(a) Calculate the equilibrium concentration of both species in 1.00 L of a solution prepared from 0.129 mol of N₂O₄ with chloroform as the solvent.

$N_{2} O_{4} (g) ⇌ 2 NO_{2} (g) K_{c} = 1.07 \times 10^{- 5}$ in chloroform

Exercises 76

Assume that the change in pressure of H₂S is small enough to be neglected in the following problem.

(a) Calculate the equilibrium pressures of all species in an equilibrium mixture that results from the decomposition of H₂S with an initial pressure of 0.824 atm.

$2 H_{2} S (g) ⇌ 2 H_{2} (g) + S_{2} (g) K_{P} = 2.2 \times 10^{- 6}$

Exercises 78

What are the concentrations of PCl₅, PCl₃, and Cl₂ in an equilibrium mixture produced by the decomposition of a sample of pure PCl₅ with [PCl₅] = 2.00 M?

$PCl_{5} (g) ⇌ PCl_{3} (g) + Cl_{2} (g) K_{c} = 0.0211$

Exercises 79

Calculate the number of grams of HI that are at equilibrium with 1.25 mol of H₂ and 63.5 g of iodine at 448 °C.

$H_{2} + I_{2} ⇌ 2 HI K_{c} = 50.2 at 448 °C$

Exercises 81

What is the minimum mass of CaCO₃ required to establish equilibrium at a certain temperature in a 6.50-L container if the equilibrium constant (K $_{c}$ ) is 0.50 for the decomposition reaction of CaCO₃ at that temperature?

$CaCO_{3} (s) ⇌ CaO (s) + CO_{2} (g)$

Exercises 84

The equilibrium constant (K $_{c}$ ) for this reaction is 5.0 at a given temperature.

$CO (g) + H_{2} O (g) ⇌ CO_{2} (g) + H_{2} (g)$

Exercises 86

Consider the equilibrium

$4 NO_{2} (g) + 6 H_{2} O (g) ⇌ 4 NH_{3} (g) + 7 O_{2} (g)$

Exercises 88

Liquid N₂O₃ is dark blue at low temperatures, but the color fades and becomes greenish at higher temperatures as the compound decomposes to NO and NO₂. At 25 °C, a value of K $_{P}$ = 1.91 has been established for this decomposition. If 0.236 moles of N₂O₃ are placed in a 1.52-L vessel at 25 °C, calculate the equilibrium partial pressures of N₂O₃(g), NO₂(g), and NO(g).

Learn 13.4 on the whiteboard

The tutor teaches the whole section, drawing it out step by step and answering your questions as you go.

Read 13.4 in the textbook · This section on openstax.org