Gibbs free energy change (G)

thermodynamic property defined in terms of system enthalpy and entropy; all spontaneous processes involve a decrease in G

standard free energy of formation $(\text{Δ} G_{\text{f}}^{^\circ})$

change in free energy accompanying the formation of one mole of substance from its elements in their standard states

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Chemistry 2e · 16.4 Free Energy

Free Energy: practice problems

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

Exercises 31
A reaction has $Δ H °$ = 100 kJ/mol and $Δ S ° = 250 J/mol\cdotK.$ Is the reaction spontaneous at room temperature? If not, under what temperature conditions will it become spontaneous?
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Exercises 33
Use the standard free energy of formation data in Appendix G to determine the free energy change for each of the following reactions, which are run under standard state conditions and 25 °C. Identify each as either spontaneous or nonspontaneous at these conditions.
(a) $MnO_{2} (s) ⟶ Mn (s) + O_{2} (g)$
(b) $H_{2} (g) + Br_{2} (l) ⟶ 2HBr (g)$
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Exercises 35
Given:
$P_{4} (s) + 5O_{2} (g) ⟶ P_{4} O_{10} (s) Δ G ° = -2697.0 kJ/mol$
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Exercises 37
Consider the decomposition of red mercury(II) oxide under standard state conditions.
$2HgO (s, red) ⟶ 2Hg (l) + O_{2} (g)$
(a) Is the decomposition spontaneous under standard state conditions?
(b) Above what temperature does the reaction become spontaneous?
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Exercises 39
Calculate ΔG° for each of the following reactions from the equilibrium constant at the temperature given.
(a) $N_{2} (g) + O_{2} (g) ⟶ 2NO (g) T = 2000 °C K_{p} = 4.1 \times 10^{-4}$
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Exercises 41
Calculate the equilibrium constant at 25 °C for each of the following reactions from the value of ΔG° given.
(a) $O_{2} (g) + 2F_{2} (g) ⟶ 2OF_{2} (g) Δ G ° = -9.2 kJ$
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Exercises 43
Calculate the equilibrium constant at the temperature given.
(a) $O_{2} (g) + 2F_{2} (g) ⟶ 2F_{2} O (g) (T = 100 °C)$
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Exercises 45
Consider the following reaction at 298 K:
$N_{2} O_{4} (g) ⇌ 2NO_{2} (g) K_{P} = 0.142$
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Exercises 47
Under what conditions is $N_{2} O_{3} (g) ⟶ NO (g) + NO_{2} (g)$ spontaneous?
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Exercises 49
Hydrogen sulfide is a pollutant found in natural gas. Following its removal, it is converted to sulfur by the reaction $2H_{2} S (g) + SO_{2} (g) ⇌ \frac{3}{8} S_{8} (s, rhombic) + 2H_{2} O (l) .$ What is the equilibrium constant for this reaction? Is the reaction endothermic or exothermic?
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Exercises 51
In the laboratory, hydrogen chloride (HCl(g)) and ammonia (NH₃(g)) often escape from bottles of their solutions and react to form the ammonium chloride (NH₄Cl(s)), the white glaze often seen on glassware. Assuming that the number of moles of each gas that escapes into the room is the same, what is the maximum partial pressure of HCl and NH₃ in the laboratory at room temperature? (Hint: The partial pressures will be equal and are at their maximum value when at equilibrium.)
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Exercises 53
Carbon dioxide decomposes into CO and O₂ at elevated temperatures. What is the equilibrium partial pressure of oxygen in a sample at 1000 °C for which the initial pressure of CO₂ was 1.15 atm?
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Exercises 55
Acetic acid, CH₃CO₂H, can form a dimer, (CH₃CO₂H)₂, in the gas phase.
$2CH_{3} CO_{2} H (g) ⟶ (CH_{3} CO_{2} H)_{2} (g)$
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Exercises 56
Determine ΔGº for the following reactions.
(a) Antimony pentachloride decomposes at 448 °C. The reaction is:
$SbCl_{5} (g) ⟶ SbCl_{3} (g) + Cl_{2} (g)$
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Exercises 58
Determine the standard free energy change, $Δ G_{f}^{^{\circ}},$ for the formation of S²⁻(aq) given that the $Δ G_{f}^{^{\circ}}$ for Ag⁺() and Ag₂S() are 77.1 kJ/mole and −39.5 kJ/mole respectively, and the solubility product for Ag₂S() is 8 10⁻⁵¹.
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Exercises 60
The evaporation of one mole of water at 298 K has a standard free energy change of 8.58 kJ.
$H_{2} O (l) ⇌ H_{2} O (g) Δ G ° = 8.58 kJ$
(a) Is the evaporation of water under standard thermodynamic conditions spontaneous?
(b) Determine the equilibrium constant, K $_{P}$ , for this physical process.
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Exercises 62
One of the important reactions in the biochemical pathway glycolysis is the reaction of glucose-6-phosphate (G6P) to form fructose-6-phosphate (F6P):
$G6P ⇌ F6P Δ G ° = 1.7 kJ$
(a) Is the reaction spontaneous or nonspontaneous under standard thermodynamic conditions?
(b) Standard thermodynamic conditions imply the concentrations of G6P and F6P to be 1 M, however, in a typical cell, they are not even close to these values. Calculate ΔG when the concentrations of G6P and F6P are 120 μM and 28 μM respectively, and discuss the spontaneity of the forward reaction under these conditions. Assume the temperature is 37 °C.
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Exercises 64
When ammonium chloride is added to water and stirred, it dissolves spontaneously and the resulting solution feels cold. Without doing any calculations, deduce the signs of ΔG, ΔH, and ΔS for this process, and justify your choices.
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Exercises 66
What happens to $Δ G$ (becomes more negative or more positive) for the following chemical reactions when the partial pressure of oxygen is increased?
(a) $S (s) + O_{2} (g) ⟶ SO_{2} (g)$
(b) $2SO_{2} (g) + O_{2} (g) ⟶ 2SO_{3} (g)$
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Key terms · 3

Gibbs free energy change (G): thermodynamic property defined in terms of system enthalpy and entropy; all spontaneous processes involve a decrease in G
standard free energy change (ΔG°): change in free energy for a process occurring under standard conditions (1 bar pressure for gases, 1 M concentration for solutions)
standard free energy of formation $(\text{Δ} G_{\text{f}}^{^\circ})$: change in free energy accompanying the formation of one mole of substance from its elements in their standard states

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Free Energy: practice problems

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

Exercises 31

A reaction has $Δ H °$ = 100 kJ/mol and $Δ S ° = 250 J/mol\cdotK.$ Is the reaction spontaneous at room temperature? If not, under what temperature conditions will it become spontaneous?

Exercises 33

Use the standard free energy of formation data in Appendix G to determine the free energy change for each of the following reactions, which are run under standard state conditions and 25 °C. Identify each as either spontaneous or nonspontaneous at these conditions.

(a) $MnO_{2} (s) ⟶ Mn (s) + O_{2} (g)$

(b) $H_{2} (g) + Br_{2} (l) ⟶ 2HBr (g)$

Exercises 35

Given:

$P_{4} (s) + 5O_{2} (g) ⟶ P_{4} O_{10} (s) Δ G ° = -2697.0 kJ/mol$

Exercises 37

Consider the decomposition of red mercury(II) oxide under standard state conditions.

$2HgO (s, red) ⟶ 2Hg (l) + O_{2} (g)$

(a) Is the decomposition spontaneous under standard state conditions?

(b) Above what temperature does the reaction become spontaneous?

Exercises 39

Calculate ΔG° for each of the following reactions from the equilibrium constant at the temperature given.

(a) $N_{2} (g) + O_{2} (g) ⟶ 2NO (g) T = 2000 °C K_{p} = 4.1 \times 10^{-4}$

Exercises 41

Calculate the equilibrium constant at 25 °C for each of the following reactions from the value of ΔG° given.

(a) $O_{2} (g) + 2F_{2} (g) ⟶ 2OF_{2} (g) Δ G ° = -9.2 kJ$

Exercises 43

Calculate the equilibrium constant at the temperature given.

(a) $O_{2} (g) + 2F_{2} (g) ⟶ 2F_{2} O (g) (T = 100 °C)$

Exercises 45

Consider the following reaction at 298 K:

$N_{2} O_{4} (g) ⇌ 2NO_{2} (g) K_{P} = 0.142$

Exercises 47

Under what conditions is $N_{2} O_{3} (g) ⟶ NO (g) + NO_{2} (g)$ spontaneous?

Exercises 49

Hydrogen sulfide is a pollutant found in natural gas. Following its removal, it is converted to sulfur by the reaction $2H_{2} S (g) + SO_{2} (g) ⇌ \frac{3}{8} S_{8} (s, rhombic) + 2H_{2} O (l) .$ What is the equilibrium constant for this reaction? Is the reaction endothermic or exothermic?

Exercises 51

In the laboratory, hydrogen chloride (HCl(g)) and ammonia (NH₃(g)) often escape from bottles of their solutions and react to form the ammonium chloride (NH₄Cl(s)), the white glaze often seen on glassware. Assuming that the number of moles of each gas that escapes into the room is the same, what is the maximum partial pressure of HCl and NH₃ in the laboratory at room temperature? (Hint: The partial pressures will be equal and are at their maximum value when at equilibrium.)

Exercises 53

Carbon dioxide decomposes into CO and O₂ at elevated temperatures. What is the equilibrium partial pressure of oxygen in a sample at 1000 °C for which the initial pressure of CO₂ was 1.15 atm?

Exercises 55

Acetic acid, CH₃CO₂H, can form a dimer, (CH₃CO₂H)₂, in the gas phase.

$2CH_{3} CO_{2} H (g) ⟶ (CH_{3} CO_{2} H)_{2} (g)$

Exercises 56

Determine ΔGº for the following reactions.

(a) Antimony pentachloride decomposes at 448 °C. The reaction is:

$SbCl_{5} (g) ⟶ SbCl_{3} (g) + Cl_{2} (g)$

Exercises 58

Determine the standard free energy change, $Δ G_{f}^{^{\circ}},$ for the formation of S²⁻(aq) given that the $Δ G_{f}^{^{\circ}}$ for Ag⁺() and Ag₂S() are 77.1 kJ/mole and −39.5 kJ/mole respectively, and the solubility product for Ag₂S() is 8 10⁻⁵¹.

Exercises 60

The evaporation of one mole of water at 298 K has a standard free energy change of 8.58 kJ.

$H_{2} O (l) ⇌ H_{2} O (g) Δ G ° = 8.58 kJ$

(a) Is the evaporation of water under standard thermodynamic conditions spontaneous?

(b) Determine the equilibrium constant, K $_{P}$ , for this physical process.

Exercises 62

One of the important reactions in the biochemical pathway glycolysis is the reaction of glucose-6-phosphate (G6P) to form fructose-6-phosphate (F6P):

$G6P ⇌ F6P Δ G ° = 1.7 kJ$

(a) Is the reaction spontaneous or nonspontaneous under standard thermodynamic conditions?

(b) Standard thermodynamic conditions imply the concentrations of G6P and F6P to be 1 M, however, in a typical cell, they are not even close to these values. Calculate ΔG when the concentrations of G6P and F6P are 120 μM and 28 μM respectively, and discuss the spontaneity of the forward reaction under these conditions. Assume the temperature is 37 °C.

Exercises 64

When ammonium chloride is added to water and stirred, it dissolves spontaneously and the resulting solution feels cold. Without doing any calculations, deduce the signs of ΔG, ΔH, and ΔS for this process, and justify your choices.

Exercises 66

What happens to $Δ G$ (becomes more negative or more positive) for the following chemical reactions when the partial pressure of oxygen is increased?

(a) $S (s) + O_{2} (g) ⟶ SO_{2} (g)$

(b) $2SO_{2} (g) + O_{2} (g) ⟶ 2SO_{3} (g)$

Key terms · 3

Gibbs free energy change (G): thermodynamic property defined in terms of system enthalpy and entropy; all spontaneous processes involve a decrease in G
standard free energy change (ΔG°): change in free energy for a process occurring under standard conditions (1 bar pressure for gases, 1 M concentration for solutions)
standard free energy of formation $(\text{Δ} G_{\text{f}}^{^\circ})$: change in free energy accompanying the formation of one mole of substance from its elements in their standard states

Learn 16.4 on the whiteboard

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

Read 16.4 in the textbook · This section on openstax.org