18.E: Chemical Thermodynamics (Exercises)

A general chemistry Libretexts Textmap organized around the textbook
Chemistry: Principles, Patterns, and Applications
by Bruce A. Averill

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These are homework exercises to accompany the Textmap created for "Chemistry: Principles, Patterns, and Applications" by Bruce A. Averill and Patricia Eldredge. Complementary General Chemistry question banks can be found for other Textmaps and can be accessed here. In addition to these publicly available questions, access to private problems bank for use in exams and homework is available to faculty only on an individual basis; please contact Delmar Larsen for an account with access permission.

Problems marked with a ♦ involve multiple concepts.

1. Electric utilities have been exploring thermal energy storage as a potentially attractive energy-storage solution for peak use. Thermal energy is extracted as steam and stored in rock, oil, or water for later conversion to electricity via heat exchangers. Which steps involve heat transfer? Which involve work done?
2. ♦ During World War II, German scientists developed the first rocket-powered airplane to be flown in combat, the Messerschmitt 163 Komet. The Komet was powered by the reaction of liquid hydrogen peroxide (\(H_2O_2\)) and hydrazine (\(N_2H_4\)) as follows:

\[2H_2O_2(l) + N_2H_4(l) \rightarrow N_2(g) + 4H_2O(g)\]

1. Determine the standard molar enthalpy of reaction.
2. What amount of work can be done by the reaction of 1.00 kg of hydrazine with a stoichiometric amount of hydrogen peroxide at 25°C at a constant pressure of 1.00 atm?
3. What is the change in internal energy under these conditions?

3. ♦ During the 1950s, pentaborane-9 was tested as a potential rocket fuel. However, the idea was abandoned when it was discovered that \(B_2O_3\), the product of the reaction of pentaborane-9 with \(O_2\), was an abrasive that destroyed rocket nozzles. The reaction is represented by the equation

\[2B_5H_9(l) + 12O_2(g) \rightarrow 5B_2O_3(s) + 9H_2O(g)\]

1. Determine the standard molar enthalpy of reaction.
2. How much work is done against a pressure of 1.0 atm when 50 lb of fuel are allowed to react with sufficient oxygen to cause the reaction to go to completion at 25°C?
3. What is ΔE for the reaction?

4. ♦ Polar explorers must be particularly careful to keep their clothes from becoming damp because the resulting heat loss could be fatal. If a polar explorer’s clothes absorbed 1.0 kg of water and the clothes dried from the polar wind, what would be the heat loss [ΔH_vap(H₂O) = 44 kJ/mol]? How much glucose must be consumed to make up for this heat loss to prevent death [ΔH_comb(glucose) = −802 kJ/mol]?

5. Propane gas is generally preferred to kerosene as a fuel for stoves in the boating industry because kerosene stoves require more maintenance. Propane, however, is much more flammable than kerosene and imposes an added risk because it is denser than air and can collect in the bottom of a boat and ignite. The complete combustion of propane produces CO₂ gas and \(H_2O\) vapor and has a value of ΔH = −2044 kJ/mol at 25°C. What is ΔE?

6. The propane in Problem 5 can be produced from the hydrogenation of propene according to the following reaction: C₃H₆(g) + H₂(g) → C₃H₈(g); ΔH = −124 kJ/mol. Given that the reaction \(\mathrm{H_2(g)}+\frac{1}{2}\mathrm{O_2(g)}\rightarrow\mathrm{H_2O(g)}\) has ΔH = −241.8 kJ/mol, what is the

1. standard enthalpy of combustion of propene?
2. value of ΔE for the combustion of propene?

7. ♦ The anaerobic conversion of sucrose, a sweetening agent, to lactic acid, which is associated with sour milk, can be described as follows:

\(\underset{\textrm{sucrose}}{\mathrm{C_{12}H_{22}O_{11}}+\mathrm{H_2O}}\rightarrow\underset{\textrm{lactic acid}}{\mathrm{4CH_3CH(OH)CO_2H}}\)

The combustion of sucrose, however, occurs as follows:

C₁₂H₂₂O₁₁(s) + 12O₂(g) → 12CO₂(g) + 11H₂O(l)

1. Which reaction is thermodynamically more favorable—the anaerobic conversion of sucrose to lactic acid or the aerobic oxidation to CO₂ and H₂O? The values of ΔH_f are as follows: lactic acid, −694.1 kJ/mol; sucrose, −222 kJ/mol; CO₂, −393.5 kJ/mol; and H₂O, −285.8 kJ/mol.
2. What is ΔE for the combustion of 12.0 g of sucrose at normal body temperature (37°C)?

8. Phosphorus exists as several allotropes, the most common being red, black, and white phosphorus. White phosphorus consists of tetrahedral P₄ molecules and melts at 44.15°C; it is converted to red phosphorus by heating at 400°C for several hours. The chemical differences between red and white phosphorus are considerable: white phosphorus burns in air, whereas red phosphorus is stable; white phosphorus is soluble in organic compounds, whereas red phosphorus is not; white phosphorus melts at 44.15°C, whereas red phosphorus melts at 597°C. If the enthalpy of fusion of white phosphorus is 0.659 kJ/mol, what is its ΔS? Black phosphorus is even less reactive than red. Based on this information, which allotrope would you predict to have the highest entropy? the lowest? Why?

9. ♦ Ruby and sapphire have a common mineral name: corundum (Al₂O₃). Although they are crystalline versions of the same compound, the nature of the imperfections determines the identity of the gem. Outline a method for measuring and comparing the entropy of a ruby with the entropy of a sapphire. How would you expect the entropies to compare with the entropy of a perfect corundum crystal?

10. ♦ Tin has two crystalline forms—α and β—represented in the following equilibrium equation:

\(\underset{\textrm{gray}}{\alpha\textrm{-tin}}\overset{18^\circ \textrm C}{\rightleftharpoons}\underset{\textrm{white}}{\beta\textrm{-tin}}\overset{232^\circ \textrm C}{\rightleftharpoons}\mathrm{Sn(l)}\)

The earliest known tin artifacts were discovered in Egyptian tombs of the 18th dynasty (1580–1350 BC), although archaeologists are surprised that so few tin objects exist from earlier eras. It has been suggested that many early tin objects were either oxidized to a mixture of stannous and stannic oxides or transformed to powdery, gray tin. Sketch a thermodynamic cycle similar to part (b) in Figure 18.15 "Two Forms of Elemental Sulfur and a Thermodynamic Cycle Showing the Transition from One to the Other" to show the conversion of liquid tin to gray tin. Then calculate the change in entropy that accompanies the conversion of Sn(l) to α-Sn using the following data: C_p(white) = 26.99, C_p(gray) = 25.77 J/(mol·K), ΔH_fus = 7.0 kJ/mol, ΔH_β → α = −2.2 kJ/mol.

11. The reaction of SO₂ with O₂ to produce SO₃ has great industrial significance because SO₃ is converted to H₂SO₄ by reaction with water. Unfortunately, the reaction is also environmentally important because SO₃ from industrial smokestacks is a primary source of acid rain. ΔH for the reaction of SO₂ with O₂ to form SO₃ is −23.49 kJ/mol, and ΔS is −22.66 J/(mol·K). Does this reaction occur spontaneously at 25°C? Does it occur spontaneously at 800°C assuming no change in ΔH and ΔS? Why is this reaction usually carried out at elevated temperatures?

12. Pollutants from industrial societies pose health risks to individuals from exposure to metals such as lead, mercury, and cadmium. The biological effects of a toxic metal may be reduced by removing it from the system using a chelating agent, which binds to the metal and forms a complex that is eliminated from the system without causing more damage. In designing a suitable chelating agent, one must be careful, however, because some chelating agents form metal complexes that are more toxic than the metal itself. Both methylamine (CH₃NH₂) and ethylenediamine (H₂NCH₂CH₂NH₂, abbreviated en) could, in principle, be used to treat heavy metal poisoning. In the case of cadmium, the reactions are as follows:

Cd²⁺+2CH₃NH₂→Cd(CH₃NH₂)₂²⁺

ΔH=−7.03 kcal/mol, ΔS=−1.58 cal/(mol⋅K)

Cd²⁺+en→Cd(en)²⁺

ΔH=−7.02 kcal/mol, ΔS=3.15 cal/(mol⋅K)

Based strictly on thermodynamic arguments, which would you choose to administer to a patient suffering from cadmium toxicity? Why? Assume a body temperature of 37°C.

13. ♦ Explosive reactions often have a large negative enthalpy change and a large positive entropy change, but the reaction must also be kinetically favorable. For example, the following equation represents the reaction between hydrazine, a rocket propellant, and the oxidizer dinitrogen tetroxide:

2N₂H₄(l) + N₂O₄(l) → 4H₂O(g) + 3N₂(g)

ΔH° = −249 kJ/mol, ΔS° = 218 J/(mol·K)

1. How much free energy is produced from this reaction at 25°C?
2. Is the reaction thermodynamically favorable?
3. What is K?
4. This reaction requires thermal ignition. Why?

14. ♦ Cesium, a silvery-white metal used in the manufacture of vacuum tubes, is produced industrially by the reaction of CsCl with CaC₂:

2CsCl(l) + CaC₂(s) → CaCl₂(l) + 2C(s) + 2Cs(g)

Compare the free energy produced from this reaction at 25°C and at 1227°C, the temperature at which it is normally run, given these values: ΔH^∘_{298 K}

= 32.0 kJ/mol, ΔS^∘_{298 K} = 8.0 J/(mol·K); ΔH^∘_{1500 K} = −0.6 kJ/mol, ΔS^∘_{1500 K} = 3.6 J/(mol·K).

1. If you wanted to minimize energy costs in your production facility by reducing the temperature of the reaction, what is the lowest temperature at which products are favored over reactants (assuming the reaction is kinetically favorable at the lower temperature)? Assume ΔH° and ΔS° vary linearly with temperature.
2. What is the ratio K_{1500 K}/K_{298 K}?

15. Dessicants (drying agents) can often be regenerated by heating, although it is generally not economically worthwhile to do so. A dessicant that is commonly regenerated is CaSO₄·2H₂O:

CaSO₄⋅2H₂O(s)→CaSO₄(s)+2H₂O(g)

ΔH^∘₂₉₈ =25.1 kJ/mol, ΔS^∘₂₉₈ =69.3 J/(mol⋅K)

Regeneration is carried out at 250°C.

1. What is ΔG° for this reaction?
2. What is the equilibrium constant at 25°C?
3. What is the ratio K_250°C/K_25°C?
4. What is the equilibrium constant at 250°C?
5. Is regeneration of CaSO₄(s)·2H₂O an enthalpy- or entropy-driven process? Explain your answer.

16. The nitrogen triiodide complex with ammonia (NI₃·NH₃) is a simple explosive that can be synthesized from common household products. When detonated, it produces N₂ and I₂. It can be painted on surfaces when wet, but it is shock sensitive when dry (even touching it with a feather can cause an explosion). Do you expect ΔG for the explosion reaction to be positive or negative? Why doesn’t NI₃·NH₃ explode spontaneously?

17. Adenosine triphosphate (ATP) contains high-energy phosphate bonds that are used in energy metabolism, coupling energy-yielding and energy-requiring processes. Cleaving a phosphate link by hydrolysis (ATP hydrolysis) can be described by the reaction ATP + H₂O⇌ADP+P_i+H⁺, where P_i symbolizes phosphate. Glycerol and ATP react to form glycerol-3-phosphate, ADP, and H⁺, with an overall K = 6.61 × 10⁵ at 37°C. The reaction of glycerol with phosphate to form glycerol-3-phosphate and water has an equilibrium constant of 2.82 × 10⁻². What is the equilibrium constant for ATP hydrolysis? How much free energy is released from the hydrolysis of ATP?

18. ♦ Consider the biological reduction of molecular nitrogen, for which the following is the minimal reaction stoichiometry under optimal conditions (P_i = phosphate):

\[8H^+ + 8e^− + N_2 + 16ATP \rightarrow H_2 + 2NH_3 + 16ADP + 16P_i\]

1. What is the approximate ratio of K_eq for this reaction and for the same reaction in the absence of ATP?
2. Given the fact that at pH 7 both the reaction of protons and electrons to give H₂ and the reaction of H₂ with N₂ to give ammonia are thermodynamically spontaneous (i.e., K >> 1), suggest a reason that nitrogen-fixing bacteria use such a large energy input to drive a reaction that is already spontaneous.

Solutions

VideoSolution

1. −4315 kJ/mol B₅H₉
2. 1340 kJ
3. −1.55 × 10⁶ kJ per 50 lb of B₅H₉

5. −2046 kJ/mol

1. aerobic conversion
2. −268 kJ

11. Yes, the reaction is spontaneous at 25°C, but its rate is very slow. The reaction is not spontaneous at 800°C (ΔG = 0.82 kJ/mol), but the reaction rate is much greater.

1. −314 kJ/mol
2. yes
3. 2.10 × 10⁴⁵
4. Ignition is required to overcome the high activation energy to reaction.

1. 4.4 kJ/mol
2. 0.17
3. 78.3
4. 13
5. entropy-driven; ΔH° > 0, so ΔS° must be positive for the reaction to be spontaneous.

17. 2.34 × 10⁷; −43.7 kJ/mol

Contributors and Attributions

• Anonymous