Textbook Question
(a) For a process that occurs at constant temperature, does the change in Gibbs free energy depend on changes in the enthalpy and entropy of the system?
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Ch.19 - Chemical Thermodynamics
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232
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Table of contents
- Ch.1 - Introduction: Matter, Energy, and Measurement140
- Ch.2 - Atoms, Molecules, and Ions192
- Ch.3 - Chemical Reactions and Reaction Stoichiometry172
- Ch.4 - Reactions in Aqueous Solution156
- Ch.5 - Thermochemistry151
- Ch.6 - Electronic Structure of Atoms137
- Ch.7 - Periodic Properties of the Elements127
- Ch.8 - Basic Concepts of Chemical Bonding143
- Ch.9 - Molecular Geometry and Bonding Theories167
- Ch.10 - Gases147
- Ch.11 - Liquids and Intermolecular Forces97
- Ch.12 - Solids and Modern Materials129
- Ch.13 - Properties of Solutions126
- Ch.14 - Chemical Kinetics175
- Ch.15 - Chemical Equilibrium107
- Ch.16 - Acid-Base Equilibria127
- Ch.17 - Additional Aspects of Aqueous Equilibria133
- Ch.18 - Chemistry of the Environment88
- Ch.19 - Chemical Thermodynamics140
- Ch.20 - Electrochemistry137
- Ch.21 - Nuclear Chemistry99
- Ch.22 - Chemistry of the Nonmetals66
- Ch.23 - Transition Metals and Coordination Chemistry69
- Ch.24 - The Chemistry of Life: Organic and Biological Chemistry11
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232Not the one you use?Change textbook
Chapter 19, Problem 50
Three of the forms of elemental carbon are graphite, diamond,and buckminsterfullerene. The entropies at 298 Kfor graphite and diamond are listed in Appendix C.(b) What would you expect for the S° value of buckminsterfullerene(Figure 12.49, p. 509) relative to the valuesfor graphite and diamond? Explain.
Verified step by step guidance1
Identify the molecular structures of graphite, diamond, and buckminsterfullerene. Graphite consists of layers of carbon atoms arranged in a hexagonal lattice, diamond is a three-dimensional tetrahedral network of carbon atoms, and buckminsterfullerene (C60) is a spherical molecule composed of 60 carbon atoms arranged in a pattern of hexagons and pentagons.
Understand that entropy (S°) is a measure of the randomness or disorder of a system. The more ways the atoms can be arranged without changing the overall structure, the higher the entropy.
Compare the structural rigidity and complexity of the three forms. Diamond has a very rigid and tightly bonded structure, leading to lower entropy. Graphite has more freedom in the layers' sliding over each other, providing slightly higher entropy.
Consider the molecular freedom of buckminsterfullerene. The spherical shape and molecular structure allow for rotation and other molecular motions that are not possible in the rigid lattice of diamond or the planar layers of graphite.
Conclude that the entropy of buckminsterfullerene would likely be higher than that of diamond due to its greater molecular freedom, but potentially similar or slightly higher than graphite depending on the extent of internal molecular motion allowed in its structure.
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Entropy (S°)
Entropy is a measure of the disorder or randomness in a system. It quantifies the number of possible microstates that correspond to a given macrostate. In thermodynamics, higher entropy values indicate greater disorder and more available energy states, which is crucial for understanding the stability and reactivity of substances.
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Entropy in Thermodynamics
Allotropes of Carbon
Allotropes are different structural forms of the same element, in this case, carbon. Graphite, diamond, and buckminsterfullerene (C60) are distinct allotropes with unique arrangements of carbon atoms, leading to different physical and chemical properties, including variations in entropy due to differences in molecular structure and bonding.
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Comparative Entropy of Allotropes
When comparing the entropies of different allotropes, one must consider their molecular complexity and structural arrangements. Graphite, with its layered structure, typically has higher entropy than diamond, which has a rigid three-dimensional lattice. Buckminsterfullerene, being a spherical molecule with a unique structure, is expected to have an entropy value that reflects its complexity, likely falling between those of graphite and diamond.
Related Practice
Textbook Question
The standard entropies at 298 K for certain group 4A elements are: C(s, diamond) = 2.43 J>mol@K, Si1s2 = 18.81 J>mol@K, Ge1s2 = 31.09 J>mol@K, and Sn1s2 = 51.818 J>mol@K. All but Sn have the same (diamond) structure. How do you account for the trend in the S° values?
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Textbook Question
Using S° values from Appendix C, calculate ΔS° values for the following reactions. In each case, account for the sign of ΔS°.
(a) C2H4(g) + H2(g) → C2H6(g)
(b) N2O4(g) → 2 NO2(g)
(c) Be(OH)2(s) → BeO(s) + H2O(g)
(d) 2 CH3OH(g) + 3 O2(g) ⟶ 2 CO2(g) + 4 H2O(g)
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