Textbook Question
(a) What is the difference between a state and a microstate of a system?
Ch.19 - Chemical Thermodynamics
Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970
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Table of contents
- Ch.1 - Introduction: Matter, Energy, and Measurement146
- Ch.2 - Atoms, Molecules, and Ions200
- Ch.3 - Chemical Reactions and Reaction Stoichiometry176
- Ch.4 - Reactions in Aqueous Solution155
- Ch.5 - Thermochemistry126
- Ch.6 - Electronic Structure of Atoms131
- Ch.7 - Periodic Properties of the Elements126
- Ch.8 - Basic Concepts of Chemical Bonding123
- Ch.9 - Molecular Geometry and Bonding Theories143
- Ch.10 - Gases147
- Ch.11 - Liquids and Intermolecular Forces91
- Ch.12 - Solids and Modern Materials122
- Ch.13 - Properties of Solutions126
- Ch.14 - Chemical Kinetics174
- Ch.15 - Chemical Equilibrium101
- Ch.16 - Acid-Base Equilibria139
- Ch.17 - Additional Aspects of Aqueous Equilibria146
- Ch.18 - Chemistry of the Environment72
- Ch.19 - Chemical Thermodynamics129
- Ch.20 - Electrochemistry142
- Ch.21 - Nuclear Chemistry101
- Ch.22 - Chemistry of the Nonmetals68
- Ch.23 - Transition Metals and Coordination Chemistry66
- Ch.24 - The Chemistry of Life: Organic and Biological Chemistry10
Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970Not the one you use?Change textbook
Chapter 19, Problem 30c
(c) In a particular spontaneous process, the number of microstates available to the system decreases. What can you conclude about the sign of ΔSsurr?
Verified step by step guidance1
Understand the concept of microstates: Microstates refer to the different ways in which the energy of a system can be distributed among its particles. An increase in the number of microstates corresponds to an increase in entropy (S).
Relate microstates to entropy: If the number of microstates decreases, it implies that the entropy of the system (ΔSsys) decreases. This is because there are fewer ways to distribute energy, indicating a more ordered state.
Consider the second law of thermodynamics: The second law states that for a spontaneous process, the total entropy of the universe (system + surroundings) must increase. Thus, if ΔSsys is negative, ΔSsurr (entropy change of the surroundings) must be positive to compensate and ensure the total entropy increases.
Conclude the sign of ΔSsurr: Since the process is spontaneous and the system's entropy decreases (ΔSsys is negative), the surroundings' entropy, ΔSsurr, must be positive to maintain the overall increase in entropy of the universe.
Summarize the relationship: A decrease in the number of microstates in a spontaneous process indicates a negative ΔSsys and a compensatory positive ΔSsurr to uphold the second law of thermodynamics.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Microstates and Entropy
Microstates refer to the different ways in which a system can be arranged at the molecular level while maintaining the same macroscopic properties. Entropy (S) is a measure of the number of microstates available to a system; higher entropy indicates more microstates. In spontaneous processes, the overall entropy of the universe tends to increase, which is linked to the distribution of microstates.
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Second Law of Thermodynamics
The Second Law of Thermodynamics states that in any spontaneous process, the total entropy of an isolated system will always increase over time. This implies that while the entropy of a system may decrease, the entropy of the surroundings must increase sufficiently to ensure that the total entropy change (system plus surroundings) is positive, leading to a spontaneous process.
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Surroundings and System Entropy Changes
In thermodynamics, the change in entropy of the surroundings (ΔS_surr) is related to the heat exchanged with the system divided by the temperature of the surroundings. If a system experiences a decrease in entropy (as indicated by a decrease in microstates), the surroundings must compensate by increasing their entropy, which typically results in a positive ΔS_surr, indicating that the surroundings gain disorder.
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Related Practice
Textbook Question
Would each of the following changes increase, decrease, or have no effect on the number of microstates available to a system: (b) decrease in volume
Textbook Question
For the isothermal expansion of a gas into a vacuum, ΔE = 0, q = 0, and w = 0. (b) Explain why no work is done by the system during this process.
Textbook Question
(b) As a system goes from state A to state B, its entropy decreases. What can you say about the number of microstates corresponding to each state?
Textbook Question
(a) In a chemical reaction, two gases combine to form a solid. What do you expect for the sign of ΔS?