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Ch.19 - Chemical Thermodynamics
All textbooksBrown 14th EditionCh.19 - Chemical ThermodynamicsProblem 29
Chapter 19, Problem 29

For the isothermal expansion of a gas into a vacuum, ΔE = 0, q = 0, and w = 0. (c) What is the “driving force” for the expansion of the gas: enthalpy or entropy?

Verified step by step guidance
1
Understand the scenario: The problem describes an isothermal expansion of a gas into a vacuum, which is also known as a free expansion. In this process, the gas expands without any external pressure opposing it.
Recall the first law of thermodynamics: ΔE = q + w, where ΔE is the change in internal energy, q is the heat exchanged, and w is the work done. In this case, ΔE = 0, q = 0, and w = 0, indicating no change in internal energy, no heat exchange, and no work done.
Consider the concept of enthalpy (H): Enthalpy is defined as H = E + PV, where E is the internal energy, P is the pressure, and V is the volume. Since there is no heat exchange or work done, enthalpy does not change significantly in this process.
Consider the concept of entropy (S): Entropy is a measure of the disorder or randomness of a system. In a free expansion, the gas molecules spread out to occupy a larger volume, increasing the disorder of the system.
Determine the driving force: Since enthalpy remains constant and entropy increases due to the increased disorder, the driving force for the expansion of the gas is the increase in entropy.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Isothermal Process

An isothermal process occurs at a constant temperature, meaning that the internal energy of an ideal gas remains unchanged during the expansion or compression. In this scenario, the heat exchanged (q) and work done (w) are balanced such that the change in internal energy (ΔE) is zero. This concept is crucial for understanding the thermodynamic behavior of gases under specific conditions.
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Enthalpy vs. Entropy

Enthalpy (H) is a measure of the total heat content of a system, while entropy (S) quantifies the degree of disorder or randomness in a system. In the context of gas expansion, entropy is often the driving force, as it reflects the tendency of systems to move towards greater disorder. Understanding the distinction between these two concepts helps clarify the thermodynamic principles at play during gas expansion.
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Thermodynamic Equilibrium

Thermodynamic equilibrium refers to a state where a system's macroscopic properties are uniform and do not change over time. In the case of gas expanding into a vacuum, the system reaches equilibrium when the gas uniformly fills the available space. This concept is essential for analyzing the conditions under which the gas expands and the role of entropy in driving the process.
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Related Practice
Textbook Question

(c) During a certain reversible process, the surroundings undergo an entropy change, ΔSsurr = -78 J/K. What is the entropy change of the system for this process?

Textbook Question
(a) What sign for ΔS do you expect when the pressure on 0.600 mol of an ideal gas at 350 K is increased isothermally from an initial pressure of 0.750 atm? (b) If the final pressure on the gas is 1.20 atm, calculate the entropy change for the process. (c) Do you need to specify the temperature to calculate the entropy change?
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

(a) What is the difference between a state and a microstate of a system?

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?