Ch.18 - Thermodynamics: Entropy, Free Energy & Equilibrium

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McMurry 8th Edition

Ch.18 - Thermodynamics: Entropy, Free Energy & Equilibrium

Problema 30

Capitolo 18, Problema 30

An ideal gas is compressed at constant temperature. What are the signs ( + , - , or 0) of ∆H, ∆S, and ∆G for the process? Explain.

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Identify that the process involves the compression of an ideal gas at constant temperature.

Recall that for an ideal gas, the internal energy (U) depends only on temperature. Since the temperature is constant, there is no change in internal energy (∆U = 0).

Understand that enthalpy (H) is related to internal energy and pressure-volume work. Since ∆U = 0 and the process is isothermal, ∆H = 0.

Recognize that entropy (S) is a measure of disorder. Compression of a gas decreases its volume, leading to a decrease in entropy (∆S < 0).

Use the Gibbs free energy equation, ∆G = ∆H - T∆S. Since ∆H = 0 and ∆S < 0, ∆G will be positive (∆G > 0) because the term -T∆S will be positive.

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Enthalpy (∆H)

Enthalpy is a measure of the total heat content of a system. In an isothermal process, such as the compression of an ideal gas at constant temperature, the internal energy remains constant, and any work done on the gas is balanced by heat exchange with the surroundings. For this process, ∆H is 0, indicating no net heat transfer into or out of the system.

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Enthalpy of Formation

Entropy (∆S)

Entropy is a measure of the disorder or randomness in a system. When an ideal gas is compressed, the number of available microstates decreases, leading to a reduction in disorder. Therefore, for this isothermal compression, ∆S is negative, reflecting a decrease in the system's entropy as the gas molecules are forced closer together.

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Entropy in Thermodynamics

Gibbs Free Energy (∆G)

Gibbs Free Energy combines enthalpy and entropy to determine the spontaneity of a process. The relationship is given by the equation ∆G = ∆H - T∆S. Since ∆H is 0 and ∆S is negative, ∆G will be positive, indicating that the process is non-spontaneous under constant temperature conditions. This means that work must be done on the system to achieve the compression.

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Gibbs Free Energy of Reactions

Pratica correlata

Domanda del libro di testo

Consider the dissociation reaction A₂(g) ⇌ 2 A(g). The following pictures represent two possible initial states and the equilibrium state of the system:

(b) What are the signs ( + , - , or 0) of ∆H, ∆S, and ∆G when the system goes from initial state 1 to the equilibrium state? Explain. Is this a spontaneous process?

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Domanda del libro di testo

Rank the situations represented by the following drawings according to increasing entropy.

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The following pictures represent equilibrium mixtures for the interconversion of A molecules (red) and X, Y, or Z molecules (blue):

What is the sign of ∆G° for each of the three reactions?

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Domanda del libro di testo

Ideal gases A (red spheres) and B (blue spheres) occupy two separate bulbs. The contents of both bulbs constitute the initial state of an isolated system. Consider the process that occurs when the stopcock is opened.

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Domanda del libro di testo

Consider again the dissociation reaction

(e) What is the value of ∆G for the dissociation reaction when the system is at equilibrium?

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Domanda del libro di testo

(d) Relate each of the pictures to the graph in Figure 18.11.

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