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Ch.18 - Thermodynamics: Entropy, Free Energy & Equilibrium
All textbooksMcMurry 8th EditionCh.18 - Thermodynamics: Entropy, Free Energy & EquilibriumProblem 56d
Chapter 18, Problem 56d

Which state in each of the following pairs has the higher entropy per mole of substance? (d) CO2 at STP or CO2 at 100 °C and 0.1 atm

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Identify the concept of entropy: Entropy is a measure of the disorder or randomness in a system. Generally, the more disordered a system, the higher its entropy.
Consider the conditions given: STP (Standard Temperature and Pressure) is defined as 0 °C (273.15 K) and 1 atm pressure. The other condition is 100 °C and 0.1 atm.
Analyze the effect of temperature on entropy: Increasing temperature generally increases the entropy of a substance because the molecules have more energy and can move more freely, leading to greater disorder.
Analyze the effect of pressure on entropy: Lowering the pressure of a gas increases its volume, allowing the gas molecules to spread out more, which increases the disorder and thus the entropy.
Compare the two states: CO_2 at STP (273.15 K, 1 atm) versus CO_2 at 100 °C (373.15 K) and 0.1 atm. Consider both the higher temperature and lower pressure in the second condition, both of which contribute to higher entropy.

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Key Concepts

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

Entropy

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. Higher entropy indicates greater disorder and more available microstates, which typically occurs at higher temperatures or in less constrained environments.
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Effect of Temperature on Entropy

Temperature has a direct impact on the entropy of a substance. As temperature increases, the kinetic energy of the molecules also increases, leading to greater molecular motion and, consequently, higher entropy. This means that a gas at a higher temperature will generally have higher entropy than the same gas at a lower temperature.
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Effect of Pressure on Entropy

Pressure influences the entropy of gases significantly. At lower pressures, gas molecules have more space to move around, resulting in higher entropy. Conversely, at higher pressures, the molecules are more confined, leading to lower entropy. Therefore, comparing states at different pressures is crucial for determining their relative entropies.
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Related Practice
Textbook Question
Consider the distribution of ideal gas molecules among three bulbs (A, B, and C) of equal volume. For each of the follow-ing states, determine the number of ways (W) that the state can be achieved, and use Boltzmann's equation to calculate the entropy of the state. (a) 2 molecules in bulb A(b) 2 molecules randomly distributed among bulbs A, B, and C
Textbook Question
Which state has higher entropy? Explain in terms of probability. (a) A perfectly ordered crystal of solid nitrous oxide

or a disordered crystal in which the molecules are oriented randomly (b) Quartz glass (an amorphous solid) or a quartz crystal
Textbook Question

Which state in each of the following pairs has the higher entropy per mole of substance? (a) H2 at 25 °C in a volume of 10 L or H2 at 25 °C in a volume of 50 L

Textbook Question

Which state in each of the following pairs has the higher entropy per mole of substance? (a) Ice at -40 °C or ice at 0 °C

Textbook Question

Which state in each of the following pairs has the higher entropy per mole of substance? (b) N2 at STP or N2 at 0 °C and 10 atm

Textbook Question

Which state in each of the following pairs has the higher entropy per mole of substance? (d) Water vapor at 150 °C and 1 atm or water vapor at 100 °C and 2 atm