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
Ch.18 - Thermodynamics: Entropy, Free Energy & Equilibrium
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McMurry 8th EditionCh.18 - Thermodynamics: Entropy, Free Energy & EquilibriumProblem 57b
McMurry 8th EditionCh.18 - Thermodynamics: Entropy, Free Energy & EquilibriumProblem 57bChapter 18, Problem 57b
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
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Entropy is a measure of the disorder or randomness in a system. In general, gases have higher entropy than liquids, and liquids have higher entropy than solids.
For gases, entropy increases with an increase in volume or a decrease in pressure, as the molecules have more space to move around.
STP (Standard Temperature and Pressure) is defined as 0 °C and 1 atm.
Compare the two conditions: N_2 at STP (0 °C, 1 atm) and N_2 at 0 °C and 10 atm.
Since the temperature is the same in both cases, focus on the pressure: lower pressure (1 atm) at STP means higher volume and thus higher entropy compared to 10 atm.
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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 microscopic configurations that correspond to a thermodynamic system's macroscopic state. Higher entropy indicates greater disorder and more available microstates, which typically occurs in gases compared to liquids and solids.
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Ideal Gas Law
The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of an ideal gas through the equation PV = nRT. This law helps predict how gases behave under different conditions, including changes in temperature and pressure, which directly affect the entropy of the gas.
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Standard Temperature and Pressure (STP)
Standard Temperature and Pressure (STP) is defined as a temperature of 0 °C (273.15 K) and a pressure of 1 atm. At STP, gases behave ideally, and their properties, including entropy, can be compared more easily. Deviations from STP, such as increased pressure or decreased temperature, can significantly alter a gas's entropy.
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Related Practice
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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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What is the entropy change when the volume of 1.6 g of O2 increases from 2.5 L to 3.5 L at a constant temperature of 75 °C? Assume that O2 behaves as an ideal gas.
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Textbook Question
Make a rough, qualitative plot of the standard molar entropy versus temperature for methane from 0 K to 298 K. Incorporate the following data into your plot: mp = -182 °C; bp = -164 °C; °S = 186.2 J/(K*mol) at 25 °C.