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Ch.18 - Free Energy and Thermodynamics
Tro - Chemistry: A Molecular Approach 4th Edition
Tro4th EditionChemistry: A Molecular ApproachISBN: 9780134112831Not the one you use?Change textbook
All textbooksTro 4th EditionCh.18 - Free Energy and ThermodynamicsProblem 32
Chapter 18, Problem 32

Calculate the change in entropy that occurs in the system when 1.00 mole of diethyl ether (C4H10O) condenses from a gas to a liquid at its normal boiling point (34.6 °C). See Table 11.7 for heats of vaporization.

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1
Identify the process: The problem involves the condensation of diethyl ether from gas to liquid at its boiling point.
Recall that the change in entropy (\( \Delta S \)) for a phase change can be calculated using the formula \( \Delta S = \frac{\Delta H_{\text{vap}}}{T} \), where \( \Delta H_{\text{vap}} \) is the heat of vaporization and \( T \) is the temperature in Kelvin.
Convert the given temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature: \( T = 34.6 + 273.15 \).
Look up the heat of vaporization (\( \Delta H_{\text{vap}} \)) for diethyl ether from Table 11.7. Ensure the units are consistent, typically in Joules per mole (J/mol).
Substitute the values of \( \Delta H_{\text{vap}} \) and \( T \) into the formula \( \Delta S = \frac{\Delta H_{\text{vap}}}{T} \) to find the change in 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. In thermodynamics, it quantifies the amount of energy in a physical system that is not available to do work. When a substance transitions from gas to liquid, such as diethyl ether condensing, the entropy typically decreases because the molecules become more ordered in the liquid state.
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Heat of Vaporization

The heat of vaporization is the amount of energy required to convert a unit mass of a substance from liquid to gas at its boiling point. This value is crucial for calculating changes in entropy during phase transitions. For diethyl ether, the heat of vaporization will provide the necessary energy value to determine the entropy change when it condenses.
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Phase Change and Temperature

Phase changes, such as condensation, occur at specific temperatures known as boiling or melting points. The normal boiling point of diethyl ether is 34.6 °C, which is the temperature at which it transitions from gas to liquid under standard atmospheric pressure. Understanding the relationship between temperature and phase changes is essential for calculating thermodynamic properties like entropy.
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Related Practice
Textbook Question

Without doing any calculations, determine the sign of ΔSsys for each chemical reaction. a. 2 KClO3(s) → 2 KCl(s) + 3 O2(g) c. Na(s) + 2 Cl2(g) → NaCl(s) d. N2(g) + 3 H2(g) → 2 NH3(g)

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Textbook Question

Two systems, each composed of two particles represented by circles, have 20 J of total energy. Which system, A or B, has the greater entropy? Why?

Textbook Question

Calculate the change in entropy that occurs in the system when 1.00 mole of isopropyl alcohol (C3H8O) melts at its melting point (-89.5 °C). See Table 11.9 for heats of fusion.

Textbook Question

Two systems, each composed of three particles represented by circles, have 30 J of total energy. How many energetically equivalent ways can you distribute the particles in each system? Which system has greater entropy?