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Ch.18 - Free Energy and Thermodynamics
Tro - Chemistry: A Molecular Approach 4th Edition
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Tutti i libri di testoTro 4th EditionCh.18 - Free Energy and ThermodynamicsProblema 32
Capitolo 18, Problema 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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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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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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Entropy in Thermodynamics

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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Heat Capacity

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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Entropy in Phase Changes
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