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Ch.9 - Thermochemistry: Chemical Energy
All textbooksMcMurry 8th EditionCh.9 - Thermochemistry: Chemical EnergyProblem 138
Chapter 9, Problem 138

Ethyl alcohol has ΔHfusion = 5.02 kJ/mol and melts at - 114.1 °C. What is the value of ΔSfusion for ethyl alcohol?

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Identify the formula to calculate the change in entropy (\( \Delta S \)) during the phase transition: \( \Delta S = \frac{\Delta H}{T} \).
Note that \( \Delta H_{\text{fusion}} \) is given as 5.02 kJ/mol.
Convert the melting point from Celsius to Kelvin by adding 273.15 to the Celsius temperature: \( T = -114.1 + 273.15 \).
Substitute the values of \( \Delta H_{\text{fusion}} \) and \( T \) (in Kelvin) into the formula: \( \Delta S = \frac{5.02 \text{ kJ/mol}}{T} \).
Ensure the units are consistent, typically converting \( \Delta H \) to J/mol if \( \Delta S \) is required in J/(mol·K).

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Key Concepts

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

Enthalpy of Fusion (ΔH<sub>fusion</sub>)

The enthalpy of fusion is the amount of energy required to change a substance from solid to liquid at its melting point. For ethyl alcohol, this value is given as 5.02 kJ/mol, indicating the energy needed to overcome intermolecular forces during the melting process.
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Entropy (ΔS)

Entropy is a measure of the disorder or randomness in a system. When a solid melts into a liquid, the entropy increases because the molecules have more freedom to move. The change in entropy during fusion (ΔS<sub>fusion</sub>) can be calculated using the relationship between enthalpy and temperature.
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Gibbs Free Energy and Phase Changes

The Gibbs free energy change (ΔG) during a phase change can be expressed as ΔG = ΔH - TΔS. At equilibrium, such as at the melting point, ΔG is zero, allowing us to relate ΔH<sub>fusion</sub> and ΔS<sub>fusion</sub> to find the entropy change using the formula ΔS<sub>fusion</sub> = ΔH<sub>fusion</sub> / T, where T is the absolute temperature in Kelvin.
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Related Practice
Textbook Question
(d) What is the kinetic energy of an electron traveling at velocity (c)?
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Textbook Question

What is the melting point of benzene in kelvin if ΔHfusion = 9.95 kJ/mol and ΔSfusion = 35.7 J/(K mol)?

Textbook Question
Metallic mercury is obtained by heating the mineral cinnabar (HgS) in air:HgS1s2 + O21g2 S Hg1l2 + SO21g2(a) Use the data in Appendix B to calculate ΔH° in kilojoules for the reaction.