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Ch.19 - Free Energy & Thermodynamics
Tro - Chemistry: A Molecular Approach 6th Edition
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Capitolo 19, Problema 31

Calculate the change in entropy that occurs in the system when 1.50 mol of isopropyl alcohol (C3H8O) melts at its melting point (-89.5 °C). See Table 12.9 for heats of fusion.

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Identify the formula for calculating the change in entropy (\( \Delta S \)) during a phase change: \( \Delta S = \frac{q_{\text{rev}}}{T} \), where \( q_{\text{rev}} \) is the heat absorbed or released during the process and \( T \) is the temperature in Kelvin.
Determine the heat of fusion (\( \Delta H_{\text{fus}} \)) for isopropyl alcohol from Table 12.9. This value represents the amount of heat required to melt one mole of the substance at its melting point.
Calculate the total heat absorbed (\( q_{\text{rev}} \)) by multiplying the heat of fusion by the number of moles: \( q_{\text{rev}} = n \times \Delta H_{\text{fus}} \), where \( n = 1.50 \) mol.
Convert the melting point from Celsius to Kelvin by adding 273.15 to the Celsius temperature: \( T = -89.5 + 273.15 \).
Substitute the values of \( q_{\text{rev}} \) and \( T \) into the entropy change formula to find \( \Delta S \): \( \Delta S = \frac{q_{\text{rev}}}{T} \).

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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 undergoes a phase change, such as melting, the entropy typically increases because the molecules move from a more ordered solid state to a less ordered liquid state.
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Entropy in Thermodynamics

Heats of Fusion

The heat of fusion is the amount of energy required to change a substance from solid to liquid at its melting point without changing its temperature. This value is crucial for calculating the change in entropy during melting, as it provides the necessary energy input needed to overcome the intermolecular forces holding the solid together.
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Heat Capacity

Phase Change Calculations

Phase change calculations involve using thermodynamic principles to determine changes in energy and entropy during transitions between solid, liquid, and gas states. For melting, the change in entropy can be calculated using the formula ΔS = ΔH_fusion / T, where ΔH_fusion is the heat of fusion and T is the absolute temperature in Kelvin. This approach is essential for quantifying the thermodynamic properties of substances during phase changes.
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