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 12.9 for heats of fusion.

검증된 단계별 안내

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 isopropyl alcohol at its melting point.

Convert the melting point from Celsius to Kelvin by adding 273.15 to the Celsius temperature: \( T = -89.5 + 273.15 \).

Substitute the values into the entropy change formula: \( \Delta S = \frac{\Delta H_{\text{fus}}}{T} \). Ensure that \( \Delta H_{\text{fus}} \) is in the same units as the temperature (usually Joules and Kelvin).

Calculate the change in entropy (\( \Delta S \)) using the values obtained in the previous steps.

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주요 개념

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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 changes state, such as melting, the entropy typically increases because the molecules move from a more ordered solid state to a less ordered liquid state.

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 phase transitions, as it provides the necessary energy input to overcome intermolecular forces in the solid state.

Phase Change Calculations

Phase change calculations involve determining the energy changes associated with 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 relationship is essential for understanding how energy and disorder change during phase transitions.

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 12.9 for heats of fusion.