The entropy change of fusion (melting) (ΔSfus) of a compound or element is

The entropy change of fusion (\(\Delta S_{\text{fus}}\)) of a compound or element refers to the change in entropy when one mole of the substance transitions from the solid phase to the liquid phase at its melting point. This change in entropy is a measure of the increase in disorder or randomness of the particles as they move from a more ordered solid state to a less ordered liquid state.

The entropy change of fusion can be calculated using the following relationship:

\[ \Delta S_{\text{fus}} = \frac{\Delta H_{\text{fus}}}{T_{\text{fus}}} \]

where:
- \(\Delta H_{\text{fus}}\) is the enthalpy change of fusion (the heat required to melt one mole of the substance) in joules per mole (\(J/mol\)).
- \(T_{\text{fus}}\) is the melting temperature of the substance in Kelvin (K).

### Example Calculation

Let's calculate \(\Delta S_{\text{fus}}\) for water as an example.

- \(\Delta H_{\text{fus}}\) for water is approximately 6.01 kJ/mol (which is 6010 J/mol).
- The melting point of water (\(T_{\text{fus}}\)) is 273.15 K.

Using the formula:

\[ \Delta S_{\text{fus}} = \frac{6010 \, \text{J/mol}}{273.15 \, \text{K}} \approx 22.0 \, \text{J/(mol·K)} \]

This means that the entropy change of fusion for water is approximately 22.0 J/(mol·K).

### Understanding \(\Delta S_{\text{fus}}\)

- **Positive \(\Delta S_{\text{fus}}\)**: This indicates that the entropy increases during the fusion process, which is typical since the liquid phase is usually more disordered than the solid phase.
- **Magnitude of \(\Delta S_{\text{fus}}\)**: The greater the \(\Delta S_{\text{fus}}\), the more significant the increase in disorder when the substance melts.

Would you like more details or have any questions?

Here are some related questions:
1. What is the relationship between enthalpy and entropy changes during a phase transition?
2. How does the entropy change of vaporization compare to the entropy change of fusion?
3. What factors affect the melting point of a substance?
4. How do you experimentally determine the enthalpy change of fusion for a substance?
5. What role does entropy play in determining the spontaneity of phase transitions?
6. Can you describe the entropy changes that occur during the solidification process?
7. How do pressure and temperature influence the phase transitions of substances?
8. What is the significance of the third law of thermodynamics in relation to entropy?

**Tip:** Always ensure to convert units appropriately when using thermodynamic equations, especially when dealing with enthalpy and entropy values.

Understand the entropy change of fusion (melting) of a compound or element with a detailed explanation and calculation example. Learn how to calculate \( \Delta S_{\text{fus}} \), the relationship with enthalpy, and its significance in thermodynamics. Example calculation provided for water.

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