Calculate the change in entropy for the fusion of 1 mole of ice (water). The melting point of water is 273 K and molar enthalpy of funsion for water `=6.0 kJ mol^(-1)`

Explanation

To calculate the change in entropy for the fusion of 1 mole of ice (water), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given data:**
- Molar enthalpy of fusion (ΔH_fusion) = 6.0 kJ/mol
- Melting point of water (T) = 273 K

2. **Convert the enthalpy from kJ to J:**
- Since 1 kJ = 1000 J, we convert:
\[ \Delta H_{fusion} = 6.0 \, \text{kJ/mol} \times 1000 \, \text{J/kJ} = 6000 \, \text{J/mol} \]

3. **Use the formula for change in entropy (ΔS):**
- The change in entropy for a phase change at constant temperature is given by:
\[ \Delta S = \frac{\Delta H_{fusion}}{T} \]

4. **Substitute the values into the formula:**
- Now, substituting the values we have:
\[ \Delta S = \frac{6000 \, \text{J/mol}}{273 \, \text{K}} \]

5. **Calculate ΔS:**
- Performing the division:
\[ \Delta S = \frac{6000}{273} \approx 21.97 \, \text{J/K/mol} \]

6. **Conclusion:**
- The change in entropy for the fusion of 1 mole of ice at its melting point is approximately:
\[ \Delta S \approx 21.97 \, \text{J/K/mol} \]

### Final Answer:
The change in entropy for the fusion of 1 mole of ice (water) is approximately **21.97 J/K/mol**.

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