At `27 ^(@)C` latent heat of fusion of a compound is 3930 J/mol. Entropy change is

Options

A. `13.10J/mol K`
B. `10.77 J/mol K`
C. `9.07 J/mol K`
D. `0.977 J/mol K`

Answer

To find the entropy change during the phase transition from solid to liquid at a given temperature, we can use the formula for entropy change (ΔS):

\[ \Delta S = \frac{Q}{T} \]

where:
- \(Q\) is the latent heat of fusion (in joules per mole),
- \(T\) is the absolute temperature (in kelvin).

### Step-by-Step Solution:

1. **Identify the given values**:
- Latent heat of fusion, \(Q = 3930 \, \text{J/mol}\)
- Temperature in Celsius, \(T = 27 \, ^\circ C\)

2. **Convert the temperature to Kelvin**:
\[ T(K) = T(°C) + 273 = 27 + 273 = 300 \, \text{K} \]

3. **Substitute the values into the entropy change formula**:
\[ \Delta S = \frac{Q}{T} = \frac{3930 \, \text{J/mol}}{300 \, \text{K}} \]

4. **Calculate the entropy change**:
\[ \Delta S = \frac{3930}{300} = 13.1 \, \text{J/K/mol} \]

### Final Answer:
The entropy change (ΔS) is approximately \(13.1 \, \text{J/K/mol}\).

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