Calculate entropy changes of fusion and vaporisation for chlorine from the following data :
`Delta_(fus) H = 6.40 kJ "mol"^(-1) m.p = -102^(@)C`
`Delta_(vap) H = 20.4 kJ mol^(-1) b.p = - 34^(@)C`

Explanation

To calculate the entropy changes of fusion and vaporization for chlorine, we will use the formula:

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

where:
- \(\Delta S\) is the change in entropy,
- \(\Delta H\) is the change in enthalpy (in Joules),
- \(T\) is the temperature in Kelvin.

### Step 1: Calculate the Entropy Change of Fusion (\(\Delta S_{fus}\))

1. **Convert \(\Delta H_{fus}\) from kJ/mol to J/mol**:
\[ \Delta H_{fus} = 6.40 \, \text{kJ/mol} = 6.40 \times 1000 \, \text{J/mol} = 6400 \, \text{J/mol} \]

2. **Convert the melting point from Celsius to Kelvin**:
\[ T_{fus} = -102^\circ C + 273 = 171 \, \text{K} \]

3. **Calculate \(\Delta S_{fus}\)**:
\[ \Delta S_{fus} = \frac{\Delta H_{fus}}{T_{fus}} = \frac{6400 \, \text{J/mol}}{171 \, \text{K}} \approx 37.4 \, \text{J/K/mol} \]

### Step 2: Calculate the Entropy Change of Vaporization (\(\Delta S_{vap}\))

1. **Convert \(\Delta H_{vap}\) from kJ/mol to J/mol**:
\[ \Delta H_{vap} = 20.4 \, \text{kJ/mol} = 20.4 \times 1000 \, \text{J/mol} = 20400 \, \text{J/mol} \]

2. **Convert the boiling point from Celsius to Kelvin**:
\[ T_{vap} = -34^\circ C + 273 = 239 \, \text{K} \]

3. **Calculate \(\Delta S_{vap}\)**:
\[ \Delta S_{vap} = \frac{\Delta H_{vap}}{T_{vap}} = \frac{20400 \, \text{J/mol}}{239 \, \text{K}} \approx 85.3 \, \text{J/K/mol} \]

### Final Results:
- The entropy change of fusion for chlorine is approximately \(37.4 \, \text{J/K/mol}\).
- The entropy change of vaporization for chlorine is approximately \(85.3 \, \text{J/K/mol}\).

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