Melting & boiling point of NaCl respectively are 1080 K & 1600K. `Delta S` for stage -I & II in `NaCl_((s)) underset(Delta H_("fus") = 30kJ)overset(I)rarr NaCl_((l)) underset(Delta H_("vap") = 160kJ)overset(II)rarr` are

Answer

To solve the problem, we need to calculate the entropy changes (ΔS) for two stages of the phase transitions of sodium chloride (NaCl): from solid to liquid (melting) and from liquid to gas (boiling).

### Step-by-Step Solution

1. **Identify Given Data**:
- Melting point (T1) of NaCl = 1080 K
- Boiling point (T2) of NaCl = 1600 K
- Enthalpy of fusion (ΔH_fus) = 30 kJ
- Enthalpy of vaporization (ΔH_vap) = 160 kJ

2. **Understand the Relationship**:
The change in entropy (ΔS) for a phase transition can be calculated using the formula:
\[ \Delta S = \frac{\Delta H}{T} \]
where ΔH is the enthalpy change and T is the temperature at which the transition occurs.

3. **Calculate ΔS for Stage I (Melting)**:
For the melting of NaCl (solid to liquid):
- ΔH_fus = 30 kJ (this is the energy absorbed during melting)
- Use the formula:
\[ \Delta S_1 = \frac{\Delta H_{fus}}{T_1} = \frac{30 \text{ kJ}}{1080 \text{ K}} \]
- Convert kJ to J for consistency in units (1 kJ = 1000 J):
\[ \Delta S_1 = \frac{30000 \text{ J}}{1080 \text{ K}} \approx 27.78 \text{ J/K} \]

4. **Calculate ΔS for Stage II (Boiling)**:
For the boiling of NaCl (liquid to gas):
- ΔH_vap = 160 kJ (this is the energy absorbed during boiling)
- Use the formula:
\[ \Delta S_2 = \frac{\Delta H_{vap}}{T_2} = \frac{160 \text{ kJ}}{1600 \text{ K}} \]
- Again, convert kJ to J:
\[ \Delta S_2 = \frac{160000 \text{ J}}{1600 \text{ K}} = 100 \text{ J/K} \]

5. **Final Results**:
- ΔS for melting (Stage I):
\[ \Delta S_1 \approx 27.78 \text{ J/K} \]
- ΔS for boiling (Stage II):
\[ \Delta S_2 = 100 \text{ J/K} \]

### Summary of Results:
- ΔS for Stage I (melting): **27.78 J/K**
- ΔS for Stage II (boiling): **100 J/K**