For the meltig of NaCI heat require is `7.26 kcal mol^(-1)` and `Delta S` increases by `6.73 cal mol^(-1) k^(-1)` . The melting point of the salt is

Options

A. `805.75 ^(@)C`
B. `500 K`
C. `1.77 K`
D. `1.77 ^(@)C`

Answer

To find the melting point of NaCl given the heat required for melting and the change in entropy, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Heat required for melting (Q) = 7.26 kcal/mol
- Change in entropy (ΔS) = 6.73 cal/mol·K

2. **Convert Units:**
- Convert Q from kcal to calories:
\[ Q = 7.26 \, \text{kcal/mol} \times 1000 \, \text{cal/kcal} = 7260 \, \text{cal/mol} \]
- ΔS is already in calories, so no conversion is needed.

3. **Use the Relationship between Q, ΔS, and Temperature (T):**
- According to the second law of thermodynamics:
\[ \Delta S = \frac{Q}{T} \]
- Rearranging this formula to find T gives:
\[ T = \frac{Q}{\Delta S} \]

4. **Substitute the Values:**
- Substitute the values of Q and ΔS into the equation:
\[ T = \frac{7260 \, \text{cal/mol}}{6.73 \, \text{cal/mol·K}} \approx 1078.75 \, \text{K} \]

5. **Convert Temperature from Kelvin to Celsius:**
- To convert from Kelvin to Celsius, use the formula:
\[ T(°C) = T(K) - 273.15 \]
- Thus:
\[ T(°C) = 1078.75 \, \text{K} - 273.15 \approx 805.60 \, °C \]

### Final Answer:
The melting point of NaCl is approximately **805.60 °C**.