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. (a) `805.75 ^(@)C`
B. (b) `500 K`
C. (c) `1.77 K`
D. (d) `1.77 ^(@)C`

Answer

To find the melting point of NaCl using the given values of heat required for melting and the change in entropy, we can use the relationship between enthalpy (ΔH), entropy (ΔS), and temperature (T). The formula we will use is:

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

### Step-by-Step Solution:

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

2. **Convert Units**:
- Convert ΔH from kcal to cal:
\[ \Delta H = 7.26 \text{ kcal/mol} \times 1000 \text{ cal/kcal} = 7260 \text{ cal/mol} \]

3. **Rearrange the Formula**:
- We need to find the temperature (T). Rearranging the formula gives:
\[ T = \frac{\Delta H}{\Delta S} \]

4. **Substitute the Values**:
- Substitute the values of ΔH and ΔS into the rearranged formula:
\[ T = \frac{7260 \text{ cal/mol}}{6.73 \text{ cal/mol·K}} \]

5. **Calculate T**:
- Performing the division:
\[ T = 1078.75 \text{ K} \]

6. **Convert Temperature to Celsius**:
- To convert from Kelvin to Celsius, subtract 273:
\[ T_{°C} = T_{K} - 273 = 1078.75 \text{ K} - 273 = 805.75 \text{ °C} \]

### Final Answer:
The melting point of NaCl is **805.75 °C**.