The enthalpy of fusion of water is 1.435 kcal/mol. The molar entropy change for the melting of ice at 0°C is ?

Options

A. 10.52 cal/(mol K)
B. 21.04 cal/(mol K)
C. 5.260 cal/(mol K)
D. 0.526 cal/(mol K).

Explanation

To find the molar entropy change for the melting of ice at 0°C, we can use the formula for entropy change (ΔS) during a phase change, which is given by:

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

Where:
- ΔS = change in entropy (in kcal/mol·K)
- ΔH = change in enthalpy (in kcal/mol)
- T = temperature (in Kelvin)

### Step 1: Identify the given values
- The enthalpy of fusion of water (ΔH) = 1.435 kcal/mol
- The temperature (T) = 0°C = 273 K (since we convert Celsius to Kelvin by adding 273)

### Step 2: Substitute the values into the formula
Now, we can substitute the values into the entropy change formula:

\[ \Delta S = \frac{1.435 \text{ kcal/mol}}{273 \text{ K}} \]

### Step 3: Perform the calculation
Now we perform the division:

\[ \Delta S = \frac{1.435}{273} \approx 0.00526 \text{ kcal/mol·K} \]

### Step 4: Convert to calories if needed
Since 1 kcal = 1000 cal, we can convert the result into calories:

\[ \Delta S \approx 0.00526 \text{ kcal/mol·K} \times 1000 \text{ cal/kcal} = 5.26 \text{ cal/mol·K} \]

### Final Answer
The molar entropy change for the melting of ice at 0°C is approximately:

\[ \Delta S \approx 5.26 \text{ cal/mol·K} \]

---