The entropy of fusion of water is 5.260 `cal//"mole" K` calculate the enthalpy of fusion of water ?

Options

A. `10.52 Kcal// mol`
B. `0.525 K Cal//mol`
C. `2.225K Cal//mol`
D. `1.435 K Cal//mol`

Explanation

To calculate the enthalpy of fusion of water given the entropy of fusion, we can follow these steps:

### Step 1: Understand the relationship between entropy and enthalpy
The enthalpy of fusion (ΔH) can be calculated using the formula:
\[ \Delta H = T \Delta S \]
where:
- \( T \) is the temperature in Kelvin,
- \( \Delta S \) is the entropy of fusion.

### Step 2: Convert the melting point of water to Kelvin
The melting point of water is 0 degrees Celsius. To convert this to Kelvin:
\[ T = 0 + 273 = 273 \text{ K} \]

### Step 3: Use the given entropy of fusion
The entropy of fusion of water is given as:
\[ \Delta S = 5.260 \text{ cal/mole K} \]

### Step 4: Substitute the values into the formula
Now, we can substitute the values of \( T \) and \( \Delta S \) into the formula:
\[ \Delta H = 273 \text{ K} \times 5.260 \text{ cal/mole K} \]

### Step 5: Calculate the enthalpy of fusion
Calculating the above expression:
\[ \Delta H = 273 \times 5.260 = 1436.58 \text{ cal/mole} \]

### Step 6: Convert calories to kilocalories
Since 1 kilocalorie = 1000 calories, we convert:
\[ \Delta H = \frac{1436.58 \text{ cal/mole}}{1000} = 1.43658 \text{ kcal/mole} \]

### Step 7: Round to appropriate significant figures
Rounding to three significant figures, we have:
\[ \Delta H \approx 1.437 \text{ kcal/mole} \]

### Final Answer
The enthalpy of fusion of water is approximately:
\[ \Delta H \approx 1.437 \text{ kcal/mole} \]

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