Enthalpy of Fusion of Water:
The enthalpy of fusion of water is given as 1.435 kilo calorie per mole. This value represents the amount of energy required to melt one mole of ice at 0°C.

Molar Entropy Change:
The molar entropy change for the melting of ice at 0°C can be calculated using the following formula:

ΔS = ΔH / T

Where ΔS is the molar entropy change, ΔH is the enthalpy of fusion, and T is the temperature at which the reaction occurs.

Calculation:
Substituting the given values, we get:

ΔS = 1.435 kcal/mol / 273.15 K

ΔS = 0.00525 kcal/(mol.K)

The molar entropy change for the melting of ice at 0°C is 0.00525 kcal/(mol.K).

Explanation:
The molar entropy change for the melting of ice at 0°C is a measure of the amount of disorder or randomness that occurs when ice melts. As ice melts, the water molecules become more disordered and free to move around, resulting in an increase in entropy. The molar entropy change can be calculated using the enthalpy of fusion and the temperature at which the reaction occurs. The higher the enthalpy of fusion, the more energy is required to melt the ice, and the lower the molar entropy change. Conversely, a lower enthalpy of fusion results in a higher molar entropy change.