Explanation:

The latent heat of fusion is the amount of heat energy required to change a substance from a solid to a liquid state without changing its temperature. In this case, we are given that the latent heat of fusion of ice is 0.333 kJ per gram.

Step 1: Convert grams to moles
To calculate the increase in entropy when 1 mole of water melts at 0 degrees Celsius, we first need to convert the given mass (in grams) to moles. The molar mass of water (H2O) is approximately 18.015 g/mol.

Step 2: Calculate the heat energy
The heat energy required to melt 1 mole of water can be calculated using the equation Q = n * ΔHf, where Q is the heat energy, n is the number of moles, and ΔHf is the latent heat of fusion. Substituting the given values, we have:
Q = 1 mol * 0.333 kJ/mol = 0.333 kJ

Step 3: Calculate the increase in entropy
The increase in entropy (ΔS) can be calculated using the equation ΔS = Q / T, where Q is the heat energy and T is the temperature in Kelvin. The melting point of water is 0 degrees Celsius, which is equivalent to 273.15 Kelvin.

Substituting the values, we have:
ΔS = 0.333 kJ / 273.15 K = 0.00122 kJ/K

To convert kJ to J, we multiply by 1000:
ΔS = 0.00122 kJ/K * 1000 J/kJ = 1.22 J/K

Finally, to convert J/K to J/K/mol, we divide by the number of moles:
ΔS = 1.22 J/K / 1 mol = 1.22 J/K/mol

Therefore, the increase in entropy when 1 mole of water melts at 0 degrees Celsius is 1.22 J/K/mol, which is approximately equal to 21.98 J/K/mol (rounded to two decimal places).

Summary:
The increase in entropy when 1 mole of water melts at 0 degrees Celsius is 21.98 J per K per mol. This value is calculated by converting the given mass of water to moles, calculating the heat energy required using the latent heat of fusion, and then dividing the heat energy by the temperature in Kelvin.