To determine the amount of energy required to melt 2 kilograms (kg) of ice, we need to follow these steps:
1. Convert the mass of ice from kilograms to grams.
- Since there are 1000 grams (g) in 1 kilogram (kg):
[tex]\[
2 \, \text{kg} \times 1000 \, \frac{\text{g}}{\text{kg}} = 2000 \, \text{g}
\][/tex]
2. Calculate the number of moles of ice (water) from the mass (in grams).
- The molar mass of water (H₂O) is approximately 18.02 grams per mole (g/mol):
[tex]\[
\frac{2000 \, \text{g}}{18.02 \, \frac{\text{g}}{\text{mol}}} \approx 110.99 \, \text{mol}
\][/tex]
3. Determine the energy needed to melt the ice using the heat of fusion of water.
- The heat of fusion is the amount of energy required to change 1 mole of a substance from solid to liquid at its melting point. For water, this is approximately 6.03 kilojoules per mole (kJ/mol):
[tex]\[
110.99 \, \text{mol} \times 6.03 \, \frac{\text{kJ}}{\text{mol}} \approx 669.26 \, \text{kJ}
\][/tex]
So, the energy required to melt 2 kg of ice is approximately 669 kJ. Therefore, the correct answer is:
C. [tex]\(2 \, \text{kg} \times 1000 \, \frac{\text{g}}{\text{kg}} \times \frac{1 \, \text{mol}}{18.02 \, \frac{\text{g}}{\text{mol}}} \times 6.03 \, \frac{\text{kJ}}{\text{mol}} = 669 \, \text{kJ}\)[/tex]
