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How much energy does it take to melt 2 kg of ice? (Refer to the table of constants for water.)

A. [tex]\(2 \, \text{kg} \times 1000 \, \text{g/kg} \times \frac{1 \, \text{mol}}{18.02 \, \text{g}} \times 40.65 \, \text{kJ/mol} = 4512 \, \text{kJ}\)[/tex]

B. [tex]\(2 \, \text{kg} \times 1000 \, \text{g/kg} \times \frac{1 \, \text{mol}}{18.02 \, \text{g}} \times 4.186 \, \text{kJ/mol} = 465 \, \text{kJ}\)[/tex]

C. [tex]\(2 \, \text{kg} \times 1000 \, \text{g/kg} \times \frac{1 \, \text{mol}}{18.02 \, \text{g}} \times 6.03 \, \text{kJ/mol} = 669 \, \text{kJ}\)[/tex]

D. [tex]\(2 \, \text{kg} \times 1000 \, \text{g/kg} \times \frac{1 \, \text{mol}}{18.02 \, \text{g}} \times (-285.83 \, \text{kJ/mol}) = -31,724 \, \text{kJ}\)[/tex]

Sagot :

GinnyAnswer
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]
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