To determine the amount of heat required to melt 45.00 grams of ice at [tex]\(0^\circ C\)[/tex], we use the concept of latent heat of fusion. The latent heat of fusion is the amount of heat required to convert a unit mass of a substance from solid to liquid at its melting point without changing its temperature.
Given data:
- Mass of ice, [tex]\( m = 45.00 \)[/tex] grams
- Latent heat of fusion of water, [tex]\( L_f = 333.7 \)[/tex] J/g
The formula to calculate the heat [tex]\( Q \)[/tex] needed to melt the ice is:
[tex]\[ Q = m \times L_f \][/tex]
Plugging in the given values:
[tex]\[ Q = 45.00 \, \text{grams} \times 333.7 \, \text{J/g} \][/tex]
Performing the multiplication:
[tex]\[ Q = 45.00 \times 333.7 = 15016.5 \, \text{J} \][/tex]
So, the amount of heat needed to melt 45.00 grams of ice at [tex]\(0^\circ C\)[/tex] is [tex]\( 15016.5 \)[/tex] Joules.
Therefore, the closest answer from the given options is [tex]\( 15,020 \, J \)[/tex].
