To solve this problem, we need to determine the amount of heat required to convert 2.5 grams of zinc from a solid to a liquid without changing its temperature. This process involves the concept of latent heat of fusion, which is the heat required per gram to change a substance from solid to liquid at its melting point.
Given the information:
- Mass of zinc ([tex]\(m\)[/tex]) = 2.5 grams
- Latent heat of fusion for zinc ([tex]\(L\)[/tex]) = 112 cal/g
The formula to calculate the heat ([tex]\(Q\)[/tex]) needed to melt a substance is:
[tex]\[ Q = m \times L \][/tex]
Substituting the given values:
[tex]\[ Q = 2.5 \, \text{grams} \times 112 \, \text{cal/gram} \][/tex]
Performing the multiplication:
[tex]\[ Q = 280 \, \text{cal} \][/tex]
Finally, rounding the answer to the nearest whole number:
[tex]\[ Q = 280 \][/tex]
Therefore, the amount of heat needed to convert 2.5 grams of zinc from a solid to a liquid without changing its temperature is 280.
