# Heat of Fusion Example Problem: Melting Ice

## Calculate the Energy Needed to Change a Solid Into a Liquid

Heat of fusion is the amount of heat energy required to change the state of matter of a substance from a solid to a liquid. It's also known as enthalpy of fusion. Its units are usually Joules per gram (J/g) or calories per gram (cal/g). This example problem demonstrates how to calculate the amount of energy required to melt a sample of water ice.

### Key Takeaways: Heat of Fusion for Melting Ice

• Heat of fusion is the amount of energy in the form of heat needed to change the state of matter from a solid to a liquid (melting.)
• The formula to calculate heat of fusion is: q = m·ΔHf
• Note that the temperature does not actually change when matter changes state, so it's not in the equation or needed for the calculation.
• Except for melting helium, heat of fusion is always a positive value.

## Example Problem

What is the heat in Joules required to melt 25 grams of ice? What is the heat in calories?

Useful information: Heat of fusion of water = 334 J/g = 80 cal/g

### Solution

﻿In the problem, the heat of fusion is given. This isn't a number you're expected to know off the top of your head. There are chemistry tables that state common heat of fusion values.

To solve this problem, you'll need the formula that relates heat energy to mass and heat of fusion:
q = m·ΔHf
where
q = heat energy
m = mass
ΔHf = heat of fusion

Temperature is not anywhere in the equation because it doesn't change when matter changes state. The equation is straightforward, so the key is to make sure you're using the right units for the answer.

To get heat in Joules:
q = (25 g)x(334 J/g)
q = 8350 J
It's just as easy to express the heat in terms of calories:
q = m·ΔHf
q = (25 g)x(80 cal/g)
q = 2000 cal
Answer: The amount of heat required to melt 25 grams of ice is 8,350 Joules or 2,000 calories.

Note: Heat of fusion should be a positive value. (The exception is helium.) If you get a negative number, check your math.

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