Question

How much heat is needed to melt 1.43 grams of ice into water from -5.34 to 84.3 c?

Answer 1

`998J`

Explanation:

We need to find three heat values; the heat to raise the ice to melting point, the heat to melt the ice into water, and the heat to raise the temperature of the water to 84.3°C. Thus, we need three equations.

`q = mcDeltaT` is what we will use, with `q_1` as the heat needed to raise the ice's temperature, `q_2` as the heat to melt it, and `q_3` as the heat to raise the water's temperature.

Note: The Specific Heat Capacity (c) for liquid water is 4.18J; for ice, 2.10J

Firstly, we need to raise the ice's temperature from -5.34°C to 0°C.

`q_1 = 1.43cancelg * "2.10J"/cancel"g°C" * 5.34cancel"°C" = 16.0J`

Secondly, find the energy needed to melt the ice. For this equation we must find the `DeltaH_"fus"`, or the energy required to melt ice, which is 334J/g of ice.
`q_2 = DeltaH_"fus" = 1.43cancelg * "334J"/cancelg = 478J`

Lastly, find the energy needed to raise the water to 84.3°C.

`q_3 = 1.43cancelg * "4.18J"/cancel"g°C" * 84.3cancel"°C" = 504J`

Now that we have all three values, add them to find the total energy required.

`16.0J + 478J + 504J = 998J`