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

Apr 25, 2018

$998 J$

#### 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.

$q = m c \Delta T$ 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.

${q}_{1} = 1.43 \cancel{g} \cdot \text{2.10J"/cancel"g°C" * 5.34cancel"°C} = 16.0 J$

Secondly, find the energy needed to melt the ice. For this equation we must find the $\Delta {H}_{\text{fus}}$, or the energy required to melt ice, which is 334J/g of ice.
${q}_{2} = \Delta {H}_{\text{fus" = 1.43cancelg * "334J}} / \cancel{g} = 478 J$

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

${q}_{3} = 1.43 \cancel{g} \cdot \text{4.18J"/cancel"g°C" * 84.3cancel"°C} = 504 J$

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

$16.0 J + 478 J + 504 J = 998 J$