# Question 05480

Apr 29, 2015

You're dealing with a phase change, so you need to determine how much heat you need to supply to the ice to get to go from solid at ${0}^{\circ} \text{C}$ to liquid at ${0}^{\circ} \text{C}$.

The equation you'll use looks like this

$q = m \cdot \Delta {H}_{\text{fus}}$, where

$q$ - the heat you need to suplly to the ice;
$m$ - the mass of the ice;
$\Delta {H}_{\text{fus}}$ - the latent heat of fusion, or enthalpy of fusion, which is the change in enthalpy you get when you heat a gram of a substance to change it from solid state to liquid state.

The enthalpy of fusion for ice has a value of 334 J/g. This means that, if you have 1 gram of ice at ${0}^{\circ} \text{C}$, you need to supply it with 334 J of heat in order to get it to liquid at ${0}^{\circ} \text{C}$.

Since you've got more than one gram of ice, you'll of course need more than 334 J of heat.

q = 35.0cancel("g") * 334"J"/cancel("g") = "11690 J"#

Expressed in kJ and rounded to three sig figs, the answer will be

$11690 \cancel{\text{J") * "1 kJ"/(1000cancel("J")) = color(green)("+11.7 kJ}}$

The + sign symbolizes that the heat is provided to the ice.