# The latent heat of fusion of water is 334 J/g. How many grams of ice at 0°C will melt by the addition of 3.34 kJ of heat energy?

Dec 19, 2014

You'll need 10 g.
Latent heat of fusion is the energy needed to melt a certain amount of substance.
In your case you need 334 J of energy to melt 1 g of ice. If you can supply 3.34 kJ of energy you have:
$Q = m {L}_{f}$ where:
$Q$ is the heat you can supply, in this case 3.34 kJ;
$m$ is the mass of the substance, our unknown;
${L}_{f}$ is the latent heat of fusion of water, 334 J/g.

Rearranging you have:
$m = \left(\frac{Q}{L} _ f\right) = \frac{3.34 \cdot {10}^{3}}{334} = 10 g$

Remember
Latent Heat is the energy your substance needs to change its phase (solid -> liquid) and is not used to increase its temperature but to change the "connections" between the particles of the substance making it change from a solid (rigid connections) to a liquid (loose connections).