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?

You'll need 10 g. of fusion is the 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=mL_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=(Q/L_f)=(3.34*10^3)/334=10g##

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).