Question

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?

Answer 1

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=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).