Question

The latent heat of fusion for ice is 6.0 kJ/mole. In order to melt 36 g of ice (solid `H_2O`) at 0°C, how much energy is required?

Answer 1

`"12 kJ"`

Explanation:

The molar latent heat of fusion, which is an alternative name given to the enthalpy of fusion, tells you how much heat is required in order to convert a specific amount of a given substance, either a gram or a mole, from solid at its melting point to liquid at its melting point.

Ice is said to have a molar enthalpy of fusion equal to

`DeltaH_"fus" = "6.0 kJ mol"^(-1)`

This means that in order to melt `1` mole of ice at its normal melting point of `0^@"C"`, you must supply it with `"6.0 kJ"` of heat.

Now, your sample of ice has a mass of `"36 g"`, so the first thing to do here is to convert it to moles by using the molar mass of water

`36 color(red)(cancel(color(black)("g"))) * ("1 mole H"_2"O")/(18.015color(red)(cancel(color(black)("g")))) = "1.998 moles H"_2"O"`

You can now use the molar enthalpy of fusion as a conversion factor to help you figure out how much heat must be supplied to your sample

`1.998 color(red)(cancel(color(black)("moles ice"))) * "6.0 kJ"/(1color(red)(cancel(color(black)("mole ice")))) = color(darkgreen)(ul(color(black)("12 kJ")))`

The answer is rounded to two sig figs.