# 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?

Jan 29, 2017

$\text{12 kJ}$

#### 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

$\Delta {H}_{\text{fus" = "6.0 kJ mol}}^{- 1}$

This means that in order to melt $1$ mole of ice at its normal melting point of ${0}^{\circ} \text{C}$, you must supply it with $\text{6.0 kJ}$ of heat.

Now, your sample of ice has a mass of $\text{36 g}$, 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

$1.998 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{moles ice"))) * "6.0 kJ"/(1color(red)(cancel(color(black)("mole ice")))) = color(darkgreen)(ul(color(black)("12 kJ}}}}$

The answer is rounded to two sig figs.