# What is the equation for the calculation of heat of fusion?

Jul 21, 2018

The enthalpy of fusion, $\Delta {H}_{\text{fus}}$, is a measured quantity, also known as the latent heat of fusion, but it is not the same as ${q}_{\text{fus}}$, the heat flow that causes melting or freezing to occur.

The only "equation" that utilizes ${q}_{\text{fus}}$ in general chemistry is:

${q}_{\text{fus" = pmnDeltaH_"fus}}$

• ${q}_{\text{fus}}$ is the heat flow at constant atmospheric pressure, that pertains to either melting or freezing. Here it is in units of $\text{kJ}$.
• $n$ is the mols of liquid being freezed, or the mols of solid being melted.
• $\Delta {H}_{\text{fus}}$ is the enthalpy of fusion, and is a positive quantity usually reported in $\text{kJ/mol}$.

The $\pm$ is assigned depending on the direction of heat flow... if one wishes to melt a solid,

${q}_{\text{fus" -= q_"melt" = nDeltaH_"fus}}$

If one wishes to freeze a liquid...

${q}_{\text{fus" -= q_"freeze" = -nDeltaH_"fus}}$

And this is because the object is the system... so

• heat flowing in to melt it must be given a positive sign, for the system gains heat to melt.
• heat flowing out to freeze it must be given a negative sign, for the system loses heat to freeze.