# Enthalpy of fusion

The melting enthalpy (Engl. Enthalpy of fusion , outdated and heat of fusion or melting energy , and last term, strictly speaking, means something else, s. U.) Refers to the energy amount required to provide a sample of fabric at its melting point at constant pressure ( isobaric ) to melt , so from the solid to the liquid state of aggregation . ${\ displaystyle \ textstyle H _ {\ text {fus}}}$

The energy supplied is used to overcome attractive intramolecular forces between the particles ( atoms , molecules or ions ) of the sample, so that the speed of the particles and thus the temperature of the substance do not increase when they melt (infinite heat capacity ).

The enthalpy of fusion of a substance has the same amount as the enthalpy of solidification that is released during its crystallization . To indicate that the sample (the system ) absorbs energy when it melts and releases / loses it when it solidifies, the enthalpy of fusion has a positive sign and the enthalpy of solidification has a negative sign :

${\ displaystyle \ textstyle H _ {\ text {fus}} = - H _ {\ text {solidified}}> 0}$

## Sizes and units

### Enthalpy of fusion

The enthalpy of fusion is an energy. In the International Size System (ISQ) it therefore has the dimension

${\ displaystyle \ dim H _ {\ text {fus}} = \ mathrm {L} ^ {2} \ cdot \ mathrm {M} \ cdot \ mathrm {T} ^ {- 2}}$

and thus in the International System of Units (SI) the coherent derived SI unit Joule :

${\ displaystyle \ left [H _ {\ text {fus}} \ right] = {\ frac {\ mathrm {kg} \ cdot \ mathrm {m} ^ {2}} {\ mathrm {s} ^ {2}} } = \ mathrm {J}}$

### Specific enthalpy of fusion

The material constant belonging to the enthalpy of fusion is the specific enthalpy of fusion . It is the enthalpy of fusion of a sample of the substance, based on the mass of the sample: ${\ displaystyle \ textstyle h _ {\ text {fus}}}$ ${\ displaystyle \ textstyle m}$

${\ displaystyle h _ {\ text {fus}} = {\ frac {H _ {\ text {fus}}} {m}}}$

Accordingly, it is specified in the unit joule per kilogram :

${\ displaystyle \ left [h _ {\ text {fus}} \ right] = {\ frac {\ mathrm {J}} {\ mathrm {kg}}}}$

### Molar enthalpy of fusion

In chemistry , the molar enthalpy of fusion is used instead of the specific one . It is the enthalpy of fusion, based on the amount of substance : ${\ displaystyle \ textstyle H _ {\ text {m, fus}}}$ ${\ displaystyle \ textstyle n}$

${\ displaystyle H _ {\ text {m, fus}} = {\ frac {H _ {\ text {fus}}} {n}}}$

The unit is therefore joules per mole :

${\ displaystyle \ left [H _ {\ text {m, fus}} \ right] = {\ frac {\ mathrm {J}} {\ mathrm {mol}}}}$

In order to obtain practical numerical values ​​for typical substances, the values ​​of the molar enthalpy of fusion are usually not given in joules per mole (J / mol), but in kilojoules per mole (kJ / mol). When calculating with molar enthalpies in kJ / mol, please note that this unit is not coherent.

The specific enthalpy of fusion and the molar enthalpy of fusion can be converted into each other using the molar mass of the substance under consideration: ${\ displaystyle M = {\ frac {m} {n}}}$

${\ displaystyle h _ {\ text {fus}} = {\ frac {H _ {\ text {m, fus}}} {M}}}$

The size symbol recommended by IUPAC for the molar enthalpy of fusion is different . ${\ displaystyle \ textstyle \ mathrm {\ Delta} _ {\ text {fus}} H}$

## Connection with the melting energy

The enthalpy of fusion results from the difference between the enthalpy of the liquid and the enthalpy of the converted solid material: ${\ displaystyle H _ {\ text {(l)}}}$${\ displaystyle H _ {\ text {(s)}}}$

${\ displaystyle \ Delta _ {\ text {fus}} H = H _ {\ text {(l)}} - H _ {\ text {(s)}}}$

Similarly, the melting energy results from the difference between their internal energies :

${\ displaystyle \ Delta _ {\ text {fus}} U = U _ {\ text {(l)}} - U _ {\ text {(s)}}}$

Because of the fundamental thermodynamic relationship

${\ displaystyle H = U + p \ cdot V}$

this results in the following relationship between melting enthalpy and energy:

${\ displaystyle \ Delta _ {\ text {fus}} H = \ Delta _ {\ text {fus}} U + p \ cdot \ left (V _ {\ text {(l)}} - V _ {\ text {( s)}} \ right)}$

## Individual evidence

1. a b ISO 80000 -5: 2007, Quantities and units - Part 5: Thermodynamics , corrected version of June 1, 2011.
2. a b ISO 80000 -9: 2009, Quantities and units - Part 9: Physical chemistry and molecular physics , April 1, 2009. Corrected by: ISO 80000-9: 2009 / Amd.1: 2011, Amendment 1 to ISO 80000- 9: 2009 , June 1, 2011.
3. ER Cohen, T. Cvitaš, JG Frey, B. Holmstrom, K. Kuchitsu, R. Marquardt, I. Mills, F. Pavese, M. Quack, J. Stohner, HL Strauss, M. Takami, AJ Thor: Quantities , Units and Symbols in Physical Chemistry , IUPAC Green Book, 3rd Edition, 2nd Printing, IUPAC & RSC Publishing, Cambridge 2008.