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thermodynamics Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of ther ...
, the enthalpy of fusion of a substance, also known as (latent) heat of fusion, is the change in its
enthalpy Enthalpy , a property of a thermodynamic system, is the sum of the system's internal energy and the product of its pressure and volume. It is a state function used in many measurements in chemical, biological, and physical systems at a constant p ...
resulting from providing
energy In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat ...
, typically
heat In thermodynamics, heat is defined as the form of energy crossing the boundary of a thermodynamic system by virtue of a temperature difference across the boundary. A thermodynamic system does not ''contain'' heat. Nevertheless, the term is al ...
, to a specific quantity of the substance to change its
state State may refer to: Arts, entertainment, and media Literature * ''State Magazine'', a monthly magazine published by the U.S. Department of State * ''The State'' (newspaper), a daily newspaper in Columbia, South Carolina, United States * '' Our ...
from a
solid Solid is one of the four fundamental states of matter (the others being liquid, gas, and plasma). The molecules in a solid are closely packed together and contain the least amount of kinetic energy. A solid is characterized by structural r ...
to a
liquid A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. As such, it is one of the four fundamental states of matter (the others being solid, gas, an ...
, at constant pressure. It is the amount of energy required to convert one mole of solid into liquid For example, when
melting Melting, or fusion, is a physical process that results in the phase transition of a substance from a solid to a liquid. This occurs when the internal energy of the solid increases, typically by the application of heat or pressure, which incre ...
1 kg of ice (at 0 °C under a wide range of pressures), 333.55 kJ of energy is absorbed with no
temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measurement, measured with a thermometer. Thermometers are calibrated in various Conversion of units of temperature, temp ...
change. The heat of solidification (when a substance changes from liquid to solid) is equal and opposite. This energy includes the contribution required to make room for any associated change in volume by displacing its environment against ambient pressure. The temperature at which the
phase transition In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states o ...
occurs is the
melting point The melting point (or, rarely, liquefaction point) of a substance is the temperature at which it changes state from solid to liquid. At the melting point the solid and liquid phase exist in equilibrium. The melting point of a substance depends ...
or the freezing point, according to context. By convention, the pressure is assumed to be unless otherwise specified.


Overview

The 'enthalpy' of fusion is a
latent heat Latent heat (also known as latent energy or heat of transformation) is energy released or absorbed, by a body or a thermodynamic system, during a constant-temperature process — usually a first-order phase transition. Latent heat can be underst ...
, because, while melting, the heat energy needed to change the substance from solid to liquid at atmospheric pressure is latent heat of fusion, as the temperature remains constant during the process. The latent heat of fusion is the enthalpy change of any amount of substance when it melts. When the heat of fusion is referenced to a unit of mass, it is usually called the specific heat of fusion, while the molar heat of fusion refers to the enthalpy change per
amount of substance In chemistry, the amount of substance ''n'' in a given sample of matter is defined as the quantity or number of discrete atomic-scale particles in it divided by the Avogadro constant ''N''A. The particles or entities may be molecules, atoms, ions, ...
in
mole Mole (or Molé) may refer to: Animals * Mole (animal) or "true mole", mammals in the family Talpidae, found in Eurasia and North America * Golden moles, southern African mammals in the family Chrysochloridae, similar to but unrelated to Talpida ...
s. The liquid phase has a higher internal energy than the solid phase. This means energy must be supplied to a solid in order to melt it and energy is released from a liquid when it freezes, because the
molecule A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioch ...
s in the liquid experience weaker
intermolecular force An intermolecular force (IMF) (or secondary force) is the force that mediates interaction between molecules, including the electromagnetic forces of attraction or repulsion which act between atoms and other types of neighbouring particles, e.g. a ...
s and so have a higher potential energy (a kind of
bond-dissociation energy The bond-dissociation energy (BDE, ''D''0, or ''DH°'') is one measure of the strength of a chemical bond . It can be defined as the standard enthalpy change when is cleaved by homolysis to give fragments A and B, which are usually radical s ...
for intermolecular forces). When liquid water is cooled, its temperature falls steadily until it drops just below the line of freezing point at 0 °C. The temperature then remains constant at the freezing point while the water crystallizes. Once the water is completely frozen, its temperature continues to fall. The enthalpy of fusion is almost always a positive quantity;
helium Helium (from el, ἥλιος, helios, lit=sun) is a chemical element with the symbol He and atomic number 2. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas and the first in the noble gas group in the periodic table. It ...
is the only known exception.
Helium-3 Helium-3 (3He see also helion) is a light, stable isotope of helium with two protons and one neutron (the most common isotope, helium-4, having two protons and two neutrons in contrast). Other than protium (ordinary hydrogen), helium-3 is the ...
has a negative enthalpy of fusion at temperatures below 0.3 K.
Helium-4 Helium-4 () is a stable isotope of the element helium. It is by far the more abundant of the two naturally occurring isotopes of helium, making up about 99.99986% of the helium on Earth. Its nucleus is identical to an alpha particle, and consis ...
also has a very slightly negative enthalpy of fusion below . This means that, at appropriate constant pressures, these substances freeze with the addition of heat. In the case of 4He, this pressure range is between 24.992 and . {, class="wikitable sortable" , - ! rowspan=2, Substance ! colspan=2, Heat of fusion , - ! (cal/g) ! (J/g) , - ,
water Water (chemical formula ) is an Inorganic compound, inorganic, transparent, tasteless, odorless, and Color of water, nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living ...
, 79.72 , 333.55 , - ,
methane Methane ( , ) is a chemical compound with the chemical formula (one carbon atom bonded to four hydrogen atoms). It is a group-14 hydride, the simplest alkane, and the main constituent of natural gas. The relative abundance of methane on ...
, 13.96 , 58.99 , - ,
propane Propane () is a three- carbon alkane with the molecular formula . It is a gas at standard temperature and pressure, but compressible to a transportable liquid. A by-product of natural gas processing and petroleum refining, it is commonly used a ...
, 19.11 , 79.96 , - ,
glycerol Glycerol (), also called glycerine in British English and glycerin in American English, is a simple triol compound. It is a colorless, odorless, viscous liquid that is sweet-tasting and non-toxic. The glycerol backbone is found in lipids known ...
, 47.95 , 200.62 , - ,
formic acid Formic acid (), systematically named methanoic acid, is the simplest carboxylic acid, and has the chemical formula HCOOH and structure . It is an important intermediate in chemical synthesis and occurs naturally, most notably in some ants. E ...
, 66.05 , 276.35 , - ,
acetic acid Acetic acid , systematically named ethanoic acid , is an acidic, colourless liquid and organic compound with the chemical formula (also written as , , or ). Vinegar is at least 4% acetic acid by volume, making acetic acid the main component ...
, 45.90 , 192.09 , - ,
acetone Acetone (2-propanone or dimethyl ketone), is an organic compound with the formula . It is the simplest and smallest ketone (). It is a colorless, highly volatile and flammable liquid with a characteristic pungent odour. Acetone is miscible wi ...
, 23.42 , 97.99 , - ,
benzene Benzene is an organic chemical compound with the molecular formula C6H6. The benzene molecule is composed of six carbon atoms joined in a planar ring with one hydrogen atom attached to each. Because it contains only carbon and hydrogen atoms ...
, 30.45 , 127.40 , - ,
myristic acid Myristic acid (IUPAC name: tetradecanoic acid) is a common saturated fatty acid with the molecular formula CH3(CH2)12COOH. Its salts and esters are commonly referred to as myristates or tetradecanoates. It is named after the binomial name for nut ...
, 47.49 , 198.70 , - ,
palmitic acid Palmitic acid (hexadecanoic acid in IUPAC nomenclature) is a fatty acid with a 16-carbon chain. It is the most common saturated fatty acid found in animals, plants and microorganisms.Gunstone, F. D., John L. Harwood, and Albert J. Dijkstra. The L ...
, 39.18 , 163.93 , - , sodium acetate , , 264–289Ibrahim Dincer and Marc A. Rosen
Thermal Energy Storage: Systems and Applications
page 155
, - ,
stearic acid Stearic acid ( , ) is a saturated fatty acid with an 18-carbon chain. The IUPAC name is octadecanoic acid. It is a waxy solid and its chemical formula is C17H35CO2H. Its name comes from the Greek word στέαρ "''stéar''", which means tallow. ...
, 47.54 , 198.91 , - ,
gallium Gallium is a chemical element with the symbol Ga and atomic number 31. Discovered by French chemist Paul-Émile Lecoq de Boisbaudran in 1875, Gallium is in group 13 of the periodic table and is similar to the other metals of the group (alumini ...
, 19.2 , 80.4 , - , paraffin wax (C25H52) , 47.8–52.6 , 200–220 These values are mostly from the CRC ''Handbook of Chemistry and Physics'', 62nd edition. The conversion between cal/g and J/g in the above table uses the thermochemical
calorie The calorie is a unit of energy. For historical reasons, two main definitions of "calorie" are in wide use. The large calorie, food calorie, or kilogram calorie was originally defined as the amount of heat needed to raise the temperature of on ...
(calth) = 4.184 joules rather than the International Steam Table calorie (calINT) = 4.1868 joules.


Examples


Solubility prediction

The heat of fusion can also be used to predict
solubility In chemistry, solubility is the ability of a substance, the solute, to form a solution with another substance, the solvent. Insolubility is the opposite property, the inability of the solute to form such a solution. The extent of the solubi ...
for solids in liquids. Provided an
ideal solution In chemistry, an ideal solution or ideal mixture is a solution that exhibits thermodynamic properties analogous to those of a mixture of ideal gases. The enthalpy of mixing is zero as is the volume change on mixing by definition; the closer to zer ...
is obtained the mole fraction (x_2) of solute at saturation is a function of the heat of fusion, the
melting point The melting point (or, rarely, liquefaction point) of a substance is the temperature at which it changes state from solid to liquid. At the melting point the solid and liquid phase exist in equilibrium. The melting point of a substance depends ...
of the solid (T_\text{fus}) and the
temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measurement, measured with a thermometer. Thermometers are calibrated in various Conversion of units of temperature, temp ...
(T) of the solution: :\ln x_2 = - \frac {\Delta H^\circ_\text{fus{R} \left(\frac{1}{T}- \frac{1}{T_\text{fus\right) Here, R is the
gas constant The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol or . It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment per ...
. For example, the solubility of
paracetamol Paracetamol, also known as acetaminophen, is a medication used to treat fever and mild to moderate pain. Common brand names include Tylenol and Panadol. At a standard dose, paracetamol only slightly decreases body temperature; it is inferior ...
in water at 298 K is predicted to be: :x_2 = \exp {\left \frac {28100 ~\text{J mol}^{-1 {8.314 ~\text{J K}^{-1} ~\text{mol}^{-1\left(\frac{1}{298 ~\text{K- \frac{1}{442 ~\text{K\right)\right = 0.0248 Since the molar mass of water and paracetamol are and and the density of the solution is , an estimate of the solubility in grams per liter is: :\frac{0.0248 \times \frac{1000 ~\text{g L}^{-1{18.0153 ~\text{g mol}^{-1}{1-0.0248} \times 151.17 ~\text{g mol}^{-1} = 213.4 ~\text{g L}^{-1} which is a deviation from the real solubility (240 g/L) of 11%. This error can be reduced when an additional
heat capacity Heat capacity or thermal capacity is a physical property of matter, defined as the amount of heat to be supplied to an object to produce a unit change in its temperature. The SI unit of heat capacity is joule per kelvin (J/K). Heat capacity i ...
parameter is taken into account.''Measurement and Prediction of Solubility of Paracetamol in Water-Isopropanol Solution. Part 2. Prediction'' H. Hojjati and S. Rohani Org. Process Res. Dev.; 2006; 10(6) pp 1110–1118; (Article)


Proof

At equilibrium the
chemical potential In thermodynamics, the chemical potential of a species is the energy that can be absorbed or released due to a change of the particle number of the given species, e.g. in a chemical reaction or phase transition. The chemical potential of a species ...
s for the pure solvent and pure solid are identical: :\mu^\circ_\text{solid} = \mu^\circ_\text{solution}\, or :\mu^\circ_\text{solid} = \mu^\circ_\text{liquid} + RT\ln X_2\, with R\, the
gas constant The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol or . It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment per ...
and T\, the
temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measurement, measured with a thermometer. Thermometers are calibrated in various Conversion of units of temperature, temp ...
. Rearranging gives: :RT\ln X_2 = -\left(\mu^\circ_\text{liquid} - \mu^\circ_\text{solid}\right)\, and since : \Delta G^\circ_\text{fus} = \mu^\circ_\text{liquid} - \mu^\circ_\text{solid}\, the heat of fusion being the difference in chemical potential between the pure liquid and the pure solid, it follows that :RT\ln X_2 = -\left(\Delta G^\circ_\text{fus}\right)\, Application of the
Gibbs–Helmholtz equation The Gibbs–Helmholtz equation is a thermodynamic equation used for calculating changes in the Gibbs free energy of a system as a function of temperature. It was originally presented in an 1882 paper entitled " Die Thermodynamik chemischer Vorgange ...
: :\left( \frac{\partial \left( \frac{\Delta G^\circ_\text{fus} } {T} \right) } {\partial T} \right)_{p\,} = -\frac {\Delta H^\circ_\text{fus {T^2} ultimately gives: :\left( \frac{\partial \left( \ln X_2 \right) } {\partial T} \right) = \frac {\Delta H^\circ_\text{fus {RT^2} or: :\partial \ln X_2 = \frac {\Delta H^\circ_\text{fus {RT^2} \times \delta T and with
integration Integration may refer to: Biology *Multisensory integration *Path integration * Pre-integration complex, viral genetic material used to insert a viral genome into a host genome *DNA integration, by means of site-specific recombinase technology, ...
: :\int^{X_2=x_2}_{X_2 = 1} \delta \ln X_2 = \ln x_2 = \int_{T_\text{fus^T \frac {\Delta H^\circ_\text{fus {RT^2} \times \Delta T the end result is obtained: :\ln x_2 = - \frac {\Delta H^\circ_\text{fus {R}\left(\frac{1}{T}- \frac{1}{T_\text{fus\right)


See also

*
Heat of vaporization The enthalpy of vaporization (symbol ), also known as the (latent) heat of vaporization or heat of evaporation, is the amount of energy (enthalpy) that must be added to a liquid substance to transform a quantity of that substance into a gas. T ...
*
Heat capacity Heat capacity or thermal capacity is a physical property of matter, defined as the amount of heat to be supplied to an object to produce a unit change in its temperature. The SI unit of heat capacity is joule per kelvin (J/K). Heat capacity i ...
*
Thermodynamic databases for pure substances Thermodynamic databases contain information about thermodynamic properties for substances, the most important being enthalpy, entropy, and Gibbs free energy. Numerical values of these thermodynamic properties are collected as tables or are calcu ...
*
Joback method The Joback method (often named Joback/Reid method) predicts eleven important and commonly used pure component thermodynamic properties from molecular structure only. Basic principles Group-contribution method The Joback method is a group- ...
(Estimation of the heat of fusion from molecular structure) *
Latent heat Latent heat (also known as latent energy or heat of transformation) is energy released or absorbed, by a body or a thermodynamic system, during a constant-temperature process — usually a first-order phase transition. Latent heat can be underst ...
*
Lattice energy In chemistry, the lattice energy is the energy change upon formation of one mole of a crystalline ionic compound from its constituent ions, which are assumed to initially be in the gaseous state. It is a measure of the cohesive forces that bin ...
*
Heat of dilution In thermochemistry, the heat of dilution, or enthalpy of dilution, refers to the enthalpy change associated with the dilution process of a component in a solution at a constant pressure. If the initial state of the component is a pure liquid (pr ...


Notes


References

* * {{DEFAULTSORT:Enthalpy Of Fusion Thermodynamic properties Enthalpy