Enthalpy of fusion - Citizendia

Molar heat content of zinc above 298. 15 K and at 1 atm pressure, showing discontinuities at the melting and boiling points. The enthalpy of melting (ΔH°m) of zinc is 7323 J/mol, and the enthalpy of vaporization (ΔH°v) is 115 330 J/mol.

The standard enthalpy of fusion (symbol: $Δ H f u s$ ), also known as the heat of fusion or specific melting heat, is the amount of thermal energy which must be absorbed or evolved for 1 mole of a substance to change states from a solid to a liquid or vice versa. In Thermodynamics and molecular chemistry, the enthalpy (denoted as H, h, or rarely as χ) is a quotient or description of Thermal energy is the sum of the sensible energy and latent energy. The mole (symbol mol) is a unit of Amount of substance: it is an SI base unit, and almost the only unit to be used to measure this A solid' object is in the States of matter characterized by resistance to Deformation and changes of Volume. Liquid is one of the principal States of matter. A liquid is a Fluid that has the particles loose and can freely form a distinct surface at the boundaries of It is also called the latent heat of fusion or the enthalpy change of fusion, and the temperature at which it occurs is called the melting point. Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature The melting point of a solid is the temperature range at which it changes state from solid to Liquid.

When you withdraw thermal energy from a liquid or solid, the temperature falls. Thermal energy is the sum of the sensible energy and latent energy. Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature When you add heat energy the temperature rises. However, at the transition point between solid and liquid (the melting point), extra energy is required (the heat of fusion). The melting point of a solid is the temperature range at which it changes state from solid to Liquid. To go from liquid to solid, the molecules of a substance must become more ordered. In Chemistry, a molecule is defined as a sufficiently stable electrically neutral group of at least two Atoms in a definite arrangement held together by For them to maintain the order of a solid, extra heat must be withdrawn. In the other direction, to create the disorder from the solid crystal to liquid, extra heat must be added.

The heat of fusion can be observed if you measure the temperature of water as it freezes. If you plunge a closed container of room temperature water into a very cold environment (say −20 °C), you will see the temperature fall steadily until it drops just below the freezing point (0 °C). The temperature then rebounds and holds steady while the water crystallizes. Once completely frozen, the temperature will fall steadily again.

The temperature stops falling at (or just below) the freezing point due to the heat of fusion. The energy of the heat of fusion must be withdrawn (the liquid must turn to solid) before the temperature can continue to fall.

The units of heat of fusion are usually expressed as:

joules per mole (the SI units)
calories per gram (old metric units now little used, except for a different, larger calorie used in nutritional contexts)
British thermal units per pound or Btu per pound-mole

Note: These are not the calories found in food. The joule (written in lower case ˈdʒuːl or /ˈdʒaʊl/ (symbol J) is the SI unit of Energy measuring heat, Electricity The mole (symbol mol) is a unit of Amount of substance: it is an SI base unit, and almost the only unit to be used to measure this This article is about the unit of energy For its use in Nutrition and Food labelling regulations, see the article on Food energy. The mole (symbol mol) is a unit of Amount of substance: it is an SI base unit, and almost the only unit to be used to measure this This article is about the unit of energy For its use in Nutrition and Food labelling regulations, see the article on Food energy. The calories found in food are more properly known as kilocalories—equal to 1000 calories. 1000 calories = 1 kilocalorie = 1 food calorie. This article is about the unit of energy For its use in Nutrition and Food labelling regulations, see the article on Food energy. Food calories are sometimes abbreviated as kcal as if small calories were being used, while calories are abbreviated as cal. Another distinguishing method, though often confusing, uses capitalisation. A Calorie is a food calorie, or 1000 calories. So 1 Cal = 1000 cal or 1 kcal

1 Reference values of common substances
2 Applications
3 Solubility prediction
- 3.1 Proof
4 See also
5 References

Reference values of common substances

Standard enthalpy change of fusion of period three.

Standard enthalpy change of fusion of period two of the periodic table of elements. The periodic table of the chemical elements is a tabular method of displaying the Chemical elements Although precursors to this table exist its invention is

Substance	Heat of fusion (cal/g)	Heat of fusion (kJ/kg)
water	79. 72	333. 55
methane	13. 96	58. 41
ethane	22. 73	95. 10
propane	19. 11	79. 96
methanol	23. 70	99. 16
ethanol	26. 05	108. 99
glycerol	47. 95	200. 62
formic acid	66. 05	276. 35
acetic acid	45. 91	192. 09
acetone	23. 42	97. 99
benzene	30. 45	127. 40
myristic acid	47. 49	198. 70
palmitic acid	39. 18	163. 93
stearic acid	47. 54	198. 91

These values are from the CRC Handbook of Chemistry and Physics, 62nd edition. The CRC Press, LLC is a publishing group which specializes in producing technical books in a wide range of subjects The conversion between cal/g and kJ/kg in the above table uses the thermochemical calorie (cal_th) = 4. This article is about the unit of energy For its use in Nutrition and Food labelling regulations, see the article on Food energy. 184 joules rather than the International Steam Table calorie (cal_INT) = 4. 1868 joules.

Applications

To heat one kilogram (about 1 litre) of water from 10 °C to 30 °C requires 20 kcal.
However, to melt ice and raise the resulting water temperature 20 °C requires extra energy. To heat ice from 0 °C to water at 20 °C requires:

(1) 80 cal/g (heat of fusion of ice) = 80 kcal for 1 kg

PLUS

(2) 1 cal/(g·°C) = 20 kcal for 1 kg to go up 20 °C

= 100 kcal

Solubility prediction

The heat of fusion can also be used to predict solubility for solids in liquids. Solubility is the characteristic Physical property referring to the ability of a given substance the Solute, to dissolve in a Solvent. Provided an ideal solution is obtained the mole fraction $(x 2)$ of solute at saturation is a function of the heat of fusion, the melting point of the solid $(T f u s)$ and the temperature (T) of the solution:

$\ln x_2 = - \frac {\Delta H^\circ_{fus}}{R} \left(\frac{1}{T}- \frac{1}{T_{fus}}\right)$

Here, R is the gas constant. In Chemistry, an ideal solution or ideal mixture is a Solution in which the Enthalpy of solution is zero the closer to zero the enthalpy of In Chemistry, the mole fraction of a component in a Mixture is the relative proportion of molecules belonging to the component to those in the mixture The melting point of a solid is the temperature range at which it changes state from solid to Liquid. Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature Relationship with the Boltzmann constant The Boltzmann constant kB (often abbreviated k) may be used in place of the gas constant by working For example the solubility of paracetamol in water at 298 K is predicted to be:

$\ln x_2 = - \frac {28100 \mbox{ J mol}^{-1}} {8.314 \mbox{ J K}^{-1} \mbox{ mol}^{-1}}\left(\frac{1}{298}- \frac{1}{442}\right) = 0.0248$

This equals to a solubility in grams per liter of:

$\frac{0.0248*\frac{1000 \mbox{ g}}{18.053 \mbox{ mol}^{-1}}}{1-0.0248}*151.17 \mbox{ mol}^{-1} = 213.4$

which is a deviation from the real solubility (240 g/L) of 11%. Paracetamol ( INN) (ˌpærəˈsiːtəmɒl -ˈsɛtə- or acetaminophen ( USAN) is a widely-used Analgesic and Antipyretic Medication The kelvin (symbol K) is a unit increment of Temperature and is one of the seven SI base units The Kelvin scale is a thermodynamic This error can be reduced when an additional heat capacity parameter is taken into account ^[1]

Proof

At equilibrium the chemical potentials for the pure solvent and pure solid are identical:

$\mu^\circ_{solid} = \mu^\circ_{solution}\,$

$\mu^\circ_{solid} = \mu^\circ_{liquid} + RT\ln X_2\,$

with $R\,$ the gas constant and $T\,$ the temperature. Specific heat capacity, also known simply as specific heat, is the measure of the heat energy required to increase the Temperature of a unit quantity In a Chemical process, chemical equilibrium is the state in which the chemical activities or Concentrations of the reactants and products have no net change In Thermodynamics and Chemistry, chemical potential, symbolized by μ, is a term introduced by the American engineer chemist and mathematical Relationship with the Boltzmann constant The Boltzmann constant kB (often abbreviated k) may be used in place of the gas constant by working Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature

Rearranging gives:

$RT\ln X_2 = - (\mu^\circ_{liquid} - \mu^\circ_{solid})\,$

and since

$\Delta G^\circ_{fus} = - (\mu^\circ_{liquid} - \mu^\circ_{solid})\,$

the heat of fusion being the difference in chemical potential between the pure liquid and the pure solid, it follows that

$RT\ln X_2 = - ( \Delta G^\circ_{fus})\,$

Application of the Gibbs-Helmholtz equation:

$\left( \frac{\partial ( \frac{\Delta G^\circ_{fus} } {T} ) } {\partial T} \right)_{p\,} = \frac {\Delta H^\circ_{fus}} {T^2}$

ultimately gives:

$\left( \frac{\partial ( \ln X_2 ) } {\partial T} \right) = \frac {\Delta H^\circ_{fus}} {RT^2}$

or:

$\partial \ln X_2 = \frac {\Delta H^\circ_{fus}} {RT^2}*\delta T$

and with integration:

$\int^{x_2=x_2}_{x_2 = 1} \delta \ln X_2 = \ln x_2 = \int_{T_fus}^T \frac {\Delta H^\circ_{fus}} {RT^2}*\Delta T$

the end result is obtained:

$\ln x_2 = - \frac {\Delta H^\circ_{fus}} {R}\left(\frac{1}{T}- \frac{1}{T_{fus}}\right)$

References

^ Measurement and Prediction of Solubility of Paracetamol in Water-Isopropanol Solution. The Gibbs–Helmholtz equation is a thermodynamic Equation useful for calculating changes in the Gibbs energy of a system as a function of temperature The European Space Agency 's INTErnational Gamma-Ray Astrophysics Laboratory ( INTEGRAL) is detecting some of the most energetic radiation that comes from space The enthalpy of vaporization, (symbol \Delta{}_{v}H also known as the heat of vaporization or heat of evaporation, is the Energy required Specific heat capacity, also known simply as specific heat, is the measure of the heat energy required to increase the Temperature of a unit quantity Specific heat capacity, also known simply as specific heat, is the measure of the heat energy required to increase the Temperature of a unit quantity Thermodynamic databases contain information about thermodynamic properties for substances the most important being Enthalpy, Entropy, and Part 2. Prediction H. Hojjati and S. Rohani Org. Process Res. Dev. ; 2006; 10(6) pp 1110 - 1118; (Article) doi:10.1021/op060074g

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Contents

Reference values of common substances

Applications

Solubility prediction

Proof

See also

References