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Encyclopedia > Enthalpy of fusion
Standard enthalpy change of fusion of period three.
Standard enthalpy change of fusion of period two of the periodic table of elements.

The enthalpy of fusion (symbol: ΔfusH), also known as the heat of fusion, 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. 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. Image File history File links Enthalpy_of_Fusion_period_three. ... Image File history File links Enthalpy_of_Fusion_period_three. ... Image File history File links Molar_heat_of_fusion_period_two. ... Image File history File links Molar_heat_of_fusion_period_two. ... The periodic table of the chemical elements, also called the Mendeleev periodic table, is a tabular display of the known chemical elements. ... t In thermodynamics and molecular chemistry, the enthalpy or heat content (denoted as H or Î”H, or rarely as Ï‡) is a quotient or description of thermodynamic potential of a system, which can be used to calculate the useful work obtainable from a closed thermodynamic system under constant pressure. ... 1. ... The mole (symbol: mol) is the SI base unit that measures an amount of substance. ... For other uses, see Solid (disambiguation). ... A liquid will usually assume the shape of its container A liquid is one of the main states of matter. ... This article includes a list of works cited or a list of external links, but its sources remain unclear because it lacks in-text citations. ... The melting point of a crystalline solid is the temperature at which it changes state from solid to liquid. ...

When you withdraw thermal energy from a liquid or solid, the temperature falls. 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). To go from liquid to solid, the molecules of a substance must become more ordered. For them to maintain the order of a solid, extra heat must be withdrawn.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. 1. ... This article includes a list of works cited or a list of external links, but its sources remain unclear because it lacks in-text citations. ... The melting point of a crystalline solid is the temperature at which it changes state from solid to liquid. ... In science, a molecule is a group of atoms in a definite arrangement held together by chemical bonds. ...

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:

1. joules per mole (the SI units)
2. calories per gram (old metric units now little used, except for a different, larger calorie used in nutritional contexts)
3. British thermal units per pound or Btu per pound-mole
• Note: These are not the calories found in food. The calories found in food are more properly known as kilocalories—equal to 1000 calories. 1000 calories = 1 kilocalorie = 1 food calorie. 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.

Bold text== Reference Values of Common Substances == The joule (IPA pronunciation: or ) (symbol: J) is the SI unit of energy. ... The mole (symbol: mol) is the SI base unit that measures an amount of substance. ... Look up si, Si, SI in Wiktionary, the free dictionary. ... A calorie is a unit of measurement for energy. ... The British thermal unit (BTU or Btu) is a unit of energy used in the Power, Steam Generation and Heating and Air Conditioning industry globally. ... A calorie refers to a unit of energy. ... A calorie refers to a unit of energy. ...

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 conversion between cal/g and kJ/kg in the above table uses the thermochemical calorie (calth) = 4.184 Joules rather than the International Steam Table calorie (calINT) = 4.1868 Joules. The CRC Press, LLC is a publishing group which specializes in producing technical books in a wide range of subjects. ... A calorie is a unit of measurement for energy. ...

## Contents

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. Provided an ideal solution is obtained the mole fraction of solute at saturation is a function of the heat of fusion, the melting point of the solid and the temperature of the solution: Solubility refers to the ability for a given substance, the solute, to dissolve in a solvent. ... In chemistry, an ideal solution is a solution where the enthalpy of solution is zero. ... The mole fraction is one way of expressing the relative concentration of a given species. ... The melting point of a crystalline solid is the temperature at which it changes state from solid to liquid. ... This article includes a list of works cited or a list of external links, but its sources remain unclear because it lacks in-text citations. ...

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

For example the solubility of paracetamol in water at 298 K is predicted to be: Paracetamol (INN) (IPA: ) or acetaminophen (USAN), is a common analgesic and antipyretic drug that is used for the relief of fever, headaches, and other minor aches and pains. ... The kelvin (symbol: K) is the SI unit of temperature and is one of the seven SI base units. ...

$ln x_2 = - frac {28100 Jmol^{-1}} {8.314JK^{-1}mole^{-1}}left(frac{1}{298}- frac{1}{442}right) = 0.0248$

This equals to a solubility in grams per liter of:

$frac{0.0248*frac{1000 g}{18.053 gmol^{-1}}}{1-0.0248}*151.17 gmol^{-1} = 213.4$

which is a deviation from the real solubility (240 g/L) of 11%. This error can be reduced when an additional heat capacity parameter is taken into account [1] To meet Wikipedias quality standards, this article or section may require cleanup. ...

### Proof

At equilibrium the chemical potentials for the pure solvent and pure solid are identical: Chemical equilibrium is the state in which the concentrations of the reactants and products have no net change over time. ... In thermodynamics and chemistry, chemical potential, symbolized by Î¼, is a term introduced in 1876 by the American mathematical physicist Willard Gibbs, which he defined as follows: Gibbs noted also that for the purposes of this definition, any chemical element or combination of elements in given proportions may be considered a...

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

or

$mu^circ_{solid} = mu^circ_{liquid} + RTlnX_2,$

with $R,$ the gas constant and $T,$ the temperature. The gas constant (also known as the universal or ideal gas constant, usually denoted by symbol R) is a physical constant used in equations of state to relate various groups of state functions to one another. ... This article includes a list of works cited or a list of external links, but its sources remain unclear because it lacks in-text citations. ...

Rearranging gives:

$RTlnX_2 = - (mu^circ_{liquid} - mu^circ_{solid}),$

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

$RTlnX_2 = - ( Delta G^circ_{fus}),$

Application of the Gibbs-Helmholtz equation: The Gibbs-Helmholtz equation is a thermodynamic relationship useful for calculating changes in the energy or enthalpy (heat content) of a system. ...

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

ultimately gives:

$left( frac{partial ( lnX_2 } {partial T} right) = frac {Delta H^circ_{fus}} {RT^2}$

or:

$partial lnX_2 = frac {Delta H^circ_{fus}} {RT^2}*delta T$

and with integration: Look up integration in Wiktionary, the free dictionary. ...

$int^{x_2=x_2}_{x_2 = 1} delta lnX_2 = ln x_2 = int_{T_fus}^T frac {Delta H^circ_{fus}} {RT^2}*Delta T$

the end result is obtained:

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

The heat of vaporization is a physical property of substances. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... Specific heat capacity, also known simply as specific heat (Symbol: C or c) is the measure of the heat energy required to raise the temperature of a given amount of a substance by one degree. ... Thermodynamic databases contain information about thermodynamic properties for substances, the most important being enthalpy, entropy, and Gibbs free energy. ...

## References

1. ^ 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) DOI:10.1021/op060074g

Results from FactBites:

 Standard enthalpy change of fusion Summary (1435 words) The heat of fusion is the heat that is absorbed to transform a substance from its solid state to its liquid state at constant, that is, to melt the solid substance. Enthalpies of fusion are positive because the solid state affords the molecules or ions that compose a pure substance the opportunity to maximize their attractive interactions with each other. The standard enthalpy change of fusion, also known as the heat of fusion, is the amount of thermal energy which must be absorbed or lost for 1 gram of a substance to change states from a solid to a liquid or vice versa.
 Key Experimental Data (4915 words) This precise evaluation of the rate of enthalpy generation relies on the non-linear regression fitting of the "fl-box" model of the calorimeter to an extensive set of temperature time measurements. The method of data analysis gives a systematic underestimate of the enthalpy output and, in consequence, a slightly negative excess rate of enthalpy generation for an extensive set of blank experiments using both light and heavy water. It is also shown that prolonged polarization of palladium cathodes in heavy water leads to bursts in the rate of enthalpy generation: the thermal output of the cells exceeds the enthalpy input (or the total energy input) to the cells by factors in excess of 40 during these bursts.
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