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Enthalpy of vaporization

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Energy to convert a liquid substance to a gas at a given pressure

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Temperature-dependency of the heats of vaporization forwater,methanol,benzene, andacetone

Inthermodynamics, theenthalpy of vaporization (symbolHvap), also known as the (latent)heat of vaporization orheat of evaporation, is the amount of energy (enthalpy) that must be added to aliquid substance totransform a quantity of that substance into agas. The enthalpy of vaporization is a function of thepressure and temperature at which the transformation (vaporization orevaporation) takes place.

The enthalpy of vaporization is often quoted for thenormal boiling temperature of the substance. Although tabulated values are usually corrected to 298 K, that correction is often smaller than theuncertainty in the measured value.

The heat of vaporization is temperature-dependent, though a constant heat of vaporization can be assumed for small temperature ranges and forreduced temperatureTr ≪ 1. The heat of vaporization diminishes with increasing temperature and it vanishes completely at a certain point called thecritical temperature (Tr = 1). Above the critical temperature, the liquid andvapor phases are indistinguishable, and the substance is called asupercritical fluid.

Units

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Values are usually quoted inJ/mol, or kJ/mol (molar enthalpy of vaporization), although kJ/kg, or J/g (specific heat of vaporization), and older units likekcal/mol, cal/g andBtu/lb are sometimes still used among others.

Enthalpy of condensation

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Theenthalpy of condensation (orheat of condensation) is by definition equal to the enthalpy of vaporization with the opposite sign: enthalpy changes of vaporization are always positive (heat is absorbed by the substance), whereas enthalpy changes of condensation are always negative (heat is released by the substance).

Thermodynamic background

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Molar enthalpy 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) is115330 J/mol.

The enthalpy of vaporization can be written as

ΔHvap=ΔUvap+pΔV{\displaystyle \Delta H_{\text{vap}}=\Delta U_{\text{vap}}+p\,\Delta V}

It is equal to the increasedinternal energy of the vapor phase compared with the liquid phase, plus the work done against ambient pressure. The increase in the internal energy can be viewed as the energy required to overcome theintermolecular interactions in the liquid (or solid, in the case ofsublimation). Hencehelium has a particularly low enthalpy of vaporization, 0.0845 kJ/mol, as thevan der Waals forces between heliumatoms are particularly weak. On the other hand, themolecules in liquidwater are held together by relatively stronghydrogen bonds, and its enthalpy of vaporization, 40.65 kJ/mol, is more than five times the energy required to heat the same quantity of water from 0 °C to 100 °C (cp = 75.3 J/K·mol). Care must be taken, however, when using enthalpies of vaporization tomeasure the strength of intermolecular forces, as these forces may persist to an extent in the gas phase (as is the case withhydrogen fluoride), and so the calculated value of thebond strength will be too low. This is particularly true of metals, which often formcovalently bonded molecules in the gas phase: in these cases, theenthalpy of atomization must be used to obtain a true value of thebond energy.

An alternative description is to view the enthalpy of condensation as the heat which must be released to the surroundings to compensate for the drop inentropy when a gas condenses to a liquid. As the liquid and gas are inequilibrium at the boiling point (Tb),ΔvG = 0, which leads to:

ΔvS=SgasSliquid=ΔvHTb{\displaystyle \Delta _{\text{v}}S=S_{\text{gas}}-S_{\text{liquid}}={\frac {\Delta _{\text{v}}H}{T_{\text{b}}}}}

As neither entropy norenthalpy vary greatly with temperature, it is normal to use the tabulated standard values without any correction for the difference in temperature from 298 K. A correction must be made if thepressure is different from 100 kPa, as the entropy of anideal gas is proportional to the logarithm of its pressure. The entropies of liquids vary little with pressure, as thecoefficient of thermal expansion of a liquid is small.[1]

These two definitions are equivalent: the boiling point is the temperature at which the increased entropy of the gas phase overcomes the intermolecular forces. As a given quantity of matter always has a higher entropy in the gas phase than in a condensed phase (ΔvS{\displaystyle \Delta _{\text{v}}S} is always positive), and from

ΔG=ΔHTΔS{\displaystyle \Delta G=\Delta H-T\Delta S},

theGibbs free energy change falls with increasing temperature: gases are favored at higher temperatures, as is observed in practice.

Vaporization enthalpy of electrolyte solutions

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Estimation of the enthalpy of vaporization of electrolyte solutions can be simply carried out using equations based on the chemical thermodynamic models, such as Pitzer model[2] or TCPC model.[3]

Selected values

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Elements

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Enthalpies of vaporization of the elements
123456789101112131415161718
Group →
↓ Period
1H0.90He0.08
2Li136Be292B508C715N5.57O6.82F6.62Ne1.71
3Na97.4Mg128Al284Si359P12.4S45Cl20.4Ar6.53
4K76.9Ca155Sc333Ti425V444Cr339Mn221Fe340Co377Ni379Cu300Zn115Ga256Ge334As32.4Se95.5Br30.0Kr9.08
5Rb75.8Sr141Y390Zr573Nb690Mo617Tc585Ru619Rh494Pd358Ag254Cd99.9In232Sn296Sb193Te114I41.6Xe12.6
6Cs63.9Ba1401 asteriskLu414Hf648Ta733W807Re704Os678Ir564Pt510Au342Hg59.1Tl165Pb179Bi179Po103At54.4Rn18.1
7Fr65Ra1131 asteriskLrn/aRfn/aDbn/aSgn/aBhn/aHsn/aMtn/aDsn/aRgn/aCnn/aNhn/aFln/aMcn/aLvn/aTsn/aOgn/a

1 asteriskLa400Ce398Pr331Nd289Pm289Sm172Eu176Gd301Tb391Dy280Ho251Er280Tm191Yb129
1 asteriskAc400Th514Pa481U417Np336Pu333Amn/aCmn/aBkn/aCfn/aEsn/aFmn/aMdn/aNon/a
 
Enthalpy in kJ/mol, measured at their respective normal boiling points
0–10 kJ/mol10–100 kJ/mol100–300 kJ/mol>300 kJ/mol

The vaporization of metals is a key step inmetal vapor synthesis, which exploits the increased reactivity of metal atoms or small particles relative to the bulk elements.

Other common substances

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Enthalpies of vaporization of common substances, measured at their respective standard boiling points:

CompoundBoiling point, at normal pressureHeat of vaporization
(K)(°C)(°F)(kJ/mol)(J/g)
Acetone3295613331.300538.9
Aluminium279225194566294.010500
Ammonia240−33.34−2823.351371
Butane272–274−130–3421.0320
Diethyl ether307.834.694.326.17353.1
Ethanol35278.3717338.6841
Hydrogen (parahydrogen)20.271−252.879−423.1820.8992446.1
Iron3134286251823406090
Isopropyl alcohol35682.618144732.2
Methane112−161−2598.170480.6
Methanol33864.714835.2[4]1104
Propane231−42−4415.7356
Phosphine185−87.7−12614.6429.4
Water373.1510021240.662257

See also

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References

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  1. ^Note that the rate of change of entropy with pressure and the rate of thermal expansion are related by theMaxwell Relation:
    (SP)T=(VT)P.{\displaystyle \left({\frac {\partial S}{\partial P}}\right)_{T}=\left({\frac {\partial V}{\partial T}}\right)_{P}.}
  2. ^Ge, Xinlei; Wang, Xidong (20 May 2009)."Estimation of Freezing Point Depression, Boiling Point Elevation, and Vaporization Enthalpies of Electrolyte Solutions".Industrial & Engineering Chemistry Research.48 (10): 5123.doi:10.1021/ie900434h.
  3. ^Ge, Xinlei; Wang, Xidong (2009). "Calculations of Freezing Point Depression, Boiling Point Elevation, Vapor Pressure and Enthalpies of Vaporization of Electrolyte Solutions by a Modified Three-Characteristic Parameter Correlation Model".Journal of Solution Chemistry.38 (9):1097–1117.doi:10.1007/s10953-009-9433-0.ISSN 0095-9782.S2CID 96186176.
  4. ^NIST
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