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Temperature-dependency of the heats of vaporization for water, methanol, benzene, and acetone

The enthalpy of vaporization, (symbol ΔHvap), also known as the heat of vaporization or heat of evaporation, is the energy required to transform a given quantity of a substance into a gas.

It is often measured at the normal boiling point of a substance; although tabulated values are usually corrected to 298 K, the correction is often smaller than the uncertainty 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 below Tr<<1.0. The heat of vaporization diminishes with increasing temperature and it vanishes completely at the critical temperature (Tr=1) because above the critical temperature the liquid and vapor phases no longer co-exist.

Contents

Units

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

Physical Model for Vaporization

Fig. 1 Schematic cross section of the proposed vaporization model for monoatomic liquids with one atomic surface layer.


Simple physical model for the liquid-gas phase transformation has been proposed recently [1] . It is suggested that the energy required to free an atom from the liquid is equivalent with the energy needed to overcome the surface resistance of the liquid. The model allows calculating the latent heat by multiplying the maximum surface area covering and atom (Fig. 1) with the surface tension and the number of atoms in the liquid. The calculated latent heat of vaporization values for the investigated 45 elements agrees well with experiments.

Enthalpy of condensation

The enthalpy of condensation (or heat of condensation) is numerically exactly equal to the enthalpy of vaporization, but has 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

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 enthalpy of vaporization can be viewed as the energy required to overcome the intermolecular interactions in the liquid (or solid, in the case of sublimation). Hence helium has a particularly low enthalpy of vaporization, 0.0845 kJ/mol, as the van der Waals forces between helium atoms are particularly weak. On the other hand, the molecules in liquid water are held together by relatively strong hydrogen 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−1 mol−1). Care must be taken, however, when using enthalpies of vaporization to measure the strength of intermolecular forces, as these forces may persist to an extent in the gas phase (as is the case with hydrogen fluoride), and so the calculated value of the bond strength will be too low. This is particularly true of metals, which often form covalently bonded molecules in the gas phase: in these cases, the enthalpy of atomization must be used to obtain a true value of the bond 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 in entropy when a gas condenses to a liquid. As the liquid and gas are in equilibrium at the boiling point (Tb), ΔvG = 0, which leads to:

\Delta\,_v S = S_{gas} - S_{liquid} = \Delta\,_v H/T_b

As neither entropy nor enthalpy 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 the pressure is different from 100 kPa, as the entropy of a gas is proportional to its pressure (or, more precisely, to its fugacity): the entropies of liquids vary little with pressure, as the compressibility of a liquid is small.

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 (\Delta\,_v S is always positive), and from

\Delta\,G = \Delta\,H - T\Delta\,S,

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

Selected values

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Elements

Enthalpies of vaporization of the elements in kJ/mol, measured at their respective normal boiling points

Group → 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
↓ Period
1 H
0.44936

He
0.0845
2 Li
145.92
Be
292.40

B
489.7
C
355.8
N
2.7928
O
3.4099
F
3.2698
Ne
1.7326
3 Na
96.96
Mg
127.4

Al
293.4
Si
300
P
12.129
S
1.7175
Cl
10.2
Ar
6.447
4 K
79.87
Ca
153.6
Sc
314.2
Ti
421
V
452
Cr
344.3
Mn
226
Fe
349.6
Co
376.5
Ni
370.4
Cu
300.3
Zn
115.3
Ga
258.7
Ge
330.9
As
34.76
Se
26.3
Br
15.438
Kr
9.029
5 Rb
72.216
Sr
144
Y
363
Zr
581.6
Nb
696.6
Mo
598
Tc
660
Ru
595
Rh
493
Pd
357
Ag
250.58
Cd
100
In
231.5
Sn
295.8
Sb
77.14
Te
52.55
I
20.752
Xe
12.636
6 Cs
67.74
Ba
142
*
Hf
575
Ta
743
W
824
Re
 715 
Os
627.6
Ir
604
Pt
510
Au
334.4
Hg
59.229
Tl
164.1
Pb
177.7
Bi
104.8
Po
60.1
At
114
Rn
16.4
7 Fr
n/a
Ra
37
**
Rf
n/a
Db
n/a
Sg
n/a
Bh
n/a
Hs
n/a
Mt
n/a
Ds
n/a
Rg
n/a
Cn
n/a
Uut
n/a
Uuq
n/a
Uup
n/a
Uuh
n/a
Uus
n/a
Uuo
n/a

* Lanthanides La
414
Ce
414
Pr
n/a
Nd
n/a
Pm
n/a
Sm
n/a
Eu
n/a
Gd
n/a
Tb
n/a
Dy
n/a
Ho
n/a
Er
n/a
Tm
n/a
Yb
n/a
Lu
n/a
** Actinides Ac
n/a
Th
514.4
Pa
n/a
U
n/a
Np
n/a
Pu
n/a
Am
n/a
Cm
n/a
Bk
n/a
Cf
n/a
Es
n/a
Fm
n/a
Md
n/a
No
n/a
Lr
n/a
0–10 kJ/mol 10–100 kJ/mol 100–300 kJ/mol >300 kJ/mol
 

Other common substances

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

Compound Heat of vaporization
(kJ mol-1)
Heat of vaporization
(kJ kg-1)
Ammonia 23.35 1371
Butane 21.0 320
Ethanol 38.6 841
Hydrogen 0.46 451.9
Methane 8.19 760
Methanol 35.3 1104
Propane 15.7 356
Phosphine 14.6 429.4
Water 40.65 2257

Water is also commonly expressed as 539.423 calories per gram

See also

References

Sears, Zemansky et al., University Physics, Addison-Wesley Publishing Company, Sixth ed., 1982, ISBN 0-201-07199-1

  1. ^ J. Garai, Physical model for vaporization, Fluid Phase Equilibria, 283, 89-92 (2009)

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