Heat of vaporization

Measurement units

Heat of vaporization values are usually reported in measurement units such as J/mol or kJ/mol and referred to as the molar heat of vaporization, although J/g or kJ/kg are also often used. Older units such as kcal/mol, cal/g, Btu/lb and others are still used sometimes.

(GNU) Diagram: Wilfried Cordes
Figure 1: Heats of vaporization versus temperature.^[1]

Temperature dependency

The heat of vaporization is not a constant. It is temperature dependent as shown in Figure 1 by the example graphs of temperature versus heat of vaporization for acetone, benzene, methanol and water.

As shown by the example graphs, the heat of vaporization of a liquid at a given temperature (other than the normal boiling point temperature) may vary significantly from the value reported at the normal boiling point of the liquid.

Estimating heat of vaporization values

Heats of vaporization can be measured calorimetrically and measured values are available from a number of sources.^[1]^[2]^[3]^[4] However, data is not always available for certain liquids or at certain temperatures. In such cases, estimation of heats of vaporization can be made by any of a large number of different methods. Four of the commonly used methods are discussed in the following sections.

Using the Clausius-Clapeyron equation

This integrated form of the Clausius-Clapeyron relation can be used to provide a good approximation of the heat of vaporization for many pure liquids:^[5]^[6]

(1)

\log _{e}\left({\frac {\;p_{2}}{p_{1}}}\right)={\frac {\;H_{v}}{R}}\left({\frac {1}{T_{1}}}-{\frac {1}{T_{2}}}\right)

which can be re-arranged to obtain:

(2)

H_{v}=R\cdot \log _{e}\left({\frac {\;p_{2}}{p_{1}}}\right)\left({\frac {\;T_{2}\cdot T_{1}}{T_{2}-T_{1}}}\right)

where:
$H_{v}$	= Heat of vaporization, in J/mol
$R$	= 8.3144 = Universal gas constant, in J/(K $\cdot$ mol)
$log_{e}$	= Logarithm on base $e$
$p_{1}$	= The liquid's vapor pressure at $T_{1}$ , in atm
$p_{2}$	= The liquid's vapor pressure at $T_{2}$ , in atm
$T_{1}$	= Temperature, in K
$T_{2}$	= Temperature, in K

Table 1: Heat of vaporization, normal boiling point
and critical temperature and pressure of various liquids ^[7]^[8]
Name	Formula	H_v	T_n		T_c	p_c
Name	Formula	( J/mol )	( °C )	( K )	( K )	( atm )
Acetic acid	C₂H₄O₂	23,700	117.9	391.1	594.8	57.1
Acetone	C₃H₆O	29,100	56.2	329.4	508.7	47.0
Benzene	C₆H₆	30,720	80.0	353.2	562.1	48.6
Butane	C₄H₁₀	22,440	– 0.5	272.7	425.2	37.5
Carbon tetrachloride	CCl₄	29,820	76.6	349.8	556.3	45.0
Chloroform	CHCl₃	29,240	61.1	334.3	536.2	54.0
Cyclopentane	C₅H₁₀	27,300	49.2	322.4	511.8	44.6
Ethanol	C₂H₆O	38,560	78.2	351.4	516.2	63.0
Hexane	C₆H₁₄	28.850	68.7	341.9	507.4	29.9
Methanol	CH₄O	35,210	64.7	337.9	513.2	78.5
Water	H₂0	40,660	100	373.2	647.3	218.3
Notes: (1) H_v = heat of vaporization at the normal boiling point (2) T_n = normal boiling point (3) T_c = critical temperature (4) p_c = absolute critical pressure

The primary Clausius-Clapeyron equation is exact. However, the above integrated form of the equation is not exact because it is necessary to make these assumptions in order to perform the integration:^[5]^[6]

The molar volume of the liquid phase is negligible compared to the molar volume of the vapor phase
The vapor phase behaves like an ideal gas
The heat of vaporization is constant over the temperature range as defined by T₁ and T₂

As an example of using the Clausius-Clapeyron equation, given that the vapor pressure of benzene is 1 atm at 353 K and 2 atm at 377 K, benzene's heat of vaporization is obtained as 32,390 J/mol within that temperature range.

Using Riedel's equation

Riedel proposed an empirical equation for estimating a liquid's heat of vaporization at its normal boiling point.^[9] The equation may be expressed as:^[7]^[10]

(3)

H_{v}={\frac {1.092\,R\,T_{n}\,(\log _{e}p_{c}-\,1.013)}{0.930-(T_{n}/T_{c})}}

where:
$H_{v}$	= Heat of vaporization, in J/mol
$R$	= 8.3144 = Universal gas constant, in J/(K $\cdot$ mol)
$T_{n}$	= The liquid's normal boiling point, in K
$T_{c}$	= The liquid's critical temperature, in K
$log_{e}$	= Logarithm on base $e$
$p_{c}$	= The liquid's critical pressure at $T_{n}$ , in bar ^[11]

For an empirical expression, equation (3) is surprisingly accurate and its error rarely exceeds 5 %. For example, using water data (see Table 1) of T_n = 373.2 K,
T_c = 647.3 K and P_c = 221.2 bar (218.3 atm), the heat of vaporization is obtained as 42,060 J/mol. That is within 3 percent of the 40,660 J/mol in Table 1.

Table 2: Application
of Trouton's rule
Name	H_v $\scriptstyle /$ T_n
Acetone	90.6
Benzene	87.3
Butane	82.3
Cyclohexane	84.8
Octane	87.3

Using Trouton's rule

Troutons's rule, dating back to 1883,^[12]^[13] is a relation between a liquid's heat of vaporization and it's normal boiling point $T_{n}$ .^[5]^[6]^[14] It provides a good approximation of the heat of vaporization at the normal boiling point of many pure substances, and it may be expressed as:

(4)

{\frac {H_{v}}{T_{n}}}\approx 87\;\,\mathrm {to} \;\,88

Table 2 provides some examples of the application of Trouton's rule.

Trouton's rule fails for liquids with boiling points below 150 K. It also fails for water, alcohols, amines and liquid ammonia.^[14]

Using Watson's equation

Given the heat of vaporization of a liquid at any temperature, its heat of vaporization at another temperature may be estimated by using the Watson equation:^[5]^[7]^[15]

(5)

{\frac {H_{v2}}{H_{v1}}}=\left[{\frac {1-(T_{2}/T_{c})}{1-(T_{1}/T_{c})}}\right]^{0.38}

which can be re-arranged to obtain:

(6)

{\frac {H_{v2}}{H_{v1}}}=\left({\frac {T_{c}-T_{2}}{T_{c}-T_{1}}}\right)^{0.38}

where:
$H_{v1}$	= Heat of vaporization of the liquid at $T_{1}$ , in J/mol
$H_{v2}$	= Heat of vaporization of the liquid at $T_{2}$ , in J/mol
$T_{1}$	= Temperature, in K
$T_{2}$	= Temperature, in K
$T_{c}$	= Critical temperature of the liquid, in K

Watson's equation has achieved wide acceptance and is simple and reliable.

References

↑ ^1.0 ^1.1 Dortmund Data Bank Online Search
↑ Carl L. Yaws (1998). Chemical properties Handbook, 1st Edition. McGraw-Hill. ISBN 0-07--073401-1.
↑ Václav Svoboda and Henry V. Kehiaian (1985). Enthalpies of Vaporization of Organic Compounds: A Critical Review and Data Compilation, IUPAC Chemical Data Series 32. Blackwell Scientific. ISBN 0-632-01529-2.
↑ Perry, R.H. and Green, D.W. (Editors) (2007). Perry's Chemical Engineers' Handbook, Eighth Edition. McGraw-Hill. ISBN 0-07-142294-3.
↑ ^5.0 ^5.1 ^5.2 ^5.3 Jean Vidal (2003). Thermodynamics: Applications in Chemical Engineering and the Petroleum Industry. Editions Technip. ISBN 2-7108-0800-5. (Equation 2.10, page 38)
↑ ^6.0 ^6.1 ^6.2 Amir Faghri and Yuwen Zhang (2006). Transport Phenomena in Multiphase Systems, 1st Edition. Academic Press. ISBN 0-12-370610-6. (Equation 2.168, Chapter 2)
↑ ^7.0 ^7.1 ^7.2 J.M. Smith, H.C. Van Ness and M.M. Abbot (2004). Introduction to Chemical Engineering Thermodynamics, 7th Edition. McGraw-Hill. ISBN 0-07-310445-0.
↑ Robert C. Weast (Editor) (1976). Handbook of Chemistry and Physics=56th Edition. CRC Press. ISBN 0-87819-455-X.
↑ L. Riedel, Chem. Ing. Tech., 26, pp. 679-683, 1954
↑ M.M. Abbott and H.C. Van Ness (1989). Schaum's Outline of Thermodynamics With Chemical Applications, 2nd Edition. McGraw-Hill. ISBN 0-07-000042-5.
↑ 1 bar = 0.98692 atm
↑ F.T. Trouton, Nature, 27, p. 292, 1883
↑ F.T. Trouton, Phil. Mag., 18, pp.54-57, 1884
↑ ^14.0 ^14.1 Bimalendu Narayan Roy (2002). Fundamentals of Classical and Statistical Thermodynamics. John Wiley & Sons. ISBN 0-470-84316-0.
↑ K.M. Watson, Thermodynamics of the Liquid States, Generalized Prediction of Properties, Ind. Eng. Chem., 35, pp.398-406, 1943

[Dortmund-1] 1.0 ^1.1 Dortmund Data Bank Online Search

[2] Carl L. Yaws (1998). Chemical properties Handbook, 1st Edition. McGraw-Hill. ISBN 0-07--073401-1.

[3] Václav Svoboda and Henry V. Kehiaian (1985). Enthalpies of Vaporization of Organic Compounds: A Critical Review and Data Compilation, IUPAC Chemical Data Series 32. Blackwell Scientific. ISBN 0-632-01529-2.

[4] Perry, R.H. and Green, D.W. (Editors) (2007). Perry's Chemical Engineers' Handbook, Eighth Edition. McGraw-Hill. ISBN 0-07-142294-3.

[Vidal-5] 5.0 ^5.1 ^5.2 ^5.3 Jean Vidal (2003). Thermodynamics: Applications in Chemical Engineering and the Petroleum Industry. Editions Technip. ISBN 2-7108-0800-5. (Equation 2.10, page 38)

[Faghri-6] 6.0 ^6.1 ^6.2 Amir Faghri and Yuwen Zhang (2006). Transport Phenomena in Multiphase Systems, 1st Edition. Academic Press. ISBN 0-12-370610-6. (Equation 2.168, Chapter 2)

[Smith-7] 7.0 ^7.1 ^7.2 J.M. Smith, H.C. Van Ness and M.M. Abbot (2004). Introduction to Chemical Engineering Thermodynamics, 7th Edition. McGraw-Hill. ISBN 0-07-310445-0.

[8] Robert C. Weast (Editor) (1976). Handbook of Chemistry and Physics=56th Edition. CRC Press. ISBN 0-87819-455-X.

[9] L. Riedel, Chem. Ing. Tech., 26, pp. 679-683, 1954

[Schaum-10] M.M. Abbott and H.C. Van Ness (1989). Schaum's Outline of Thermodynamics With Chemical Applications, 2nd Edition. McGraw-Hill. ISBN 0-07-000042-5.

[11] 1 bar = 0.98692 atm

[12] F.T. Trouton, Nature, 27, p. 292, 1883

[13] F.T. Trouton, Phil. Mag., 18, pp.54-57, 1884

[Roy-14] 14.0 ^14.1 Bimalendu Narayan Roy (2002). Fundamentals of Classical and Statistical Thermodynamics. John Wiley & Sons. ISBN 0-470-84316-0.

[15] K.M. Watson, Thermodynamics of the Liquid States, Generalized Prediction of Properties, Ind. Eng. Chem., 35, pp.398-406, 1943

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Heat of vaporization

Contents

Measurement units

Temperature dependency