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In thermodynamics, Trouton's rule states that the (molar) entropy of vaporization is almost the same value, about 85–88 J/(K·mol), for various kinds of liquids at their boiling points.^[1] The entropy of vaporization is defined as the ratio between the enthalpy of vaporization and the boiling temperature. It is named after Frederick Thomas Trouton.

It is expressed as a function of the gas constant $R$ :

\Delta {\bar {S}}_{\text{vap}}\approx 10.5R.

A similar way of stating this (Trouton's ratio) is that the latent heat is connected to boiling point roughly as

{\frac {L_{\text{vap}}}{T_{\text{boiling}}}}\approx 85{-}88\ {\frac {\text{J}}{{\text{K}}\cdot {\text{mol}}}}.

Trouton’s rule can be explained by using Boltzmann's definition of entropy to the relative change in free volume (that is, space available for movement) between the liquid and vapour phases.^[2]^[3] It is valid for many liquids; for instance, the entropy of vaporization of toluene is 87.30 J/(K·mol), that of benzene is 89.45 J/(K·mol), and that of chloroform is 87.92 J/(K·mol). Because of its convenience, the rule is used to estimate the enthalpy of vaporization of liquids whose boiling points are known.

The rule, however, has some exceptions. For example, the entropies of vaporization of water, ethanol, formic acid and hydrogen fluoride are far from the predicted values. The entropy of vaporization of XeF₆ at its boiling point has the extraordinarily high value of 136.9 J/(K·mol).^[4] The characteristic of those liquids to which Trouton’s rule cannot be applied is their special interaction between molecules, such as hydrogen bonding. The entropy of vaporization of water and ethanol shows positive deviance from the rule; this is because the hydrogen bonding in the liquid phase lessens the entropy of the phase. In contrast, the entropy of vaporization of formic acid has negative deviance. This fact indicates the existence of an orderly structure in the gas phase; it is known that formic acid forms a dimer structure even in the gas phase. Negative deviance can also occur as a result of a small gas-phase entropy owing to a low population of excited rotational states in the gas phase, particularly in small molecules such as methane – a small moment of inertia $I$ giving rise to a large rotational constant $B$ , with correspondingly widely separated rotational energy levels and, according to Maxwell–Boltzmann distribution, a small population of excited rotational states, and hence a low rotational entropy. The validity of Trouton's rule can be increased by considering^{[citation needed]}

\Delta {\bar {S}}_{\text{vap}}\approx 4.5R+R\ln T.

Here, if $T = 400 K$ , the right hand side of the equation equals $10.5 R$ , and we find the original formulation for Trouton's rule.

References

^ Compare 85 J/(K·mol) in David Warren Ball (20 August 2002). Physical Chemistry. ISBN 9780534266585. and 88 J/(K·mol) in Daniel L. Reger; Scott R. Goode; David W. Ball (27 January 2009). Chemistry: Principles and Practice. ISBN 9780534420123.
^ Dan McLachlan Jr.; Rudolph J. Marcus (1957). "The statistical-mechanical basis of Trouton's rule". J. Chem. Educ. 34 (9): 460. Bibcode:1957JChEd..34..460M. doi:10.1021/ed034p460.
^ Shutler, P. M. E.; Cheah, H. M. (1998). "Applying Boltzmann's definition of entropy". European Journal of Physics. 19 (4): 371–377. Bibcode:1998EJPh...19..371S. doi:10.1088/0143-0807/19/4/009. ISSN 0143-0807.
^ R. Bruce King, ed. (2005). Encyclopedia of Inorganic Chemistry (2nd ed.). Wiley. ISBN 978-0-470-86078-6.

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+{{Short description|Linear relation between entropy of vaporization and boiling point}}{{Redirect|Trouton's ratio|Trouton's ratio in the context of viscosity|Viscosity#Newtonian and non-Newtonian fluids}}[[File:Enthalpies of melting and boiling for pure elements versus temperatures of transition.svg|right|thumb|400px|alt=A log–log plot of the enthalpies of melting and boiling versus the melting and boiling temperatures for the pure elements. The linear relationship between the enthalpy of vaporization and the boiling point is Trouton's rule. A similar relationship is shown for the [[Enthalpy of fusion|enthalpy of melting]].|Enthalpies of melting and boiling for pure elements versus temperatures of transition, demonstrating Trouton's rule]]
-'''Trouton’s rule''' states that the [[entropy of vaporization]] is almost the same value, about 87–88 J K<sup>−1</sup> mol<sup>−1</sup>, for various kinds of [[liquid]]s. The entropy of vaporization is defined as the ratio between the [[enthalpy]] of vaporization and the boiling temperature. It is named after [[Frederick Thomas Trouton]].
+In [[thermodynamics]], '''Trouton's rule''' states that the (molar) [[entropy of vaporization]] is almost the same value, about 85–88&nbsp;J/(K·mol), for various kinds of [[liquid]]s at their [[boiling point]]s.<ref>Compare 85&nbsp;J/(K·mol) in {{cite book |url=https://books.google.com/books?id=SpIV3J_mwiMC&pg=PA87 |title=Physical Chemistry |author=David Warren Ball|date=20 August 2002 |isbn=9780534266585 }} and 88&nbsp;J/(K·mol) in {{cite book |url=https://books.google.com/books?id=OUIaM1V3ThsC&pg=PA206 |title=Chemistry: Principles and Practice |author1=Daniel L. Reger |author2=Scott R. Goode |author3=David W. Ball |date=27 January 2009 |isbn=9780534420123 }}</ref> The entropy of [[vaporization]] is defined as the ratio between the [[enthalpy]] of vaporization and the [[boiling]] temperature. It is named after [[Frederick Thomas Trouton]].
-Mathematically, it can be expressed as:
+It is expressed as a function of the [[gas constant]] {{mvar|R}}:
-:<math>\Delta \bar S_{vap} = 10.5R </math>
+: <math>\Delta \bar S_\text{vap} \approx 10.5 R.</math>
-where R is the [[gas constant]]
+A similar way of stating this ('''Trouton's ratio''') is that the [[latent heat]] is connected to boiling point roughly as
-Trouton’s rule is valid for many liquids; for instance, the entropy of vaporization of [[toluene]] is 87.30 J K<sup>−1</sup> mol<sup>−1</sup>, that of [[benzene]] is 89.45 J K<sup>−1</sup> mol<sup>−1</sup>, and that of [[chloroform]] is 87.92 J K<sup>−1</sup> mol<sup>−1</sup>. Because of its convenience, the rule is used to estimate the enthalpy of vaporization of liquids whose [[boiling point]]s are known.
+: <math>\frac{L_\text{vap}}{T_\text{boiling}} \approx 85{-}88\ \frac{\text{J}}{\text{K} \cdot \text{mol}}.</math>
-The rule, however, has some exceptions. For example, the entropies of vaporization of water, [[ethanol]], and [[formic acid]] are far from the predicted values. The characteristic of those liquids to which Trouton’s rule cannot be applied is their special interaction between molecules such as [[hydrogen bonding]]. The entropy of vaporization of water and ethanol shows positive deviance from the rule; this is because the hydrogen bonding in the liquid phase lessens the entropy of the phase. In contrast, the entropy of vaporization of formic acid has negative deviance. This fact indicates the existence of an orderly structure in the gas phase; it is known that formic acid forms a [[dimer]] structure even in the gas phase. Negative deviance can also occur as a result of a small gas phase entropy owing to a low population of excited rotational states in the gas phase, particularly in small molecules such as methane - a small moment of inertia I giving rise to a large rotational constant B, with correspondingly widely separated rotational energy levels and, via Maxwell-Boltzmann distribution, a small population of excited rotational states and hence a low rotational entropy.
-Trouton's rule validity can be increased by considering
+Trouton’s rule can be explained by using [[Boltzmann's entropy formula|Boltzmann's definition of entropy]] to the relative change in free volume (that is, space available for movement) between the liquid and [[Vapor|vapour phase]]s.<ref>{{cite journal | doi = 10.1021/ed034p460 | title = The statistical-mechanical basis of Trouton's rule | author1 = Dan McLachlan Jr. | author2= Rudolph J. Marcus | journal = J. Chem. Educ. | year = 1957 | volume = 34 | issue = 9 | page = 460| bibcode = 1957JChEd..34..460M }}</ref><ref name="ShutlerCheah1998">{{cite journal |last1=Shutler |first1=P. M. E. |last2=Cheah |first2=H. M. |title=Applying Boltzmann's definition of entropy |journal=European Journal of Physics |volume=19 |issue=4 |year=1998 |pages=371–377 |issn=0143-0807 |doi=10.1088/0143-0807/19/4/009 |bibcode=1998EJPh...19..371S}}</ref> It is valid for many liquids; for instance, the [[entropy]] of vaporization of [[toluene]] is 87.30&nbsp;J/(K·mol), that of [[benzene]] is 89.45&nbsp;J/(K·mol), and that of [[chloroform]] is 87.92&nbsp;J/(K·mol). Because of its convenience, the rule is used to estimate the enthalpy of vaporization of liquids whose boiling points are known.
-:<math>\Delta \bar S_{vap} = 4.5R + R\ln T</math>
+The rule, however, has some exceptions. For example, the entropies of vaporization of [[Properties of water|water]], [[ethanol]], [[formic acid]] and [[hydrogen fluoride]] are far from the predicted values. The entropy of vaporization of {{chem2|XeF6}} at its boiling point has the extraordinarily high value of 136.9&nbsp;J/(K·mol).<ref>{{cite book |title=Encyclopedia of Inorganic Chemistry |year=2005 |publisher=Wiley |isbn=978-0-470-86078-6 |edition=2nd |editor=R. Bruce King}}</ref> The characteristic of those liquids to which Trouton’s rule cannot be applied is their special interaction between molecules, such as [[hydrogen bonding]]. The entropy of vaporization of water and ethanol shows positive deviance from the rule; this is because the hydrogen bonding in the liquid phase lessens the entropy of the phase. In contrast, the entropy of vaporization of formic acid has negative deviance. This fact indicates the existence of an orderly structure in the gas phase; it is known that formic acid forms a [[Dimer (chemistry)|dimer]] structure even in the gas phase. Negative deviance can also occur as a result of a small gas-phase entropy owing to a low population of excited rotational states in the gas phase, particularly in small molecules such as methane{{snd}} a small [[moment of inertia]] {{mvar|I}} giving rise to a large [[rotational constant]] {{mvar|B}}, with correspondingly widely separated rotational energy levels and, according to [[Maxwell–Boltzmann distribution]], a small population of excited rotational states, and hence a low rotational entropy. The validity of Trouton's rule can be increased by considering{{CN|date=July 2021}}
-Here, if ''T'' = 400 K, we find the original formulation for Trouton's rule
+: <math>\Delta \bar S_\text{vap} \approx 4.5R + R \ln T.</math>
-Another equation which ''T''<sub>boiling</sub> < 2100 K is  Δ''H''<sub>boiling</sub> = 87 ''T''<sub>boiling</sub> − 0.4 J/K.
+Here, if {{math|1=''T'' = 400 K}}, the right hand side of the equation equals {{math|10.5''R''}}, and we find the original formulation for Trouton's rule.
-== Further reading ==
+== References ==
-* {{cite journal | title = On Molecular Latent Heat | author = Trouton, Frederick | journal = Philosophical Magazine | year = 1884 | volume = 18 | pages = 54 &ndash; 57 | url = http://books.google.com/books?id=zpAOAAAAIAAJ&pg=PR3&lpg=PR3&dq=trouton+philosophical+magazine+1884&source=bl&ots=DQyO93kGtA&sig=KGq-vyD3M_dlrSMFAtVJE8DHKKw&hl=en&sa=X&oi=book_result&resnum=4&ct=result#PPA54,M2}} - Publication of Trouton's rule
+{{reflist}}
-* [[Peter Atkins|Atkins, Peter]] (1978). ''Physical Chemistry'' [[Oxford University Press]] ISBN 0-7167-3539-X
+== Further reading ==
-[[Category:Chemistry theories]]
+* {{cite journal | title = On Molecular Latent Heat | author = Trouton, Frederick | journal = Philosophical Magazine | year = 1884 | volume = 18 | issue = 110 | pages = 54&ndash;57 | url = https://books.google.com/books?id=zpAOAAAAIAAJ&q=trouton+philosophical+magazine+1884&pg=PR3 | doi=10.1080/14786448408627563}} - Publication of Trouton's rule
+* [[Peter Atkins|Atkins, Peter]] (1978). ''Physical Chemistry'' [[Oxford University Press]] {{ISBN|0-7167-3539-3}}
+{{States of matter}}
-{{chem-stub}}
+[[Category:Chemistry theories]]
-[[fr:Règle de Trouton]]
+[[Category:Thermodynamic properties]]
-[[nl:Regel van Trouton]]
-[[ja:トルートンの規則]]
-[[pl:Reguła Troutona]]

v t e States of matter (list)
State	Solid Liquid Gas / Vapor Supercritical fluid Plasma
Low energy	Bose–Einstein condensate Fermionic condensate Degenerate matter Quantum Hall Rydberg matter Strange matter Superfluid Supersolid Photonic molecule
High energy	QCD matter Quark–gluon plasma Color-glass condensate
Other states	Colloid Crystal Liquid crystal Time crystal Quantum spin liquid Exotic matter Programmable matter Dark matter Antimatter Magnetically ordered Antiferromagnet Ferrimagnet Ferromagnet String-net liquid Superglass
Phase transitions	Boiling Boiling point Condensation Critical line Critical point Crystallization Deposition Evaporation Flash evaporation Freezing Chemical ionization Ionization Lambda point Melting Melting point Recombination Regelation Saturated fluid Sublimation Supercooling Triple point Vaporization Vitrification
Quantities	Enthalpy of fusion Enthalpy of sublimation Enthalpy of vaporization Latent heat Latent internal energy Trouton's rule Volatility
Concepts	Baryonic matter Binodal Compressed fluid Cooling curve Equation of state Leidenfrost effect Macroscopic quantum phenomena Mpemba effect Order and disorder (physics) Spinodal Superconductivity Superheated vapor Superheating Thermo-dielectric effect