Enthalpies of melting and boiling for pure elements versus temperatures of transition, demonstrating Trouton's rule
It is expressed as a function of the gas constantR:
A similar way of stating this (Trouton's ratio) is that the latent heat is connected to boiling point roughly as
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 inertiaI giving rise to a large rotational constantB, 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]
Here, if T = 400 K, the right hand side of the equation equals 10.5R, and we find the original formulation for Trouton's rule.
Referencesedit
^Compare 85 J/(K·mol) in David Warren Ball (20 August 2002). Physical Chemistry. ISBN9780534266585. and 88 J/(K·mol) in Daniel L. Reger; Scott R. Goode; David W. Ball (27 January 2009). Chemistry: Principles and Practice. ISBN9780534420123.
^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. ISBN978-0-470-86078-6.
Further readingedit
Trouton, Frederick (1884). "On Molecular Latent Heat". Philosophical Magazine. 18 (110): 54–57. doi:10.1080/14786448408627563. - Publication of Trouton's rule
trouton, rule, trouton, ratio, redirects, here, trouton, ratio, context, viscosity, viscosity, newtonian, newtonian, fluids, thermodynamics, states, that, molar, entropy, vaporization, almost, same, value, about, various, kinds, liquids, their, boiling, points. Trouton s ratio redirects here For Trouton s ratio in the context of viscosity see Viscosity Newtonian and non Newtonian fluids 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 Enthalpies of melting and boiling for pure elements versus temperatures of transition demonstrating Trouton s ruleIt is expressed as a function of the gas constant R DS vap 10 5R displaystyle 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 LvapTboiling 85 88 JK mol displaystyle 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 DS vap 4 5R Rln T displaystyle 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 5R and we find the original formulation for Trouton s rule References edit 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 Further reading editTrouton Frederick 1884 On Molecular Latent Heat Philosophical Magazine 18 110 54 57 doi 10 1080 14786448408627563 Publication of Trouton s rule Atkins Peter 1978 Physical Chemistry Oxford University Press ISBN 0 7167 3539 3 Retrieved from https en wikipedia org w index php title Trouton 27s rule amp oldid 1200838585, wikipedia, wiki, book, books, library,
