
In
thermodynamics
Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws o ...
, Trouton's rule states that the
entropy of vaporization is almost the same value, about 85–88 J/(K·mol), for various kinds of
liquid
A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. As such, it is one of the four fundamental states of matter (the others being solid, gas, an ...
s at their
boiling points. The entropy of
vaporization
Vaporization (or vaporisation) of an element or compound is a phase transition from the liquid phase to vapor. There are two types of vaporization: evaporation and boiling. Evaporation is a surface phenomenon, whereas boiling is a bulk phenomenon. ...
is defined as the ratio between the
enthalpy
Enthalpy , a property of a thermodynamic system, is the sum of the system's internal energy and the product of its pressure and volume. It is a state function used in many measurements in chemical, biological, and physical systems at a constant ...
of vaporization and the
boiling
Boiling is the rapid vaporization of a liquid, which occurs when a liquid is heated to its boiling point, the temperature at which the vapour pressure of the liquid is equal to the pressure exerted on the liquid by the surrounding atmosphere. T ...
temperature. It is named after
Frederick Thomas Trouton.
It is be expressed as a function of the
gas constant
The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol or . It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment p ...
:
:
A similar way of stating this (Trouton's ratio) is that the
latent heat
Latent heat (also known as latent energy or heat of transformation) is energy released or absorbed, by a body or a thermodynamic system, during a constant-temperature process — usually a first-order phase transition.
Latent heat can be underst ...
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.
It is valid for many liquids; for instance, the
entropy
Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodyna ...
of vaporization of
toluene
Toluene (), also known as toluol (), is a substituted aromatic hydrocarbon. It is a colorless, water-insoluble liquid with the smell associated with paint thinners. It is a mono-substituted benzene derivative, consisting of a methyl group (CH3) ...
is 87.30 J/(K·mol), that of
benzene
Benzene is an organic chemical compound with the molecular formula C6H6. The benzene molecule is composed of six carbon atoms joined in a planar ring with one hydrogen atom attached to each. Because it contains only carbon and hydrogen ato ...
is 89.45 J/(K·mol), and that of
chloroform
Chloroform, or trichloromethane, is an organic compound with formula C H Cl3 and a common organic solvent. It is a colorless, strong-smelling, dense liquid produced on a large scale as a precursor to PTFE. It is also a precursor to various re ...
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
Water (chemical formula ) is an inorganic, transparent, tasteless, odorless, and nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living organisms (in which it acts as ...
,
ethanol
Ethanol (abbr. EtOH; also called ethyl alcohol, grain alcohol, drinking alcohol, or simply alcohol) is an organic compound. It is an alcohol with the chemical formula . Its formula can be also written as or (an ethyl group linked to a h ...
,
formic acid
Formic acid (), systematically named methanoic acid, is the simplest carboxylic acid, and has the chemical formula HCOOH and structure . It is an important intermediate in chemical synthesis and occurs naturally, most notably in some ants. Est ...
and
hydrogen fluoride are far from the predicted values. The entropy of vaporization of at its boiling point has the extraordinarily high value of 136.9 J/(K·mol).
The characteristic of those liquids to which Trouton’s rule cannot be applied is their special interaction between molecules, such as
hydrogen bonding
In chemistry, a hydrogen bond (or H-bond) is a primarily electrostatic force of attraction between a hydrogen (H) atom which is covalently bound to a more electronegative "donor" atom or group (Dn), and another electronegative atom bearing ...
. 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
The moment of inertia, otherwise known as the mass moment of inertia, angular mass, second moment of mass, or most accurately, rotational inertia, of a rigid body is a quantity that determines the torque needed for a desired angular accele ...
giving rise to a large
rotational constant
In rotordynamics, the rigid rotor is a mechanical model of rotating systems. An arbitrary rigid rotor is a 3-dimensional rigid object, such as a top. To orient such an object in space requires three angles, known as Euler angles. A special ri ...
, with correspondingly widely separated rotational energy levels and, according to
Maxwell–Boltzmann distribution
In physics (in particular in statistical mechanics), the Maxwell–Boltzmann distribution, or Maxwell(ian) distribution, is a particular probability distribution named after James Clerk Maxwell and Ludwig Boltzmann.
It was first defined and use ...
, a small population of excited rotational states, and hence a low rotational entropy. The validity of Trouton's rule can be increased by considering
:
Here, if , the right hand side of the equation equals , and we find the original formulation for Trouton's rule.
See also
*
Frederick Thomas Trouton
References
Further reading
* - Publication of Trouton's rule
*
Atkins, Peter (1978). ''Physical Chemistry''
Oxford University Press
Oxford University Press (OUP) is the university press of the University of Oxford. It is the largest university press in the world, and its printing history dates back to the 1480s. Having been officially granted the legal right to print book ...
{{States of matter
Chemistry theories
Thermodynamic properties