Enthalpies of melting and boiling for pure elements versus temperatures of transition

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 of the ...

, Trouton's rule states that the

entropy of vaporization In thermodynamics, the entropy of vaporization is the increase in entropy upon vaporization of a liquid. This is always positive, since the degree of disorder increases in the transition from a liquid in a relatively small volume to a vapor or ...

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, a ...

s at their

boiling point The boiling point of a substance is the temperature at which the vapor pressure of a liquid equals the pressure surrounding the liquid and the liquid changes into a vapor. The boiling point of a liquid varies depending upon the surrounding envir ...

s. The entropy of vaporization 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. Th ...

temperature. It is named after Frederick Thomas Trouton. It is be expressed as a function of the gas constant : :

\Delta \bar S_\text \approx 10.5 R.

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

\frac \approx 8588\ \frac.

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 thermodynam ...

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) at ...

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 atoms, ...

is 89.45 J/(K·mol), and that of

chloroform Chloroform, or trichloromethane, is an organic compound with chemical formula, formula Carbon, CHydrogen, HChlorine, Cl3 and a common organic solvent. It is a colorless, strong-smelling, dense liquid produced on a large scale as a precursor to ...

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 a ...

ethanol Ethanol (abbr. EtOH; also called ethyl alcohol, grain alcohol, drinking alcohol, or simply alcohol) is an organic compound. It is an Alcohol (chemistry), alcohol with the chemical formula . Its formula can be also written as or (an ethyl ...

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. Es ...

and

hydrogen fluoride Hydrogen fluoride (fluorane) is an inorganic compound with the chemical formula . This colorless gas or liquid is the principal industrial source of fluorine, often as an aqueous solution called hydrofluoric acid. It is an important feedstock i ...

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. 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 Dimer may refer to: * Dimer (chemistry), a chemical structure formed from two similar sub-units ** Protein dimer, a protein quaternary structure ** d-dimer * Dimer model, an item in statistical mechanics, based on ''domino tiling'' * Julius 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 acceler ...

giving rise to a large rotational constant , 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 used ...

, a small population of excited rotational states, and hence a low rotational entropy. The validity of Trouton's rule can be increased by considering :

\Delta \bar S_\text \approx 4.5R + R \ln T.

Here, if , the right hand side of the equation equals , and we find the original formulation for Trouton's rule.

See also

References

Further reading