The Eötvös rule, named after the Hungarian physicist Loránd (Roland) Eötvös (1848–1919) enables the prediction of the surface tension of an arbitrary liquid pure substance at all

temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measurement, measured with a thermometer. Thermometers are calibrated in various Conversion of units of temperature, temp ...

s. The

density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...

molar mass In chemistry, the molar mass of a chemical compound is defined as the mass of a sample of that compound divided by the amount of substance which is the number of moles in that sample, measured in moles. The molar mass is a bulk, not molecular, ...

and the critical temperature of the liquid have to be known. At the critical point the surface tension is zero. The first assumption of the Eötvös rule is: 1. The surface tension is a linear function of the temperature. :This assumption is approximately fulfilled for most known liquids. When plotting the surface tension versus the temperature a fairly straight line can be seen which has a surface tension of zero at the critical temperature. The Eötvös rule also gives a relation of the surface tension behaviour of different liquids in respect to each other: 2. The temperature dependence of the surface tension can be plotted for all liquids in a way that the data collapses to a single master curve. To do so either the molar mass, the density, or the molar volume of the corresponding liquid has to be known. More accurate versions are found on the main page for surface tension.

The Eötvös rule

If ''V'' is the molar volume and ''T''_c the critical temperature of a liquid the surface tension γ is given by :

\gamma V^ = k(T_c - T)\,

where ''k'' is a constant valid for all liquids. The Eötvös constant has a value of 2.1×10⁻⁷ J/(K· mol^2/3). More precise values can be gained when considering that the line normally passes the temperature axis 6 K before the critical point: :

\gamma V^ = k(T_c - 6 \ \mathrm - T)\,

The molar volume ''V'' is given by the molar mass ''M'' and the density ρ :

V = M / \rho\,

The term

\gamma V^

is also referred to as the "molar surface tension" γ_mol : :

\gamma_ = \gamma V^\,

A useful representation that prevents the use of the unit mol^−2/3 is given by the

Avogadro constant The Avogadro constant, commonly denoted or , is the proportionality factor that relates the number of constituent particles (usually molecules, atoms or ions) in a sample with the amount of substance in that sample. It is an SI defining c ...

N_A : :

\gamma = k' \left( \frac \right)^(T_c - 6 \ \mathrm - T) = k' \left( \frac \right)^(T_c - 6 \ \mathrm - T)

John Lennard-Jones Sir John Edward Lennard-Jones (27 October 1894 – 1 November 1954) was a British mathematician and professor of theoretical physics at the University of Bristol, and then of theoretical science at the University of Cambridge. He was an im ...

and Corner showed in 1940 by means of the statistical mechanics the constant ''k''′ is nearly equal to the

Boltzmann constant The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas constant, ...

Water

For water, the following equation is valid between 0 and 100 °C. :

\gamma = 0.07275 \ \mathrm \cdot (1-0.002 \cdot (T - 291 \ \mathrm))

History

As a student, Eötvös started to research surface tension and developed a new method for its determination. The Eötvös rule was first found phenomenologically and published in 1886. In 1893

William Ramsay Sir William Ramsay (; 2 October 1852 – 23 July 1916) was a Scottish chemist who discovered the noble gases and received the Nobel Prize in Chemistry in 1904 "in recognition of his services in the discovery of the inert gaseous element ...

and Shields showed an improved version considering that the line normally passes the temperature axis 6 K before the critical point.

and Corner published (1940) a derivation of the equation by means of statistical mechanics. In 1945

E. A. Guggenheim Edward Armand Guggenheim FRS (11 August 1901 in Manchester – 9 August 1970) was an English physical chemist, noted for his contributions to thermodynamics. Life Guggenheim was born in Manchester 11 August 1901, the son of Armand Guggenheim and ...

gave a further improved variant of the equation.

References

{{DEFAULTSORT:Eotvos rule Physical chemistry Thermodynamic equations