# Loschmidt constant

The Loschmidt constant NL is a named after Josef Loschmidt physical constant that specifies the number of molecules per unit volume of an ideal gas under normal conditions:

Its value is in accordance with current measurement accuracy:

Where the bracketed numbers indicate the estimated standard deviation of 0.000 002 4.

## Correlations with other variables

It is related to the Avogadro constant NA on the molar volume of an ideal gas under normal conditions, Vm0 over

Together. The relationship can also be the universal gas constant R, the normal pressure P0 = 101 325 Pa, and the normal temperature T0 = 273.15 K can be expressed:

This also provides a connection to the Boltzmann constant k:

CODATA used as size symbol for the Avogadro constant n0. The symbol L is used as an alternative to NA for the Avogadro constant - therefore, this form should be avoided for the Avogadro constant.

## Historical and name of the constant

The Italian physicist Amedeo Avogadro postulated in 1811 that equal volumes of different ideal gases contain the same number of molecules ( Avogadrosches Act).

First time it was in 1865 (after Avogadro's death) the Austrian physicist and chemist Josef Loschmidt (then known as Joseph Loschmidt ) to determine this number of molecules in order of magnitude ( see below). Loschmidt's student and later friend Ludwig Boltzmann called the derived results Loschmidt number of molecules ( particles ) of an ideal gas at normal pressure and temperature per volume than ( the physical size of ) Loschmidt constant. The Loschmidt constant multiplied by the CGS unit cubic centimeter ( cm3) is called Loschmidt number indicates ( in Gaussian CGS system ):

1909 ( after both Loschmidt and Avogadro had already died ) proposed by the French chemist Jean -Baptiste Perrin specifying the size rather than particle number per unit volume, but as the number of particles per mole under the name Avogadro's number before. The Avogadro number ( in the SI system ) is therefore at, how many particles of a mass of 1 mole is. In German-speaking countries, however, the name Loschmidt number or Avogadro number was used. However, now with a different meaning, namely as a synonym for Avogadro's number.

The Avogadro number in the SI system multiplied by the SI unit mol -1 is the (physical size ) Avogadro constant:

The Avogadro constant (not the Avogadro constant) is used to reshape molecular to molar quantities. In the CODATA recommendations for physical constants, the Loschmidt constant is contained in the CODATA 1986 publication.

## Loschmidt's work "On the size of the air molecules "

The work that established in the Loschmidt in 1865 later named after him Loschmidt number, in 1866 published as an article "On the size of the air molecules ." It built on the kinetic theory of gases and related results of Clausius, Maxwell and OE Meyer. Loschmidt defined there, although the number of air molecules contained in unit volume, a numerical value for this but he did not give to. The aim of his work was called a preliminary approximation of the size of the diameter of the air molecules under normal conditions, here Loschmidt'scher molecular diameter s0 of an ideal gas. s0 was calculated from a so-called " condensation coefficient " and from the known value of the mean free path λ for air at 0 ° C. The Loschmidt constant NL can it - again on the mean free path - after

Be calculated. Pressing the now generally recommended value of Avogadro 's constant or the Avogadro constant as Loschmidt molecular diameter, so is s0 = 0.361 nm Loschmidt result from 1865 was s0 = 0.970 nm, ie 2.7 times the actual value. However, he also made a statement to the statistical uncertainty of its results. Original quote: " This value is to be taken of course, only as a rough approximation, but it is certainly not ten times too big or too small." So he is right.

For the mean free path Loschmidt were two different values: the value of λ determined by Maxwell = 62 nm and a newer, much larger, and - as was proven later - less precise, published by OE Meyer value of λ = 140 nm Today, for the mean free path of an ideal gas under normal conditions λ = 68 nm Maxwell applies had Loschmidt then used instead Meyers value of the mean free path for its calculation, it would come out for s0 = 0.429 nm. This alternative result has an amazingly small inaccuracy of only the 1.28 -fold of the actual value. Translated into the Loschmidt constant corresponds NL ≈ 2.092 2 · 1025 m-3, or as usually on the molar volume of ideal gas ( 22.4 l ) in relation ( Avogadro's number ): NL ≈ 4.686 · 1023 m -3, which corresponds to the today usual value NA ≈ 6.022 · 1023 mol -1.