Effusion (physics)

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On the left the schematic representation of the effusion through a hole size that is smaller than the mean free path of the molecules.
The larger hole on the right side allows diffusion , i.e. H. the simultaneous passage of several molecules in both directions.

In physics, the diffusion of individual atoms or molecules of a gas (less often a liquid) through a solid is referred to as effusion (from Latin effusio, pouring out ) , if they move through openings in the molecular lattice (see also crystal lattice ) that are smaller as the mean free path (see also Brownian molecular motion) of the effusing molecule.

If the openings are larger than the mean free path, there is a common leak through which gases and liquids diffusively distribute and mix.

As with diffusion and osmosis (through a semipermeable membrane ), the particle flow follows any potential difference that may be present (e.g. a pressure or concentration gradient ).

The effusion rate of a certain gas depends primarily on the molecular mass of the gas , in addition to temperature, hole size and any pressure differences that may exist . Using a defined experimental set-up, the molecular mass of unknown substances can be determined in order to then find out which chemical formula the substance has by means of combustion analysis . Today, much more accurate mass spectrometry is used instead , which manages with minimal amounts of substance.

Well-known examples

• It is known from airship travel that hydrogen-filled floats gradually lose their gas filling. Under normal conditions there are no effusion-proof vessels for helium gas .
• Some aromatic hydrocarbons in fuels, such as gasoline , diesel , and kerosene , effuse through certain plastics . The passage from tanks or canisters into the air led to the intoxication of motorists who had been exposed to their effects for too long, and which also dangerously increased the risk of explosion in the vicinity of unsuitable containers.
• In the case of molecular beam epitaxy (MBE), which takes place in an ultra-high vacuum (UHV) , effusion cells provide the flow of material. They contain a melt that is heated to over 1,000 degrees (e.g. gallium for GaAs MBE). The partial pressure and thus the material flow are a function of the temperature. The crucibles, which have to be made of a high-melting material (e.g. boron nitride ), are electrically heated and have an outlet opening.
• During the enrichment of uranium for nuclear fission , gaseous uranium hexafluoride (UF ₆ ) can be driven through membranes . Since the lighter ²³⁵ UF ₆ effuses slightly faster than the ²³⁸ UF ₆ , the lighter nuclide can be enriched. This technique was used during the Manhattan Project at Oak Ridge; the required system (code name K-25) occupied an area of ​​17 hectares.

Regularities

The by Thomas Graham even without knowledge of atomic or molecular structures and relationships found, and in 1833 published Graham's Law says that the discharge rates of different gases at the same pressure to the square roots of their densities are inversely proportional. It also applies very precisely to the effusion of liquids and gases, since the density is a function of the molecular mass and this represents a good approximation of the (average) molecular diameter. In addition, in the phase of passage through the wall, even non-gases and substances with the lowest viscosity obey the gas laws because - and as long as they move in this area as isolated atoms or molecules - these are essentially without neighbors.

According to Graham's law, there is a simple relationship between the effusion rates of two substances under otherwise identical conditions:

${\displaystyle {\frac {{\text{Rate}}_{1}}{{\text{Rate}}_{2}}}={\sqrt {\frac {M_{2}}{M_{1}}}}}$

• Rate ₁ : rate of effusion of gas 1
• Rate ₂ : rate of effusion of gas 2
• M ₁ : molar mass of gas 1
• M ₂ : molar mass of gas 2

The effusion rate of a gas is calculated as follows:

${\displaystyle {\text{Rate}}={\frac {pA_{0}N_{\mathrm {A} }}{\sqrt {2\pi MRT}}}}$

• Rate: rate of effusion of the gas
• p : pressure
• A ₀ : Area of ​​the hole through which the effusion takes place
• N _A : Avogadro's constant
• M : molar mass
• R : universal gas constant
• T : temperature

In the vicinity of the absolute zero point of the temperature , special conditions prevail that the effusion u. a. due to the lack of thermal molecular movements.

The hydrodynamic rule described by Evangelista Torricelli around 1644 , called Torricelli's theorem or also the Torricellian theorem, does not correctly describe the effusion in its original version - which he was not interested in either - but later versions, the 'very thick walls' and' take into account small outlet openings' etc., come relatively close to it.

See also: outflow velocity

Individual evidence

1. ^ KJ Laidler and JH Meiser: Physical Chemistry . Ed .: Benjamin / Cummings. 1982, ISBN 0-8053-5682-7 .
2. ↑ Steven S. Zumdahl: Chemical Principles . Houghton Mifflin Harcourt Publishing Company, Boston 2008, ISBN 978-0-547-19626-8 , p. 164.
3. ^ Peter Atkins : Physical Chemistry. 6th edition. Oxford University Press, 1998, ISBN 0-19-850101-3