Hertz–Knudsen equation

In surface chemistry, the Hertz–Knudsen equation, also known as Knudsen–Langmuir equation describes evaporation rates, named after Heinrich Hertz and Martin Knudsen.

Definition

Non-dissociative adsorption (Langmuirian adsorption)

The Hertz–Knudsen equation describes the non-dissociative adsorption of a gas molecule on a surface by expressing the variation of the number of molecules impacting on the surfaces per unit of time as a function of the pressure of the gas and other parameters which characterise both the gas phase molecule and the surface:[1][2]

where:

Quantity Description
ASurface area (in m2)
NNumber of gas molecules
t Time (in s)
φFlux of the gas molecules (in m−2 s−1)
αAnomalous evaporation coefficient, 0 ≤ α ≤ 1, to match experimental results to theoretical predictions (Knudsen noted that experimental fluxes are lower than theoretical fluxes)[3]
pThe gas pressure (in Pa)
MMolar mass (in kg mol−1)
mMass of a particle (in kg)
kBBoltzmann constant
TTemperature (in K)
RGas constant (J mol−1 K−1)
NAAvogadro constant (mol−1)

Since the equation result has the units of s−1 it can be assimilated to a rate constant for the adsorption process.

See also

  • Langmuir (unit)

References

  1. Kolasinski, Kurt W. (2012). Surface Science: Foundations of Catalysis and Nanoscience, Third Edition. p. 203. doi:10.1002/9781119941798.
  2. R. B. Darling, EE-527: Micro Fabrication, Virginia University (retrieved Feb. 9 2015).
  3. Holyst, Robert; Litniewski, Marek; Jakubczyk, Daniel (2015). "A molecular dynamics test of the Hertz–Knudsen equation for evaporating liquids". Soft Matter. 11 (36): 7201–7206. doi:10.1039/c5sm01508a.
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