Hertz–Knudsen equation

Not to be confused with 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
A Surface area (in m2)
N Number of gas molecules
t Time (in s)
φ Flux of the gas molecules (in m−2 s−1)
α Anomalous evaporation coefficient, 0 ≤ α ≤ 1, to match experimental results to theoretical predictions (Knudsen noted that experimental fluxes are lower than theoretical fluxes)[3]
p The gas pressure (in Pa)
M Molar mass (in kg mol−1)
m Mass of a particle (in kg)
kB Boltzmann constant
T Temperature (in K)
R Gas constant (J mol−1 K−1)
NA Avogadro 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

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.