Hertz–Knudsen equation

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

Applications

Non-dissociative adsorption (Langmuirian adsorption)

The Hertz–Knudsen equation describes the sticking of gas molecules on a surface by expressing the time rate of change of the concentration of molecules on the surface as a function of the pressure of the gas and other parameters.

${\displaystyle {\frac {1}{A}}{\frac {\mathrm {d} N}{\mathrm {d} t}}\equiv \phi ={\frac {\alpha p}{\sqrt {2\pi mk_{B}T}}}={\frac {\alpha p}{\sqrt {2\pi MRT}}},}$

where:^[1][2]

Quantity	Description
A	Surface area (in m^2)
N	Number of gas molecules
φ	Flux of the gas molecules (in m^−2 s^−1)
α	Sticking coefficient of the gas molecules onto the surface, 0≤α≤1
p	The 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)

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).