Physics:Hertz–Knudsen equation
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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]
- [math]\displaystyle{ \frac{\mathrm{d}N}{\mathrm{d}t} \equiv \varphi = \frac{\alpha p}{\sqrt{2\pi m k_\text{B} T}} = \frac{\alpha p N_A}{\sqrt{2\pi M RT}}, }[/math]
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 | Sticking coefficient of the gas molecules onto the surface, 0 ≤ α ≤ 1 |
| 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.
Applications
Microkinetic Modelling
See also
References
- ↑ Kolasinski, Kurt W. (2012). Surface Science: Foundations of Catalysis and Nanoscience, Third Edition. p. 203. doi:10.1002/9781119941798.
- ↑ R. B. Darling, EE-527: Micro Fabrication, Virginia University (retrieved Feb. 9 2015).
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