:Hertz–Knudsen equation
{{Short description|Surface chemistry evaporation rate equation}}
{{Distinguish | 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:{{cite book|last1=Kolasinski|first1=Kurt W.|title=Surface Science: Foundations of Catalysis and Nanoscience, Third Edition|year=2012|page=203|doi=10.1002/9781119941798}}R. B. Darling, [http://www.virlab.virginia.edu/nanoscience_class/lecture_notes/Microfabrication_Supporting_materials_files/R_B_Darling%20-%20Washington%20U%20-%20PhysicalVaporDeposition.pdf EE-527: Micro Fabrication], Virginia University (retrieved Feb. 9 2015).
:
where:
| class="wikitable"
! scope="col" | Quantity ! scope="col" | 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){{cite journal |last1=Holyst |first1=Robert |last2=Litniewski |first2=Marek |last3=Jakubczyk |first3=Daniel |date=2015 |title=A molecular dynamics test of the Hertz–Knudsen equation for evaporating liquids |journal=Soft Matter |volume=11 |issue=36 |pages=7201–7206 |doi=10.1039/c5sm01508a}} |
| 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 per area, it can be assimilated to a rate constant for the adsorption process.