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:

$\frac{\mathrm{d}N}{A\mathrm{d}t}\equiv \phi =\frac{\alpha p}{\sqrt{2\pi m{k}_{\text{B}}T}}=\frac{\alpha p{N}_A}{\sqrt{2\pi MRT}},$

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)
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

• Langmuir (unit)