# Diffusion Coefficient still doesn't make sense in air at STP

## Summary:

The units of the Diffusion Coefficient (cm2/sec) don't look like a mass transfer units.
I want to compare diffusion of a tracer gas with a low exposure limit (e.g. isoflurane) to the advection of air by a ventilation system. When will diffusion exceed advection? I can't make sense of diffusion constant to compare transfer rates or velocities.
At room temperature the diffusion coeeficient is generally around 0.2 cm2/sec for many gases. So what does that mean for the dispersal of a tracer gas (like ether vapors or isoflurane) in a calm indoor environment? What are the full units that are cancelling out? I'd love some citations if you have them.
There was a similar post about diffusion coefficient in 2010, and the reply finished with, "I can't get much more intuitive than that", which seems to be circular thinking when his explanation was rather obtuse. He said it was a velocity x density, which would be cm/s x gm/cm3, which would cancel out to be gm/sec.cm2.
I'm a moderately decent chemist, with units anyways, and the explanations of diffusion of gases at tracer levels in air is generally highly simplistic, like the sensing of vailla as it diffuses through a room, or highly theoretical and involving Boltzman constants, degrees Kelvin, etc. Can this be simplified and still approximate decent rigor?

Borek
Mentor
I am not sure I understand where the problem is. Fick's first law says the flux (amount of the substance that travels) is directly proportional to the gradient of the concentration (amount of substance per volume) - so the amount of substance (in whatever units) is present in nominator on both sides of the equation and the proportionality coefficient doesn't have to contain it.

BvU
Homework Helper
Hello @Rooner1 , !

Are you familiar with Fick's law ? The Wiki lemma explains the dimension of the diffusion coefficient ##D##

Wikipedia said:
$$J = - D {d\phi\over dx}$$where
• J is the diffusion flux, of which the dimension is amount of substance per unit area per unit time. J measures the amount of substance that will flow through a unit area during a unit time interval.
• D is the diffusion coefficient or diffusivity. Its dimension is area per unit time.
• φ (for ideal mixtures) is the concentration, of which the dimension is amount of substance per unit volume.
• x is position, the dimension of which is length.

There was a similar post about diffusion coefficient in 2010, and the reply finished with, "I can't get much more intuitive than that"
Pity you don't give the link; I can't find it.

Can this be simplified and still approximate decent rigor?
I like that !

Say mol/cm³ is the concentration φ. You can replace mol by the number of particles.
Then the concentration gradient is of course: φ' = dφ/dx, if we have a one dimensional setting, i.e. the concentration is constant along lines in the y-z-plane.
This yields (mol/cm³) / cm or mol/cm^4 as unit for φ'.
The Flux J is the number of mols or particles, respectively, streaming through a unit area in the y-z-plane, in one time unit, leading to the following unit: mol/(cm² s) as unit for J.
(Actually it is dn/dt/dA, n being the number and A the area, but this leads to the same units of course.)
So to get the diffusion coefficient, being the proportionality J/φ', which division you can hopefully do on your own.