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

In summary, Fick's law states that the flux or amount of a substance that travels through a unit area is directly proportional to the concentration gradient on both sides of the equation. This equation can be simplified by replacing mol/cm³ concentrations with the number of particles per cm³. The concentration gradient is then expressed as φ' = dφ/dx, where dφ/dx is the rate of change of φ with respect to x. The diffusion coefficient is then mol/cm^4.
  • #1
Rooner1
4
1
TL;DR 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?
 
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  • #2
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.
 
  • #3
Hello @Rooner1 , :welcome: !

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.
Rooner1 said:
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.

Rooner1 said:
Can this be simplified and still approximate decent rigor?
I like that :smile: !
 
  • #4
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.
 

1. What is a diffusion coefficient?

The diffusion coefficient is a measure of how quickly particles move and spread out in a given medium. It is a fundamental property of matter and is used to describe various processes such as the movement of molecules in a gas or the spread of pollutants in water.

2. Why doesn't the diffusion coefficient make sense in air at STP?

The diffusion coefficient is affected by several factors, including temperature, pressure, and the properties of the medium. At standard temperature and pressure (STP), the properties of air are not ideal for diffusion to occur efficiently. This is because the density and viscosity of air at STP are not conducive to rapid particle movement and diffusion.

3. Can the diffusion coefficient in air at STP be calculated?

Yes, the diffusion coefficient in air at STP can be calculated using the kinetic theory of gases and the properties of air at STP. However, the resulting value may not accurately reflect the actual diffusion behavior in this specific condition.

4. How does the diffusion coefficient in air at STP compare to other conditions?

The diffusion coefficient in air at STP is generally lower than in other conditions, such as higher temperatures or pressures. This is because at STP, the particles in air have less energy and are more tightly packed together, making it more difficult for them to move and diffuse.

5. Are there any practical applications for understanding the diffusion coefficient in air at STP?

Although the diffusion coefficient in air at STP may not be as relevant in everyday situations, it is still important to understand for certain applications. For example, it can be useful in predicting the spread of pollutants or contaminants in the atmosphere at STP conditions.

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