Can Fick's First Law Determine Diffusion Rate Without Surface Concentration?

[tpernini]

TL;DR Summary

Calculate diffusion rate of gas emitted from pond

Trying to determine diffusion rate of a gas emitted from a body of water. I believe Fick's first law may apply:

J = -D * (dc/dx)

where:
J = diffusion rate [mg/s×cm2]
D = diffusivity constant (can be looked up based on type of gas and local air temperature)
dc = change in concentration from water surface to some distance above
dx = height from water surface to some distance above

So I can look up D, I know the concentration as measured at height "h" above the water, and dx = h. I don't know the concentration at the water surface. Can Fick's first law be used to compute diffusion rate in this situation, or is there a better
approach?

Thanks!

 

[BillTre]

This similar to a problem common in aquaculture, where the amount of fish in a pond is limited by that amounts of O₂ and CO₂ in the water (as well as temperature and other factors).
Viewed from that background, I think you are missing out on some factors that will influence the result:

• which gasses (they have different properties when dissolved in water, pH and ions can be important)
• gas concentrations in the water
• is this an instantaneous determination or one over an extended period of time?
• depth and mixing of the water are important if long time frames are examined

Aquacultural engineers have a long (economically driven) history of addressing these issues.
Water circulation (top to bottom) is often important in these kinds of gas exchange.

 

[tpernini]

Thank you for the reply. Let's assume I know nothing about the water or gas content in the water (because I don't). Perhaps a simplified version of this problem would be as follows. Let's say we have a large box with an open top filled with standard air (nitrogen, oxygen, etc). The bottom of the box has many pinholes through which a given gas "X" is seeping into the box. What is the diffusion rate of gas "X" over the distance from the bottom of the box to the top?

 

[BillTre]

Let's assume I know nothing about the water or gas content in the water (because I don't).

I don't know how you are going to determine a rate of diffusion without knowing the concentration of gasses dissolved in the water, since the higher concentration in the water is what drives the diffusion into the air.

Maybe you could assume an equilibrium with normal atmospheric concentrations, but at equilibrium the net diffusion rate would just be zero.

Let's say we have a large box with an open top filled with standard air (nitrogen, oxygen, etc). The bottom of the box has many pinholes through which a given gas "X" is seeping into the box. What is the diffusion rate of gas "X" over the distance from the bottom of the box to the top?

Concentrations that drive diffusion undefined.
Insufficient information.