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

• tpernini
In summary, the conversation discusses determining the diffusion rate of a gas emitted from a body of water using Fick's first law. Factors such as the type of gas, local air temperature, and concentration at different heights above the water surface are important to consider. It is also mentioned that this is a common problem in aquaculture and that water circulation can affect gas exchange. However, there is not enough information provided to determine the diffusion rate without knowing the gas and water content. A simplified example of this problem is discussed, but it is noted that the concentration of gasses in the water is necessary to calculate the diffusion rate.
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!

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.

jrmichler
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?

tpernini said:
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.

tpernini said:
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.

## 1. How does temperature affect the diffusion of gas from a pond?

The rate of diffusion increases with increasing temperature. This is because as temperature increases, the kinetic energy of the gas molecules also increases, causing them to move faster and spread out more quickly.

## 2. What factors influence the rate of diffusion of gas from a pond?

The rate of diffusion is influenced by several factors, including temperature, pressure, concentration gradient, and molecular weight. Higher temperatures, lower pressures, steeper concentration gradients, and lighter molecules all result in faster diffusion rates.

## 3. How does the size of the pond affect the diffusion of gas?

The size of the pond does not have a direct effect on the rate of diffusion. However, a larger pond may have a larger surface area, which can increase the rate of diffusion as there is more surface area for gas molecules to pass through.

## 4. Does the type of gas affect its diffusion from a pond?

Yes, the type of gas does affect its diffusion rate. Lighter gases, such as hydrogen and helium, diffuse more quickly than heavier gases, such as carbon dioxide and sulfur dioxide. This is due to the difference in molecular weight and the resulting difference in average molecular speed.

## 5. How does wind or water movement impact the diffusion of gas from a pond?

Wind or water movement can significantly impact the diffusion of gas from a pond. These movements can create turbulence and increase the surface area of the pond, allowing for faster diffusion. However, strong winds can also cause the gas to disperse and decrease the concentration gradient, slowing down the diffusion rate.

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