Fick's Law of Diffusion

In summary, the conversation discusses the calculation of oxygen concentration at the interior end of a trachea in an insect. The length and cross-sectional area of the trachea, as well as the concentration of oxygen in the air outside the insect and the diffusion constant, are given. The equation used to solve for the change in concentration is rearranged and the final concentration is calculated to be 0.0873 kg/m3.
  • #1
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Suppose that a tracheae is 1.17 mm long with a cross-sectional area of 1.01 x 10-9m2. The concentration of oxygen in the air outside the insect is 0.659 kg/m3, and the diffusion constant is 1.99 x 10-5 m2/s. If the mass per second of oxygen is diffusing through a trachea is 1.50 x 10-12 kg/s, then find the oxygen concentration at the interior end of the tube.

m= (DA(deltaC))t / L



I re-arranged the equation to solve for the change in concentration, (delta)C.
deltaC = mL / DA. I know the given value for the outside concentration will be moved over to the other side. I think that the concentration given for the outside of the insect would be the same as initial concentration and the concentration I am solving for would be the final concentration but not exactly sure on this. So I added the concentration given to the other side of the equation to isolate the final concentration. I calculated this to be 8.73E8 kg/s, however this is incorrect. Any suggestions?
 
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  • #2
haleyy89 said:
Suppose that a tracheae is 1.17 mm long with a cross-sectional area of 1.01 x 10-9m2. The concentration of oxygen in the air outside the insect is 0.659 kg/m3, and the diffusion constant is 1.99 x 10-5 m2/s. If the mass per second of oxygen is diffusing through a trachea is 1.50 x 10-12 kg/s, then find the oxygen concentration at the interior end of the tube.

m= (DA(deltaC))t / L

I re-arranged the equation to solve for the change in concentration, (delta)C.
deltaC = mL / DA.
You lost the 't' when re-arranging.

to isolate the final concentration. I calculated this to be 8.73E8 kg/s, however this is incorrect. Any suggestions?
Using your formula and data, I make delta C to be 0.0873 kg/m3
 

What is Fick's Law of Diffusion?

Fick's Law of Diffusion is a scientific law that describes the rate of diffusion, which is the movement of particles from an area of high concentration to an area of low concentration. It states that the rate of diffusion is directly proportional to the concentration gradient and the surface area, and inversely proportional to the distance and the diffusion coefficient.

What factors affect the rate of diffusion according to Fick's Law?

According to Fick's Law, the rate of diffusion is affected by four main factors: the concentration gradient, the surface area, the distance, and the diffusion coefficient. A larger concentration gradient, surface area, and diffusion coefficient will result in a faster rate of diffusion, while a larger distance will result in a slower rate of diffusion.

How is Fick's Law used in scientific research?

Fick's Law is used in various scientific fields, including physiology, chemistry, and engineering, to understand and predict the movement of particles. It is often used to study diffusion in biological systems, such as the exchange of gases in the lungs, or in industrial processes, such as the diffusion of chemicals in a solution.

Can Fick's Law be applied to all types of diffusion?

No, Fick's Law is only applicable to diffusion in a homogeneous medium, where the concentration gradient and diffusion coefficient are constant. It cannot be applied to non-uniform systems, such as diffusion in porous materials or non-Newtonian fluids.

How was Fick's Law developed?

Fick's Law was first described by German physiologist Adolf Fick in 1855. He formulated the law based on his experiments on the diffusion of gases in liquids. Over the years, the law has been further refined and applied to different fields, leading to the development of various versions of Fick's Law.

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