Solving Diffusion Question: Estimating Time for Uniform Mixture

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In summary, the conversation discusses an experiment involving a dilute isotopic mixture of helium gas and a spherical vessel. The question asks for an estimate of the time needed for a uniform mixture to form and suggests a different method for achieving this. Relevant equations mentioned include pi (diameter/2)^2 for area, pv = nrt for gas pressure and temperature, and Fick's law of diffusion for mass flux. The solution involves calculating the area and using it to determine the length needed for Fick's law.
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Ryan Hillier
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Homework Statement Question
This is an experiment on a dilute isotopic mixture of helium gas. A spherical vessel of
diameter 1 m is first filled with 4He gas to one atmosphere pressure. Then a small
amount of 3He gas is introduced through a valve on one side of the vessel. Make a
rough estimate of how long one must wait before a uniform mixture has formed (use
the result for the time dependence of the root mean square travel distance in a
random walk in 1D.) Suggest a better way to make a uniform mixture.

Homework Equations



Area = pi (diameter/2)^2 , pv =nrt , ficks law of diffusion , Mass flux = 1/3lv

The Attempt at a Solution


I am not sure where to start from. I am reading about fick's law of diffusion right now however I'd love tobe pointed out in the right direction.

Since the question asks for time dependence then isn't second law the most obvious equation to use ?
edit: hm.. as i was reading i came across this idea.. how about i get the area first, then divide volume by area to give me the 'length' which i can plug into ficks equation if I am not mistaken.
Appreciate your help.
 
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  • #2
If you need a length, there is one given in the problem statement: 1 meter. A factor of 2 does not matter here.
 

FAQ: Solving Diffusion Question: Estimating Time for Uniform Mixture

1. What is diffusion and why is it important in science?

Diffusion is the process by which particles move from an area of high concentration to an area of low concentration. It is important in science because it is a fundamental mechanism for many physical and chemical processes, such as the movement of molecules in cells and the mixing of substances in a solution.

2. How is the time for a uniform mixture estimated in diffusion?

The time for a uniform mixture to be reached in diffusion can be estimated using Fick's laws of diffusion, which take into account factors such as the concentration gradient, diffusion coefficient, and distance traveled.

3. What are the units for diffusion coefficient?

The units for diffusion coefficient depend on the system of measurement being used. In the International System of Units (SI), the units for diffusion coefficient are square meters per second (m2/s).

4. How does temperature affect the rate of diffusion?

Temperature has a direct effect on the rate of diffusion. As temperature increases, the kinetic energy of particles also increases, leading to faster movement and therefore faster diffusion.

5. Can the time for a uniform mixture be accurately predicted in all cases?

No, the time for a uniform mixture cannot be accurately predicted in all cases. This is because diffusion is affected by many variables, such as the type of particles and the medium in which they are diffusing, making it difficult to accurately predict the exact time for a uniform mixture to be reached.

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