Help with Diffusion Homework: Find Concentration 300mm from Closed End

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In summary, the conversation discusses a diffusion experiment involving a tube filled with water and a plug of substance at one closed end. The diffusion constant and initial concentration of the substance are known, and the distribution of particles can be described by an integral equation. The question asks for an expression for the concentration of the substance at a specific distance from the closed end.
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Kimko
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Homework Statement



We have a tube filled with water where there is a plug of substance at one closed end. Diffusion constant of this substance is known and its concentration at t=0 is given as:
Co(x)= 10mg/ml if x<= 100mm
Co(x)= 0mg/ml if x> 100mm
Distribution of particles from the plug in 1-D is given as:

C(x,t)=1/(4piDt)^(1/2) * int{ Co(x') e^[-(x-x')^2/(4Dt)] dx'}

Write an expression for the concentration of the substance (in integral form) as seen 300mm from the closed end.

The Attempt at a Solution


I assume that x=100mm and x'=300mm
I really don't know what to do next, need help.
 
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C(x,t)=1/(4piDt)^(1/2) * int{ Co(x') e^[-(x-x')^2/(4Dt)] dx'}C(300mm,t)=1/(4piDt)^(1/2) * int{ Co(300mm) e^[-(100mm-300mm)^2/(4Dt)] dx'}
 

1. What is diffusion?

Diffusion is the process by which molecules move from an area of high concentration to an area of low concentration. This movement is driven by the random motion of molecules and does not require any external energy input.

2. How is concentration related to diffusion?

Concentration refers to the amount of a substance in a given volume. In diffusion, molecules move from areas of high concentration to areas of low concentration, resulting in a gradual decrease in concentration over time.

3. How do you calculate concentration?

Concentration can be calculated by dividing the amount of a substance by the volume in which it is contained. For example, if there are 300 molecules of a substance in a volume of 1 liter, the concentration would be 300 molecules/L.

4. How do you find the concentration 300mm from a closed end?

The concentration at a specific distance from a closed end can be calculated using the diffusion equation, which takes into account factors such as the diffusion coefficient and the time elapsed. Alternatively, you could use experimental methods such as measuring the amount of substance at different distances and plotting a concentration gradient curve.

5. How does diffusion play a role in everyday life?

Diffusion is a fundamental process that occurs in many natural and man-made systems. It is responsible for the transport of essential molecules in biological organisms, the mixing of gases in the atmosphere, and the spread of odors and pollutants in the air. It is also used in various industrial processes such as water purification and food preservation.

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