Calculating Average Distance Diffused

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In summary: First, the question is asking for the average distance a molecule of insulin will diffuse in water in one hour. To find this, we can use the diffusion length equation: (2 x D x t)^0.5. Here, we need to use the diffusion coefficient given in the problem (8.2 × 10−7 cm^2/s) and the time of one hour (3600 seconds). Plugging these values into the equation, we get a diffusion length of 0.07683749085 cm/hour. This means that, on average, a molecule of insulin will diffuse 0.07683749085 cm in one hour.Now, for the
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fishes
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Homework Statement


In a simple model of diffusion in one dimension the quantity D can be shown to be given by half the product of the mean free path and the rms speed of the diffusing particle. Calculate the average distance a molecule of insulin will diffuse in water in one hour if its diffusion coefficient is 8.2 × 10−7 cm^2/s.

Homework Equations



J = −D(dc/dx)
Diffusion length = (2 x D x t)^0.5 -Einsteins

Do I need the mean free path and rms speed equations here?

The Attempt at a Solution


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The thing confusing me is the wording of the problem, do I need to use the mean free path and rms speed equations or is the question just making a statement? Can I get away with subbing in D and t = 3600s? Is that finding the same thing - in that case the answer would be Diffusion Length = (2 x 8.2 × 10−7 cm2/s. x 3600s)2 = 0.07683749085cm/hour?
Thanks in advance.
 
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Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 
  • #3
It would interpret this problem differently. If the initial concentration is zero, and, if C0 is the concentration at the boundary, then the concentration as a function of time and distance is given by:
[tex]C=C_0erfc\left(\frac{x}{2\sqrt{Dt}}\right)[/tex]
To get the average distance traveled, use:
[tex]x_{ave}=\frac{\int_0^\infty{xCdx}}{\int_0^\infty{Cdx}}[/tex]

Chet
 

1. What is the formula for calculating average distance diffused?

The formula for calculating average distance diffused is: average distance diffused = (total distance diffused) / (number of particles)

2. How do you measure the total distance diffused?

The total distance diffused can be measured by taking the difference between the initial position and final position of each particle and then adding up all the values for each particle.

3. What is the unit of measurement for average distance diffused?

The unit of measurement for average distance diffused will depend on the unit of measurement used for the total distance diffused. For example, if the total distance diffused is measured in meters, then the average distance diffused will also be in meters.

4. Can average distance diffused be negative?

No, average distance diffused cannot be negative. This is because it is calculated by dividing the total distance diffused by the number of particles, and both of these values are always positive.

5. How can calculating average distance diffused be useful in scientific research?

Calculating average distance diffused can be useful in scientific research as it can help determine the degree of diffusion of particles in a particular substance or environment. This information can then be used to understand the properties and behavior of the substance, and can also aid in the development of new materials or processes.

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