# Calculating Average Distance Diffused

1. Oct 5, 2014

### fishes

1. The problem statement, all variables and given/known data
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.

2. Relevant 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?

3. The attempt at a solution

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?

Last edited: Oct 5, 2014
2. Oct 10, 2014

### Greg Bernhardt

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. Oct 10, 2014

### Staff: Mentor

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:
$$C=C_0erfc\left(\frac{x}{2\sqrt{Dt}}\right)$$
To get the average distance traveled, use:
$$x_{ave}=\frac{\int_0^\infty{xCdx}}{\int_0^\infty{Cdx}}$$

Chet