Diffusion

Atomic Collision Molecules in a gas make collisions with each other as well as the wall. There is an average time and average distance between collisions.

Mean Free Path A particle of radius r must avoid other particles so it traces a cylinder of radius 2r. The length of the cylinder is the speed times the time. There are N/V particles in the volume, but they move reducing the path. The combination gives the mean free path.

Random Walk A molecule will move in random directions after each collision. If it starts in one place it will eventually move away. The motion is called a random walk.

Concentrated Region Molecules in a concentrated region will disperse into the rest of the medium. The difference in concentrations is the concentration gradient. C1 Dx C2

Diffusion Constant Different materials pass through an area at different rates. Depends on concentrate Depends on medium C1 Dx A D O2 in air: D = 1.8 x 10-5 m2/s O2 in water: D = 1.0 x 10-9 m2/s DNA in water: D = 1.3 x 10-12 m2/s C2

Fick’s Law The rate of diffusion depends on the concentration gradient, area, and diffusion constant. J measures mol/m3. There is a diffusion time t for diffusion in one direction over a distance Dx.