One of the big unknowns in Fick’s equation above is the diffusion coefficient, ���.
The diffusion coefficient (or diffusivity) is a proportionality constant between the molar flux due to molecular diffusion and the gradient in the concentration of the species (or the driving force for diffusion).
On a theoretical basis, the diffusion coefficient is proportional to the mean squared displacement divided by the time elapsed: �∝⟨�2⟩�
How do we determine it?
- Experiments
- Theory
- Estimation
Properties will influence the diffusion coefficient of molecule � in solution �:
- molecular size of � and/or �
- molecular weight of � and/or �
- molecular properties (e.g., charge, ionic strength, dipole moment) of � and/or �
- temperature
- pressure
Exercise:
What systems can demonstrate diffusion?
- gas/gas ?
- gas/liquid ?
- gas/solid ?
- liquid/liquid ?
- liquid/solid ?
- solid/solid ?
Solution
What are some typical values of diffusion coefficients?
As a reminder, these values are measured in �2/�.
Which coefficients will be largest?
- gases?
- liquids?
- solids?
By how much? Take a guess.
Exercise: Diffusion in a cell membrane
Cell membranes play a significant role in determining the rate of chemical transport into and out of the cell. Major components of the cell membrane are phospholipids, amphipathic molecules which form bilayers (shown below) with a hydrophobic core surrounding the cell. The hydrophobic tails produce what is essentially a separate ‘organic’ phase surrounded by an aqueous environment inside and outside the cell. Small, uncharged molecules such as urea cross this membrane by simple diffusion.
Assume that urea is diffusing out of the cell at steady state and that the environment both inside and outside of the cell is well mixed.
- Qualitatively sketch the concentration profile of urea in the cell, across the membrane and into the surrounding aqueous environment.
- What information (parameters) would you need to estimate the rate of mass transfer of urea from the cell? Discuss how each parameter would influence the diffusion rate and why.
- Using the information from part b, propose an equation for the rate of diffusion of urea from the cell at steady state.
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