Fick's law links three factors
Definition
Fick's law
Fick's law states that diffusion rate is proportional to surface area and concentration difference, and inversely proportional to membrane thickness.
- The relationship is rate of diffusion∝surface area×concentration differencemembrane thickness\displaystyle \text{rate of diffusion}\propto\frac{\text{surface area}\times\text{concentration difference}}{\text{membrane thickness}}rate of diffusion∝membrane thicknesssurface area×concentration difference.
- The symbol ∝\propto∝ means is proportional to, so the expression shows how the variables change together rather than giving a universal constant.
- The concentration difference is the size of the concentration gradient across the membrane.
- The membrane thickness represents the diffusion distance through the exchange surface.
Exam technique
- Use ∝\propto∝, not ===, when you write Fick's law as the stated proportional relationship.
- In an explanation, identify the changed factor and link it directly to an increase or decrease in the rate of diffusion.
Numerator factors increase the rate
- Surface area and concentration difference are in the numerator, so increasing either one increases the diffusion rate when the other variables stay constant.
- If surface area doubles, diffusion rate doubles, provided concentration difference and membrane thickness do not change.
- If concentration difference triples, diffusion rate triples, provided surface area and membrane thickness do not change.
Example
- An exchange surface becomes three times larger while its concentration difference doubles and its thickness stays constant.
- The relative change is 3×2=63\times2=63×2=6.
- The diffusion rate becomes 6\boxed{6}6 times greater.
Thickness has an inverse effect
- Membrane thickness is in the denominator, so increasing thickness decreases diffusion rate when surface area and concentration difference stay constant.
- Halving membrane thickness halves the diffusion distance and doubles the diffusion rate.
- Multiplying thickness by four divides the diffusion rate by four.
Example
- A membrane becomes thinner from 0.30 mm0.30\,\mathrm{mm}0.30mm to 0.10 mm0.10\,\mathrm{mm}0.10mm while the numerator stays constant.
- The thickness is divided by 333 because 0.30÷0.10=30.30\div0.10=30.30÷0.10=3.
- The diffusion rate therefore becomes 3\boxed{3}3 times greater.
Calculate a relative diffusion value
Definition
Rate of diffusion
The rate of diffusion is the amount of a substance that moves by diffusion across a surface in a given time.
- Substitute the values into surface area×concentration differencemembrane thickness\displaystyle \frac{\text{surface area}\times\text{concentration difference}}{\text{membrane thickness}}membrane thicknesssurface area×concentration difference.
- Calculate the numerator first, then divide by the thickness and keep the units supplied in the question.
- When comparing two exchange surfaces, calculate the expression for each one and divide one value by the other to find the fold change.
Example
- An exchange surface has area 60 mm260\,\mathrm{mm}^260mm2, concentration difference 4.0 mmol dm−34.0\,\mathrm{mmol\,dm^{-3}}4.0mmoldm−3 and thickness 0.20 mm0.20\,\mathrm{mm}0.20mm.
- relative diffusion value=60×4.00.20\displaystyle \text{relative diffusion value}=\frac{60\times4.0}{0.20}relative diffusion value=0.2060×4.0
- relative diffusion value=1200\displaystyle \text{relative diffusion value}=\boxed{1200}relative diffusion value=1200
Apply the law to exchange surfaces
- Alveoli and villi have large surface areas, so more molecules can diffuse at the same time.
- Their thin walls reduce membrane thickness, which raises the rate because thickness is in the denominator.
- Ventilation, blood flow and the removal of absorbed substances maintain concentration differences across exchange surfaces.
Self review
- Write Fick's law using the proportionality symbol.
- What does the symbol ∝\propto∝ mean?
- How does doubling surface area affect diffusion rate if other factors stay constant?
- How does halving membrane thickness affect diffusion rate?
- Why do blood flow and ventilation increase diffusion rate?
