Fick's Law and What Sets the Rate of Exchange
For a fixed gas, temperature and barrier material, total net diffusion rate increases with exchange area and concentration difference, and decreases with diffusion distance. The relationship supports calculations about exchange surfaces.
What a learner can do afterwards
- Interprets net diffusion and predicts how area, concentration difference, distance and diffusion coefficient affect rate; distinguishes total transfer from transfer per unit area.
- Predicts effects of diffusion distance, including doubling and inverse targets, and identifies the controls needed to test distance alone.
- Explains how thin alveolar walls shorten diffusion paths and identifies the gas partial-pressure gradient driving air-to-blood exchange.
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Fick's law models total net diffusion rate: rate = D × area × concentration difference / distance. D is the diffusion coefficient. For a fixed substance, temperature and barrier material, take D as constant. With other factors fixed, greater area or concentration difference increases rate; greater distance reduces it.
Alveoli provide a large combined exchange area. Oxygen crosses the thin alveolar lining and capillary wall into blood; carbon dioxide crosses the other way. Thin walls shorten this path. For exchange between air and blood, compare each gas's partial pressure, the pressure due to that gas. Total oxygen carried in blood is not the same measure. A one-cell-thick lining is not the shortest path physically possible.
With other factors fixed, divide the original rate by the distance change factor. A rate of 20 units per second becomes 10 when distance doubles. A rate of 15 becomes 5 when distance triples. Halving distance doubles rate. For an inverse target, distance factor = 1 / required rate factor. To make rate five times as large by changing distance alone, reduce distance to one fifth.
The bars compare rates in units per second, not wall thicknesses.
For several changes, multiply the area and concentration-difference factors, then divide by the distance factor. If area and distance both increase fivefold, the factor is 5 / 5 = 1. If area triples and distance increases sixfold, it is 3 / 6 = 0.5. Keep concentration difference and D fixed in these examples. Multiply the original rate by the final factor. A factor of 0.5 means half.
Net rate is the amount transferred overall per second, allowing for movement both ways. It is not the speed of an individual molecule. At equal concentrations, molecules can still cross both ways, but net transfer is zero. If D changes, include its factor too: doubling D doubles rate when other factors stay fixed.
For the same substance in the same medium, find concentration difference by subtracting the lower value from the higher value. Net diffusion is towards the lower concentration. Values of 7 and 2 give a difference of 5. Adding 2 to both gives 9 and 4, still a difference of 5. Swapping the two sides reverses net diffusion.
Concentrations use matching arbitrary units. Their difference is 7 - 2 = 5.
Adding identical exchange patches increases total area and total transfer, without changing transfer per unit area. The original patches still work at the same rate. To test distance alone, compare barriers with different distances but equal area, concentration difference and D. If several factors change, a rate change cannot be attributed to distance alone.
With other factors fixed, total net rate rises with area and concentration difference and falls with distance. Combine changes using their multiplication and division factors.
Lesson, questions and flashcards written for this dataset. OpenStax Biology 2e gas-exchange material was consulted for facts; its prose was not adapted.
Readings and extra questions written for this dataset. Diffusion and Osmosis is a linked Khan Academy video.
More to read
Following oxygen into blood
Imagine tracing oxygen from an alveolus into a nearby capillary. It must cross the alveolar lining and capillary wall. Their thin layers keep the diffusion path short. Many alveoli provide a large combined area for this transfer.
Structure does not determine exchange by itself. Oxygen needs a favourable gradient. Across the air-to-blood barrier, compare oxygen partial pressures, not the total oxygen carried in blood. Oxygen normally enters blood because its partial pressure is higher in alveolar air than in incoming blood. Carbon dioxide follows its own gradient in the other direction.
A prediction about a thicker barrier needs controlled conditions. If distance alone doubles, the model predicts half the original rate. If area, gradient or the diffusion coefficient also changes, include those changes before calculating the result.
Area available for exchange
A larger cell can have more total surface area while having less surface area for each unit of volume. These statements describe different comparisons.
When a cell grows without changing shape, its volume increases faster than its surface area. There is then more material to supply for each unit of outer surface. This does not mean the total surface area has decreased.
Fick's law describes transfer across an exchange surface under stated conditions. It does not by itself tell you how much oxygen a cell or animal needs. Demand also depends on the amount of living tissue and its activity.
Keep these questions separate when comparing exchange systems: how much surface is available, how quickly material can cross it, and how much material the tissues need. Folded surfaces and many small compartments can provide a large exchange area within a limited space.
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