What sets the rate of diffusion, and Fick's law

Two people breathe the same air at the same pace. Why does one of them get far less oxygen into the blood? Breath for breath, the air going into both of them carries exactly the same amount of oxygen. But one of them has lungs damaged by years of smoking. The walls between the tiny air sacs have broken down, leaving fewer, bigger sacs. That person is breathless climbing a flight of stairs, even though nothing about the air they breathe is any different. Same air in, less oxygen out, so the answer lies in the lungs themselves.

The rate of diffusion is how much of a substance crosses a surface each second. It is not how fast each particle moves. And it is not how long something takes to reach the middle of a block. Four factors set that rate: surface area, the concentration gradient, the diffusion distance and temperature. The table shows where each one is listed. Learn all four, because knowing an extra one costs you nothing. Surface area first. Make the surface bigger, and more particles can cross at the same moment, so the rate goes up. Each particle moves no faster than before. There are more places to get through at once. Fewer, bigger air sacs in place of many small ones: more surface, or less? Less surface. Fewer, bigger sacs have less wall between them, so less oxygen gets into the blood each second.

The concentration gradient is the second factor: the difference in concentration between the two sides. Make that difference bigger, a steeper gradient, and far more particles cross from the crowded side than come back. The rate goes up. Blood in a capillary carries oxygen at a concentration of ten units, and three muscle fibres sit beside it. Inside them, the oxygen concentration is seven units in fibre A, two units in fibre B and five units in fibre C. Into which fibre will oxygen diffuse fastest, and why? Fibre B. The difference between the blood and fibre B is the biggest, so its gradient is the steepest. Here is each difference on its own line. Ten take away seven is three, for fibre A. Ten take away two is eight, for B. Ten take away five is five, for C. Then the comparison. The difference in concentration is bigger for fibre B than for A or C, so oxygen diffuses into B fastest. A student answers: fibre B, because oxygen diffuses from a high concentration to a low concentration. That reason is true, so why would it score nothing here? It is a definition of diffusion, true of all three fibres. The question needs a comparison that says why B beats the other two. One examiner's report on a Foundation paper, about a question like this, says it in one line. For the reason, a definition of diffusion was insufficient; a comparison was required. The fix is the comparison frame: the difference in concentration is bigger for one than the other, so the substance diffuses into that one faster.

Diffusion distance is the third factor: how far the particles have to travel to get across. Make the surface thinner, and the particles have less far to go. They get across sooner, so more cross each second, and the rate goes up. Now a membrane twice as thick. Does the rate go up, or down? It goes down. Doubling the distance slows the rate, because the trip through takes longer. This is what the features of an exchange surface were doing all along. A large surface area is the first factor. A wall one cell thick is a short diffusion distance. A blood supply and ventilation keep the gradient steep. Temperature is the fourth factor. At a higher temperature the particles have more kinetic energy, more energy of movement, so they move faster and the rate goes up. That makes temperature the only one of the four that changes how fast each particle moves. And diffusion has no best temperature. Nothing is denatured, and warmer means faster particles.

In an answer, every feature needs its factor named beside it. A tadpole takes in oxygen from pond water through its gills. Give three features that would raise the rate oxygen diffuses into its blood, naming the factor each one changes. Which three features would you give, each with its factor? Gills with a larger surface area, and the factor is surface area. A thinner gill surface, and the factor is diffusion distance. Blood flowing quickly through the gills, carrying oxygen away, and the factor is the concentration gradient, kept steep. Warmer water is a fair fourth answer, and its factor is temperature: the particles move faster. A student writes: the tadpole gets more oxygen because there is more oxygen in the water. What is missing from that sentence about oxygen in the water? The gradient. More oxygen in the water makes a bigger concentration difference across the gill surface, so the concentration gradient is steeper and oxygen diffuses in faster. The same report, on a question about these factors, records this. Less than ten per cent of students gained both marks in this question and lots of responses about size were seen, which was not enough to gain the mark. Some students wrote about the concentration of oxygen in the water but failed to go on to mention the concentration gradient. The same report adds that the most common correct responses were temperature and surface area. If those two come to mind first, the next step is saying how each one changes the rate. The habit that earns it: name the factor, then compare the two situations.

Fick's law puts three of the factors into one relationship. It is named after Adolf Fick, a physiologist who first set it out in eighteen fifty-five. This part is only for the separate biology students named on screen. If that is not you, skip ahead to the recap; everything before this point is for everyone. The rate of diffusion is proportional to the surface area times the concentration difference, divided by the thickness of the membrane. Proportional to means the rate changes in step. Double the surface area, and the rate doubles. Double the concentration difference, and it doubles too. Now, thickness sits alone on the bottom. What does doubling it do to the rate? It halves the rate. A thicker membrane always means a slower rate. Two surfaces to compare. Surface P has an area of a hundred and twenty units, a concentration difference of fifteen units, and a thickness of nought point five micrometres. Surface Q has an area of eighty units, a concentration difference of thirty units, and a thickness of two thousand nanometres. First, the units, on their own line. One micrometre is a thousand nanometres, so two thousand nanometres is two micrometres. Now P's relative rate. A hundred and twenty times fifteen is one thousand eight hundred. Divided by nought point five, that is three thousand six hundred arbitrary units. Arbitrary units are numbers for comparing, with no real unit attached. Q has the bigger concentration difference, and its thickness is now two micrometres. Work out Q's relative rate, then how many times faster P is. Q comes to one thousand two hundred, so P is three times faster. Eighty times thirty is two thousand four hundred. Divided by two, that is one thousand two hundred. Three thousand six hundred divided by one thousand two hundred is three. Check that it makes sense. Q is the thicker one, so it should come out slower, and it does, even with the bigger concentration difference. One more: damage leaves surface P with a third of its area, and nothing else changes. With a third of its area left, what is P's new relative rate? One thousand two hundred arbitrary units, a third of before, and no better than Q. That third is a made-up number, but the idea is real. Fewer, bigger air sacs in a smoker's lungs mean less surface, and so a slower rate.

Time to pull the four factors together, one question at a time. Which factor is the only one that changes how fast each particle moves? Temperature. The other three change how many particles cross, not how fast each one goes. Now a cell membrane gets thicker. What happens to the rate, and why? The rate goes down. The diffusion distance is longer, so fewer particles get across each second. Here's another: a gill folds so its surface area doubles. What happens to the rate? The rate goes up, because more particles can cross at once. With Fick's law, double the area means double the rate. One more: why does the smoker get less oxygen from the same air? Fewer, bigger air sacs mean less surface area, so less oxygen diffuses into the blood each second, whatever the air carries.

If the four factors make sense now, put a thumbs up on this one, because you've nailed it. If it hasn't clicked yet, keep the playlist saved for another go. Nobody gets this first time.

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