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Surface area to volume ratio: why size limits diffusion questions
Surface area to volume ratio and how it falls as an organism gets larger, the effect of shape as well as size, Fick's law as a proportionality, why diffusion time rises with the square of distance, how single-celled organisms and flatworms manage without an exchange system, and the features shared by every specialised exchange surface.
5 original questions · 16 marks · the surface area to volume ratio: why size limits diffusion notes · Exchange surfaces and gas exchange
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A cube-shaped organism has sides of 0.5 mm. A second organism of the same shape has sides of 2.0 mm. Calculate the surface area to volume ratio of each, giving a unit, and calculate how many times greater the smaller organism's ratio is.
Mark scheme
- M1 ratio is surface area divided by volume, which for a cube simplifies to 6 divided by the length of a side
- A1 smaller organism: 6 ÷ 0.5 = 12 mm⁻¹, with the unit given as one over length
- M1 larger organism: 6 ÷ 2.0, worked in the same length unit as the first
- A1 larger organism gives 3 mm⁻¹, so the smaller ratio is four times greater
A flatworm 0.3 mm thick supplies all of its cells with oxygen by diffusion across its body surface. A block of tissue one centimetre thick cannot. Explain the difference.
Mark scheme
- B1 surface area rises with the square of length while volume rises with the cube, so the surface area to volume ratio falls as an organism gets thicker
- B1 demand for oxygen goes with the volume of respiring tissue, so each unit of surface has more tissue to supply in the larger body
- B1 diffusion time rises with the square of the distance, so ten times further takes about a hundred times as long
- A1 over a centimetre diffusion would take hours and could never meet demand, whereas the flatworm's flattened shape keeps every cell a fraction of a millimetre from the outside
A sphere and a flattened sheet contain identical volumes of tissue. The sphere has a surface area to volume ratio of 2.4 and the sheet one of 8.8. Compare the two shapes as exchange surfaces.
Mark scheme
- B1 the sheet's ratio is about 3.7 times the sphere's, even though the two contain the same volume of material
- B1 the sheet therefore has far more surface serving each unit of volume, while the sphere is the shape with the least surface possible for a given volume
- B1 the centre of the sphere is also much further from the nearest surface than any point in the sheet, so the diffusion distance is longer in the sphere as well
A hibernating dormouse curls its body into a tight ball. Suggest how this reduces the rate at which it loses heat to its surroundings.
State the relationship known as Fick's law, naming all three of the quantities on which the rate of diffusion across a surface depends.
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