4-7 Factors Affecting Diffusion Rate - TSA:V (Cambridge AS & A Level Biology, 9700)

Main ideas / lessons

• Diffusion rate depends on geometry, especially the total surface area to volume ratio (TSA:V).
• Most cells are microscopic because as cell size increases, TSA:V decreases, making diffusion too slow for materials (e.g., oxygen) to reach the cell’s interior fast enough.
• Distance of diffusion is the limiting factor: even if a larger object has more surface area, a larger interior volume means particles must travel farther, which significantly slows diffusion.
• Comparisons must be fair:
  • Don’t assume “smaller volume = always fills first” if the minimum distance of diffusion is the same.
  • In some cases, different shapes/sizes can fill at almost the same time if the minimum diffusion distance is equal.

Core methodology / calculation steps (as presented)

1) Use the idea of total surface area : volume ratio (TSA:V)

• In exams they may accept writing “TSA:V” or “TSA to V”.

2) For cubic objects, compute total surface area

• Each cube has 6 faces.
• Surface area of a cube = (6 \times \text{side length} \times \text{side length})

Example (cubes with side lengths 1 mm, 5 mm, 10 mm):

• Cube 1 mm side:
  • ( \text{TSA} = 6 \times 1 \times 1 = 6 \,\text{mm}^2)
• Cube 5 mm side:
  • ( \text{TSA} = 6 \times 5 \times 5 = 150 \,\text{mm}^2)
• Cube 10 mm side:
  • ( \text{TSA} = 6 \times 10 \times 10 = 600 \,\text{mm}^2)

3) Compute volume for each cube

• Volume of a cube = (side length)(^3)

Example:

• 1 mm cube: volume (= 1^3 = 1 \,\text{mm}^3)
• 5 mm cube: volume (= 5^3 = 125 \,\text{mm}^3)
• 10 mm cube: volume (= 10^3 = 1000 \,\text{mm}^3)

4) Calculate TSA:V ratios

• ( \text{TSA:V} = (\text{total surface area}) : (\text{volume}))
• Then simplify for comparison.

Given simplifications in the video:

• Small cube: (6 : 1)
• Medium cube: (150 : 125) simplified to (6 : 5)
• Large cube: (600 : 1000) simplified to (3 : 5)

Conclusion from ratios:

• Smaller cube → largest TSA:V
• Larger cube → smallest TSA:V
• As TSA:V decreases with size, diffusion becomes much slower because the distance through the object becomes greater.

Conceptual explanation using jelly cubes

• Two jelly cubes A (small) and B (large) are immersed in pink solution.
• Observation: the small cube becomes fully pink first, even though the larger cube has greater total surface area.

Reason (2D cross-section concept):

• For the small cube, pink solution needs to diffuse a short distance to reach the entire volume.
• For the large cube, although surface area is larger, there are more empty interior spaces, so diffusion must travel a longer distance, and diffusion slows greatly.

Real-life analogy: oxygen and mitochondria

• Mitochondria produce ATP using oxygen (via aerobic respiration).
• Small vs large cells:
  • Small cell: higher TSA:V → oxygen diffuses a short distance to mitochondria → stays alive.
  • Large cell: lower TSA:V → oxygen must diffuse a longer distance → arrives too slowly → ATP becomes insufficient → cell dies.

Conclusion: extremely large cells are generally not evolutionarily feasible.

“Tricky questions” rule: compare minimum diffusion distance

• When comparing a cube A and a cuboid B, the key is the minimum distance of diffusion, not just volume.
• In the example:
  • Although volumes differ (A is smaller, B is larger), both have the same minimum diffusion distance (1 mm).
  • Therefore, A and B fill up at almost the same time because particles only need to travel that minimum distance to fill the relevant interior.

Speakers / sources featured

• The instructor / presenter (unnamed in the subtitles) teaching “TSA:V” and jelly cube demonstrations.
• No other sources or named speakers are explicitly identified in the subtitles.