Key ideas
Why cells stay small, how fast substances move through them, and how temperature affects rates are all questions of scale. Surface area, volume and distance explain most of them.
- Surface area grows with the square of size and volume with the cube, so the surface-area-to-volume ratio falls as a cell grows: 6 ÷ L for a cube and 3 ÷ r for a sphere.
- Diffusion time grows with the square of the distance, so large cells need transport systems or flattened and folded shapes.
- Q₁₀ is the factor by which a rate increases for a 10 °C rise. Many biological reactions have Q₁₀ close to 2.
- Percentage change in mass, (final − initial) ÷ initial × 100, is used for osmosis experiments with potato cylinders.
Key equations
cube: SA ÷ V = 6 ÷ Lsphere: SA ÷ V = 3 ÷ rt ∝ x²Q₁₀ = (R₂ ÷ R₁)^(10 ÷ (T₂ − T₁))% change = (final − initial) ÷ initial × 100
Worked example
A cube of side 1 cm has SA ÷ V = 6 cm⁻¹, and a cube of side 2 cm has 3 cm⁻¹, so doubling the size halves the ratio. A reaction rate that goes from 2.0 to 4.0 units between 20 °C and 30 °C has Q₁₀ = 2. A potato piece of 2.5 g that weighs 2.8 g after soaking has gained (2.8 − 2.5) ÷ 2.5 × 100 = 12 %.
Common mistakes
- Thinking a bigger cell has a bigger surface-area-to-volume ratio. It is smaller.
- Using the final mass as the denominator for percent change. Divide by the initial mass.
- Applying Q₁₀ over a temperature range other than 10 °C without using the exponent.
Practice
Test yourself with practice questions on this topic: Cells and transport