A spherical cell relies entirely on simple diffusion across its outer membrane to supply oxygen for aerobic respiration. The maximum rate of oxygen diffusion into the cell is given by the equation:
J=P⋅A⋅ΔC J = P \cdot A \cdot \Delta C J=P⋅A⋅ΔCwhere P=2.0×10−5 m s−1P = 2.0 \times 10^{-5}\text{ m s}^{-1}P=2.0×10−5 m s−1 is the permeability coefficient of the membrane, A A\,A is the surface area of the cell, and ΔC=1.5×10−2 mol m−3\Delta C = 1.5 \times 10^{-2}\text{ mol m}^{-3}ΔC=1.5×10−2 mol m−3 is the concentration gradient across the membrane.
The rate of oxygen consumption by the cell is constant per unit volume: Q=1.2×10−1 mol m−3 s−1Q = 1.2 \times 10^{-1}\text{ mol m}^{-3}\text{ s}^{-1}Q=1.2×10−1 mol m−3 s−1.
What is the maximum radius RRR (in micrometres, μm\mu\text{m}μm) that this cell can reach before its oxygen consumption rate exceeds its maximum oxygen diffusion rate?
2.5 μm2.5\ \mu\text{m}2.5 μm
7.5 μm7.5\ \mu\text{m}7.5 μm
15.0 μm15.0\ \mu\text{m}15.0 μm
22.5 μm22.5\ \mu\text{m}22.5 μm
17 exam-style questions on OCR GCSE Biology 2.2 The challenges of size, covering 2.2.1 Exchange surfaces and surface area : volume ratio, 2.2.2 Substances transported in organisms, 2.2.3 The human circulatory system, 2.2.4 The heart and blood vessels, 2.2.5 Red blood cells and plasma, 2.2.6 Uptake of water and mineral ions by plants, 2.2.7 Transpiration and translocation, 2.2.8 Xylem and phloem, 2.2.9 Environmental factors and water uptake, and 2.2.10 Using a potometer. Each one has a worked solution and a mark scheme showing where the marks go.