A spherical biological cell of radius r=30 μmr = 30\ \mu\text{m}r=30 μm has a plasma membrane of thickness x=10 nmx = 10\ \text{nm}x=10 nm. The permeability coefficient of the membrane to oxygen is P=2.5×10−6 m s−1P = 2.5 \times 10^{-6}\ \text{m}\ \text{s}^{-1}P=2.5×10−6 m s−1. The oxygen concentration outside the cell is CoutC_{\text{out}}Cout, and the concentration inside is CinC_{\text{in}}Cin, such that the concentration difference is ΔC=Cout−Cin=4.0×10−3 mol dm−3\Delta C = C_{\text{out}} - C_{\text{in}} = 4.0 \times 10^{-3}\ \text{mol}\ \text{dm}^{-3}ΔC=Cout−Cin=4.0×10−3 mol dm−3.
According to Fick’s Law, the rate of diffusion of a substance into a cell is given by:
Rate of Diffusion=P×A×ΔCx \text{Rate of Diffusion} = \frac{P \times A \times \Delta C}{x} Rate of Diffusion=xP×A×ΔCwhere A A\,A is the cell surface area.
Assuming the cell is perfectly spherical, what is the rate of diffusion of oxygen per unit volume of the cell?
1.0×102 mol dm−3 s−11.0 \times 10^2\ \text{mol}\ \text{dm}^{-3}\ \text{s}^{-1}1.0×102 mol dm−3 s−1
1.0×105 mol dm−3 s−11.0 \times 10^5\ \text{mol}\ \text{dm}^{-3}\ \text{s}^{-1}1.0×105 mol dm−3 s−1
1.0×108 mol dm−3 s−11.0 \times 10^8\ \text{mol}\ \text{dm}^{-3}\ \text{s}^{-1}1.0×108 mol dm−3 s−1
1.0×10−2 mol dm−3 s−11.0 \times 10^{-2}\ \text{mol}\ \text{dm}^{-3}\ \text{s}^{-1}1.0×10−2 mol dm−3 s−1