Unit 40: Fick’s Law
Practice Problems
Note: problem difficulty is ranked using a star system.
(*) One-star problems are fundamental to the unit, and can be done relatively quickly. Use these problems to introduce yourself to the material.
(**) Two-star problems are more difficult, and require an understanding of one or two key concepts. Use these problems to test your understanding of the material.
(***) Three-star problems are the most difficult, and require some creative thinking in addition to a deep familiarity with multiple key concepts. Use these problems to challenge yourself; if you can complete one of these, you’re on your way to mastering the material.
*Q40.1) Consider a cell membrane covered in 10nm x 10nm pores through which ions can flow.
a) Calculate the particle flux through a single pore if 500 particles flow through it in 10ms.
b) If the membrane is 5nm thick and the difference in concentration across the membrane is 100 mol/L, what’s the diffusion coefficient of the ions?
**Q40.2) A particle flux J flows through a pore of area A in a cell membrane due to diffusion. What flux would flow through another pore in the same membrane with twice the area of the first pore?
A) J/2
B) J
C) 2J
D) J/4
E) 4J
***Q40.3) A spherical cell of radius 5μm contains cytoplasm with a concentration of 0.02 molar NaCl. Individual Na⁺ and Cl⁻ ions are able to diffuse across the cell membrane through pores which occupy 5% of the cell’s total membrane area. If the diffusion coefficient of Na⁺ and Cl⁻ across the membrane is 2.0 x 10⁻¹² m²/s and the membrane is 10nm thick, what would be the molar flow rate of ions across the cell membrane at the instant it’s placed in a solution of 0.2 molar NaCl?