Diffusion Rate Calculator

Calculate diffusion rate using Fick's first law: J = -D * dC/dx. Find flux, diffusion coefficient, or concentration gradient for biological transport across membranes and tissues.

🧬 Cell Biology📐 J = D × (C1-C2) / Δx🧬 Biology
Diffusion coefficient D (m²/s)
Concentration gradient ΔC (mol/m³)
Distance Δx (m)
Please enter valid values.

Formula & Reference

VariableSymbolFormulaUnits
Diffusion Rate Calculator—J = D × (C1-C2) / Δxmol/m²·s

Step-by-Step Examples

Example 1
O2 Across Cell Membrane

D(O2 in lipid) = 1.5x10^-9 m²/s. dC = 100 mol/m³. dx = 10 nm = 10^-8 m.

  • J = 1.5x10^-9 x 100 / 10^-8
  • = 1.5x10^-9 x 10^10 = 15 mol/m²/s
  • Very fast flux due to thin membrane and high D of O2
✓ J = 15 mol/m²·s (very fast O2 diffusion)
Example 2
Glucose Across 1 cm

D(glucose in water) = 6x10^-10 m²/s. dC = 1 mol/m³. dx = 0.01 m.

  • J = 6x10^-10 x 1 / 0.01 = 6x10^-8 mol/m²/s
  • t = (0.01)² / 6x10^-10 = 166,667 s = 46 hours
  • Diffusion over 1 cm takes 46 hours: too slow for organisms!
✓ t = 46 hours: diffusion alone too slow for large organisms
Example 3
Time to Cross Membrane

How long does a molecule take to diffuse 10 nm (cell membrane)?

  • t = x²/D = (10^-8)² / 10^-9
  • = 10^-16 / 10^-9 = 10^-7 s = 100 nanoseconds
  • Membrane crossing is nearly instantaneous
✓ t = 100 ns: crossing membrane is essentially instant

Real-World Applications

🧬
Cell Biology
Explains why cells need transport proteins for polar molecules and why cells cannot be too large.
🏥
Respiratory Physiology
O2 diffuses from alveoli to blood in ~0.25 s across 0.5 μm barrier. Fick law governs this exchange.
🧪
Drug Delivery
Drug diffusion through tissues determines how effectively drugs reach target cells from blood vessels.
💡
Bioengineering
Tissue engineering scaffold design must account for diffusion limits: cells within 200 μm of blood supply.

Common Mistakes to Avoid

⚠️
Fick law is for passive diffusion

Only applies to molecules moving down their concentration gradient (no energy required). Active transport is different: requires ATP to move against gradient.

⚠️
D depends on molecule size and medium

Small molecules (O2, CO2, H2O) have higher D. Large molecules (proteins, DNA) have very small D. D in membrane << D in water for charged molecules.

⚠️
Diffusion time scales as x²

t = x²/D. Doubling distance: 4x longer time. Explains why large organisms evolved circulatory systems: diffusion is too slow at cm to meter scales.

Frequently Asked Questions

What is Fick's first law? ▾
J = -D * (dC/dx). The flux J (mol/m²/s) is proportional to the concentration gradient dC/dx (negative sign: flux from high to low concentration). D is the diffusion coefficient.
What determines the diffusion coefficient? ▾
Molecule size (inversely), medium viscosity, temperature. D = kT/(6πηr) (Stokes-Einstein). Bigger molecule or more viscous medium: smaller D.
Why do organisms need circulatory systems? ▾
Diffusion time scales as x²/D. Across 1 mm: minutes. Across 1 cm: hours. Across 1 m: years. Circulatory systems convect materials faster than diffusion can at organism scales.
What is osmosis? ▾
Diffusion of water (solvent) across a semipermeable membrane down its concentration gradient (from low solute to high solute). Same principle as molecular diffusion but applies to water.
What is active transport? ▾
Movement of molecules against their concentration gradient, requiring ATP energy. Na+/K+ ATPase, proton pumps, ABC transporters. Maintains non-equilibrium conditions in cells.

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