Diffusion Coefficient
D = kT/(6πηr) (Stokes-Einstein). Fick's laws govern mass transport. Essential for transport phenomena in gases, liquids, and solids.
Why This Chemistry Calculation Matters
Why: Diffusion governs mass transport in chemical, biological, and engineering systems. D quantifies spread rate.
How: Stokes-Einstein: D = kT/(6πηr) for spherical particles. Fick's laws: J = -D(dC/dx); RMS distance √(2Dt).
- ●Gases D ~ 10⁻⁵ m²/s; liquids ~ 10⁻⁹ m²/s; solids ~ 10⁻¹² m²/s.
- ●Temperature increases D; viscosity decreases it.
- ●RMS distance √(2Dt) gives typical spread over time.
⚗️ Sample Examples — Click to Load
Calculation Mode
Results
Diffusion Coefficient
m²/s
Type
normal
Similar to: Glucose in Water (Sugar molecule in aqueous solution)
Temperature Effect: 1.00×
Viscosity Effect: 1.00×
Visualizations
Diffusion Coefficient Comparison
Step-by-Step Calculation
Stokes-Einstein Equation
Temperature: 298.15 K
Viscosity: 8.90e-4 Pa·s
Particle Radius: 1.00e-9 m
Boltzmann constant: k = 1.38e-23 J/K
D = (1.38e-23) × (298.15) / (6π × 8.90e-4 × 1.00e-9)
Diffusion Coefficient: D = 2.45e-10 m²/s
⚠️For educational and informational purposes only. Verify with a qualified professional.
🔬 Chemistry Facts
D = kT/(6πηr). Stokes-Einstein for spherical particles.
— IUPAC
Fick's first law: J = -D × (dC/dx). Flux proportional to gradient.
— Transport
RMS diffusion distance √(2Dt) gives typical spread.
— NIST
D varies 10⁷× from gases to solids at 25°C.
— Reference
📋 Key Takeaways
- • Diffusion coefficient (D) quantifies how fast particles spread through a medium.
- • Stokes-Einstein: D = kT/(6πηr) for spherical particles in liquids.
- • Fick's laws relate flux to concentration gradient: J = -D × (dC/dx).
- • RMS diffusion distance √(2Dt) gives typical spread over time.
- • Typical D: gases ~10⁻⁵ m²/s, liquids ~10⁻⁹ m²/s, solids ~10⁻¹² m²/s.
What is Diffusion Coefficient?
The diffusion coefficient (D) is a fundamental physical property that quantifies how fast particles, molecules, or atoms move through a medium due to random thermal motion. It represents the rate at which a substance spreads from regions of high concentration to regions of low concentration.
🔬 Key Concepts
Molecular Motion
- 1Particles move randomly due to thermal energy
- 2Net movement from high to low concentration
- 3Rate depends on temperature, viscosity, and particle size
Typical Values
- Gases: 10⁻⁵ to 10⁻⁴ m²/s
- Liquids: 10⁻¹² to 10⁻⁹ m²/s
- Solids: 10⁻¹⁵ to 10⁻¹² m²/s
How Diffusion Works
Diffusion occurs through several mechanisms depending on the medium and conditions. Understanding these processes is crucial for predicting mass transport in chemical, biological, and engineering systems.
Gas Diffusion
Fastest diffusion due to low density and weak intermolecular forces. Molecules move freely with frequent collisions.
- D ~ 10⁻⁵ m²/s
- Temperature dependent
- Pressure dependent
Liquid Diffusion
Moderate diffusion rate. Molecules move through solvent with hydrodynamic drag. Follows Stokes-Einstein equation.
- D ~ 10⁻⁹ m²/s
- Viscosity dependent
- Size dependent
Solid Diffusion
Slowest diffusion. Atoms move through crystal lattice via vacancies or interstitial sites. Requires high temperature.
- D ~ 10⁻¹² m²/s
- Temperature activated
- Lattice dependent
When to Use Diffusion Calculations
Diffusion coefficient calculations are essential in numerous scientific and engineering applications where mass transport plays a critical role.
🧪 Chemical Engineering
- • Separation processes (distillation, extraction)
- • Reactor design and mixing
- • Membrane filtration
- • Drug delivery systems
- • Catalysis and surface reactions
🧬 Biological Systems
- • Nutrient transport in cells
- • Drug diffusion through tissues
- • Protein-protein interactions
- • Neurotransmitter release
- • Oxygen transport in blood
🌍 Environmental Science
- • Air pollution dispersion
- • Groundwater contamination
- • Ocean mixing processes
- • Soil nutrient transport
- • Atmospheric chemistry
⚙️ Materials Science
- • Alloy formation
- • Doping semiconductors
- • Corrosion processes
- • Sintering ceramics
- • Thin film deposition
Diffusion Formulas
Stokes-Einstein Equation
where: D = diffusion coefficient, k = Boltzmann constant, T = temperature, η = viscosity, r = particle radius
Fick's First Law
where: J = flux (mol/(m²·s)), D = diffusion coefficient, ∂C/∂x = concentration gradient
Fick's Second Law
Solution: C(x,t) = C₀ × erfc(x / (2√(Dt)))
RMS Diffusion Distance
where: x_rms = root mean square distance, D = diffusion coefficient, t = time
Reference Diffusion Coefficients
Typical diffusion coefficients at 25°C vary by orders of magnitude: gases ~10⁻⁵ m²/s, liquids ~10⁻⁹ m²/s, solids ~10⁻¹² m²/s.
| Substance | D (m²/s) | Medium |
|---|---|---|
| Oxygen in Air | 2.00e-5 | Gas |
| CO₂ in Air | 1.60e-5 | Gas |
| Water Vapor in Air | 2.40e-5 | Gas |
| Glucose in Water | 6.70e-10 | Liquid |
| Oxygen in Water | 2.10e-9 | Liquid |
| Na⁺ in Water | 1.33e-9 | Liquid |
| Cl⁻ in Water | 2.03e-9 | Liquid |
| Hemoglobin in Water | 6.90e-11 | Liquid |
❓ Frequently Asked Questions
When does Stokes-Einstein apply?
For spherical particles in dilute solutions. Deviations occur for non-spherical molecules, concentrated solutions, or very small particles.
What is RMS diffusion distance?
√(2Dt) gives the root-mean-square distance a particle travels in time t. It represents the typical spread of a diffusing front.
📚 Official Data Sources
Important Considerations
⚠️ Stokes-Einstein Limitations
Assumes spherical particles, dilute solutions, and continuum fluid. Not valid for molecules comparable to solvent size.
✓ Best Practices
Use NIST data for critical work. Report temperature and solvent. Consider viscosity and particle shape corrections.
⚠️ Disclaimer: This calculator provides estimates for educational purposes. Stokes-Einstein applies to spherical particles in dilute solutions. For critical research, verify results with primary literature and NIST databases.