Calculate diffusion coefficients for gases and liquids using Stokes-Einstein, Chapman-Enskog, and Wilke-Chang equations with temperature dependence.
The diffusion coefficient (D) quantifies how fast molecules spread through a medium due to random thermal motion. It's a fundamental property in physical chemistry, chemical engineering, and materials science that governs mass transfer rates in gases, liquids, and solids. Understanding diffusion is essential for designing reactors, separation processes, drug delivery systems, and environmental transport models.
For gases, the Chapman-Enskog theory provides rigorous predictions based on kinetic theory, relating D to temperature, pressure, molecular masses, and intermolecular potential parameters (Lennard-Jones σ and ε). For liquids, the Stokes-Einstein equation relates D to temperature, solvent viscosity, and solute molecular radius. The Wilke-Chang correlation offers an empirical alternative for estimating liquid-phase diffusion coefficients from molar volumes.
This calculator computes diffusion coefficients using all three methods, displays temperature dependence curves, and provides a comprehensive reference table of measured diffusion coefficients for common gas and solute pairs. It handles both self-diffusion and binary diffusion, with unit conversions between cm²/s, m²/s, and ft²/h.
This calculator provides quick estimates of diffusion coefficients essential for chemical engineering design, mass transfer calculations, and understanding molecular transport — without needing to look up and manually compute from complex equations. This diffusion coefficient calculator helps you compare outcomes quickly and reduce avoidable mistakes when making day-to-day care decisions. Use the estimate as a planning baseline and confirm final decisions with a qualified professional when risk is high.
Stokes-Einstein: D = kT / (6πηr), where k = Boltzmann constant, T = temperature (K), η = solvent viscosity (Pa·s), r = solute radius (m). Chapman-Enskog: D₁₂ = 0.00266·T^(3/2) / (P·M₁₂^(1/2)·σ₁₂²·Ω_D), where P = pressure (atm), M₁₂ = reduced mass, σ₁₂ = collision diameter (Å), Ω_D = collision integral.
Result: D = 1.10 × 10⁻⁹ m²/s
For a small molecule (r = 2.0 Å) diffusing in water at 25°C (η = 0.89 mPa·s): D = (1.381×10⁻²³ × 298) / (6π × 8.9×10⁻⁴ × 2.0×10⁻¹⁰) = 1.10 × 10⁻⁹ m²/s.
Gas-phase diffusion is 10,000 times faster than liquid-phase diffusion because gas molecules have much greater kinetic energy and far fewer intermolecular interactions. In gases at ambient conditions, D is typically 0.1–1.0 cm²/s and increases with T^(3/2) while being inversely proportional to pressure. In liquids, D is typically 0.5–5.0 × 10⁻⁵ cm²/s and increases with temperature primarily due to decreasing viscosity.
The Chapman-Enskog theory derives from Boltzmann's transport equation and provides the most rigorous framework for gas-phase diffusion. It requires Lennard-Jones potential parameters (σ and ε/k) which are tabulated for many molecules. The collision integral Ω_D is a dimensionless function of the reduced temperature T* = kT/ε that accounts for the attractive and repulsive parts of the intermolecular potential.
Diffusion coefficients are critical inputs for mass transfer equipment design: absorption columns, distillation trays, membrane separators, catalytic reactors, and crystallizers. In biological systems, diffusion governs oxygen transport in tissues, drug release from polymer matrices, and nutrient uptake by microorganisms. Environmental models use D to predict pollutant spreading in air and groundwater.
It quantifies the rate at which molecules spread through a medium. Higher D means faster diffusion. Typical values: gases ~10⁻⁵ m²/s, liquids ~10⁻⁹ m²/s, solids ~10⁻¹² m²/s.
For gases, D ∝ T^(3/2). For liquids (Stokes-Einstein), D ∝ T/η, and since viscosity decreases with temperature, D increases roughly exponentially with T.
It relates the diffusion coefficient to the solvent viscosity and solute size: D = kT/(6πηr). It assumes the solute is a hard sphere much larger than the solvent molecules.
For solutes comparable in size to solvent molecules, near glass transitions, in polymer solutions, and for non-spherical molecules. Corrections or molecular dynamics simulations may be needed.
Predicting binary gas-phase diffusion coefficients from molecular properties. It's derived from kinetic theory and requires Lennard-Jones parameters for the collision integral.
Common methods include Taylor dispersion, pulsed-field gradient NMR (PFG-NMR), fluorescence recovery after photobleaching (FRAP), and dynamic light scattering (DLS). This keeps planning practical and lowers the chance of preventable errors.