Diffusion Coefficient
Calculate D using the Stokes-Einstein equation
✅ What This Calculator Is & Why It Matters
The Diffusion Coefficient Calculator uses the Stokes-Einstein equation to determine how quickly a particle, molecule, or ion moves through a liquid medium purely due to random thermal (Brownian) motion.
Why does it matter? Diffusion is the engine of life at the molecular level. Oxygen diffuses from your blood into your cells, nutrients spread through gels and tissues, and drug molecules migrate through biological membranes. The diffusion coefficient tells pharmaceutical scientists whether a drug can passively reach its target site in a clinically useful timeframe.
✅ The Formula Explained Simply
The Stokes-Einstein equation links thermal energy (kT) to molecular size and the viscosity of the surrounding liquid:
D = (kᴮ × T) / (6π × η × r)
Where D is the diffusion coefficient, kᴮ is Boltzmann's constant, T is temperature (Kelvin), η is the dynamic viscosity of the solvent, and r is the hydrodynamic radius of the particle.
✅ 3-5 Real-World Examples
Example 1: Small Molecule Drug in Water
A small drug molecule (r ≈ 0.5 nm) in water at 37°C (310K).
Result: D ≈ 4-5 × 10⁻¹⁰ m²/s. It diffuses rapidly, reaching target tissues quickly.
Example 2: Large Protein in Water
A large protein (r ≈ 5 nm) in water at 25°C.
Result: D drops to roughly 4 × 10⁻¹¹ m²/s. It moves 10 times slower than the small molecule.
✅ FAQ Section (Google PAA Targeted)
What is the hydrodynamic radius?
It is the effective size of a particle as it moves through a liquid. A molecule that attracts a large shell of water molecules (hydration shell) has a much larger hydrodynamic radius than its bare physical size would suggest.
Does temperature affect diffusion?
Yes, dramatically. Higher temperatures provide more kinetic energy to both the solvent and solute, speeding diffusion. Halving the absolute temperature (Kelvin) will roughly halve the diffusion coefficient.
✅ Pro-Tips for Diffusion Calculations
- Units of D: The diffusion coefficient is always expressed in units of m²/s or cm²/s. Always verify your units before entering viscosity (η in Pa·s or mPa·s) and radius (in meters or nanometers).
✅ Related Calculators
✅ AI Explanation of Results
Our AI compares your calculated D to known values for common molecules (water, glucose, albumin), giving you an intuitive sense of the scale and confirming whether your molecular size input is physically reasonable.
About the Diffusion Coefficient Calculator
Analyze gas behaviors at STP, calculate partial pressures, rates of effusion, or diffusion coefficients with standard gas equations.
This precision chemistry tool is designed for academic reference, laboratory workflows, and student education. It provides instant, real-time computational results with standard formulas and dimensional analysis inputs.