1. What is the Diffusion Coefficient?

The diffusion coefficient (D) measures how quickly particles diffuse in a fluid. In water, it depends on temperature, viscosity, and particle size according to the Stokes-Einstein equation.

2. How Does the Calculator Work?

The calculator uses the Stokes-Einstein equation:

Where:

• \( D \) — Diffusion coefficient (m²/s)
• \( R \) — Universal gas constant (8.314 J/mol·K)
• \( T \) — Absolute temperature (K)
• \( N_A \) — Avogadro's number (6.022×10²³ mol⁻¹)
• \( \eta \) — Dynamic viscosity (Pa·s)
• \( r \) — Hydrodynamic radius of particle (m)

Explanation: The equation relates the random motion of particles in a fluid to temperature and resistance from viscosity.

3. Importance of Diffusion Coefficient

Details: The diffusion coefficient is crucial for understanding molecular transport in biological systems, chemical reactions, and industrial processes.

4. Using the Calculator

Tips: Enter temperature in Kelvin, viscosity in Pascal-seconds (0.00089 Pa·s for water at 25°C), and particle radius in meters. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is typical diffusion coefficient in water?
A: For small molecules at 25°C, typically 10⁻⁹ to 10⁻¹⁰ m²/s. For example, glucose is ~6.7×10⁻¹⁰ m²/s.

Q2: How does temperature affect diffusion?
A: Diffusion increases with temperature (directly proportional in this equation).

Q3: What is the hydrodynamic radius?
A: The effective radius of a particle including any solvation shell or hydration layer.

Q4: What are limitations of this equation?
A: Best for spherical particles in dilute solutions. May not apply for very small particles or complex shapes.

Q5: How to measure viscosity?
A: Use a viscometer or look up standard values (water is ~0.89 mPa·s at 25°C).