1. What is the Diffusion Coefficient?

The diffusion coefficient (D) is a proportionality constant between the molar flux due to molecular diffusion and the gradient in the concentration of the species. It describes how quickly particles spread out from an area of high concentration to an area of low concentration.

2. How Does the Calculator Work?

The calculator uses the equation for 1D diffusion:

Where:

• \( D \) — Diffusion coefficient (m²/s)
• \( x \) — Root mean square displacement (m)
• \( t \) — Time (s)

Explanation: This equation comes from Einstein's relation for Brownian motion, showing how the mean squared displacement of particles relates to time and the diffusion coefficient.

3. Importance of Diffusion Coefficient

Details: The diffusion coefficient is crucial in many fields including physics, chemistry, biology, and engineering. It helps predict how substances will spread in different media, which is important for processes like drug delivery, chemical reactions, and material science.

4. Using the Calculator

Tips: Enter the displacement in meters and time in seconds. Both values must be positive numbers. The calculator will compute the diffusion coefficient in square meters per second (m²/s).

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for diffusion coefficients?
A: Diffusion coefficients vary widely depending on the medium and temperature. In liquids at room temperature, typical values range from 10⁻⁹ to 10⁻¹¹ m²/s for small molecules.

Q2: How does temperature affect diffusion coefficient?
A: The diffusion coefficient generally increases with temperature, following an Arrhenius-type relationship in many cases.

Q3: What's the difference between 1D, 2D and 3D diffusion?
A: The dimensionality affects the prefactor in the equation. For 2D diffusion, D = x²/(4t), and for 3D diffusion, D = x²/(6t).

Q4: Can this be used for biological cells?
A: Yes, but intracellular diffusion can be more complex due to crowding and compartmentalization, which may require modified models.

Q5: What are the limitations of this simple model?
A: This assumes free diffusion in a homogeneous medium without obstacles or interactions between particles.