Diffusion Coefficient Calculator
Calculate the diffusion coefficient of a spherical particle in a liquid using the Stokes-Einstein equation.
Calculation Parameters
Adjust the values below.
Calculated Result
Diffusion Coefficient (D)
Expert Tip
Ensure units are correctly formatted (e.g. Kelvin for gas temperatures and liters for volumes) to get chemically accurate outputs.
How this Calculator Works
This calculator allows you to solve Diffusion Coefficient problems dynamically. Adjust the input parameters using the sliders or selection menu below:
- Temperature (T, °C) (Range: 0 to 100, Default: 25)
- Solvent Viscosity (η, cP or mPa·s) (Range: 0.1 to 10.0, Default: 0.89)
- Hydrodynamic Radius (r, nm) (Range: 0.1 to 10.0, Default: 1.0)
The results are computed instantly and updated in the results panel on the right.
Formula & Methodology
where k_B = 1.3806 × 10⁻²³ J/K, and r is the particle radius
Where:
- Temperature: Parameter value.
- Solvent Viscosity: Parameter value.
- Hydrodynamic Radius: Parameter value.
Step-by-Step Calculation Example
To calculate Diffusion Coefficient manually, follow these steps:
- Identify the input parameters. For example:
- Temperature (T, °C) = 25
- Solvent Viscosity (η, cP or mPa·s) = 0.89
- Hydrodynamic Radius (r, nm) = 1.0
- Apply the formula:
D = (k_B * T) / (6 * π * η * r)
where k_B = 1.3806 × 10⁻²³ J/K, and r is the particle radius - Verify the calculated value which is updated instantly in the results panel on the right.
Frequently Asked Questions
What is the Stokes-Einstein equation for diffusion? ▼
D = (k_B × T) / (6 × π × η × r), where k_B is Boltzmann constant, T is temperature (K), η is dynamic viscosity, and r is hydrodynamic radius.
How does temperature affect diffusion coefficient? ▼
Increasing temperature increases particle kinetic energy and reduces fluid viscosity, increasing the diffusion coefficient D.
What are SI units for diffusion coefficient? ▼
The SI unit for diffusion coefficient D is square meters per second (m²/s), often expressed as cm²/s in laboratory work.