Understanding the movement of molecules in a medium is an important aspect of various scientific fields, including physics, chemistry, and engineering. One way to measure this movement is by calculating the diffusion coefficient, which quantifies the rate of molecular diffusion in a medium. Our easy-to-use Diffusion Coefficient Calculator can help you determine this value based on the temperature, viscosity, and molecular weight of the medium.
Formula
The diffusion coefficient (D) can be calculated using the following formula:
D = (k * T) / (6 * π * η * r)
Where:
- D is the diffusion coefficient (cm²/s)
- k is the Boltzmann constant (1.380649 × 10^-23 J/K)
- T is the temperature (K)
- η is the viscosity (cP)
- r is the molecular radius (m)
It’s important to note that our calculator assumes the molecule to be spherical and uses the Stokes-Einstein equation to determine the diffusion coefficient.
Example
To calculate the diffusion coefficient of a substance, you’ll need the temperature, viscosity, and molecular weight. Let’s use the following values:
Temperature (T): 300 K Viscosity (η): 0.001 Pa·s Molecular Weight (M): 28 g/mol
First, we need to convert the molecular weight to the molecular radius (r). Using the molecular weight and the ideal gas law, we can estimate the molecular radius:
r ≈ (3 * M) / (4 * π * N * ρ)
Where N is the Avogadro’s number (6.022 x 10^23 mol^(-1)) and ρ is the density of the substance (kg/m³). Assuming a density of 1.25 kg/m³ for our example, we get:
r ≈ (3 * 28) / (4 * π * (6.022 x 10^23) * 1.25) ≈ 1.95 x 10^(-10) m
Now we can plug these values into the formula for the diffusion coefficient:
D = (1.380649 × 10^-23 J/K * 300 K) / (6 * π * 0.001 Pa·s * 1.95 x 10^(-10) m) * 10000 ≈ 3.284 x 10^(-5) cm²/s
So, the diffusion coefficient for this substance is approximately 3.284 x 10^(-5) cm²/s.
Conclusion
The Diffusion Coefficient Calculator provides an easy way to calculate the diffusion coefficient for a given substance. By inputting the temperature, viscosity, and molecular weight, you can obtain an estimate of the rate of molecular diffusion. This information can be helpful in various applications, from understanding transport phenomena in porous materials to analyzing the diffusion of pollutants in air or water.