Mass Diffusing Rate Through Solid Boundary Sphere Calculator

Formula Used:

\[ \text{Mass Diffusing Rate} = \frac{4\pi \times \text{Inner Radius} \times \text{Outer Radius} \times \text{Diffusion Coefficient} \times (\text{Mass Concentration A1} - \text{Mass Concentration A2})}{\text{Outer Radius} - \text{Inner Radius}} \]

Inner Radius (ri):

Outer Radius (ro):

Diffusion Coefficient (Dab):

m²/s

Mass Concentration A in Mixture 1 (ρa1):

kg/m³

Mass Concentration A in Mixture 2 (ρa2):

kg/m³

Mass Diffusing Rate (mr):

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1. What is Mass Diffusing Rate Through Solid Boundary Sphere?

The Mass Diffusing Rate through a solid boundary sphere quantifies the rate at which mass transfers through a spherical shell due to molecular diffusion. It's a key parameter in chemical engineering and materials science for analyzing mass transfer processes.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ \text{Mass Diffusing Rate} = \frac{4\pi \times r_i \times r_o \times D_{ab} \times (\rho_{a1} - \rho_{a2})}{r_o - r_i} \]

Where:

\( r_i \) — Inner radius of the sphere (m)
\( r_o \) — Outer radius of the sphere (m)
\( D_{ab} \) — Diffusion coefficient when A diffuses with B (m²/s)
\( \rho_{a1} \) — Mass concentration of component A in mixture 1 (kg/m³)
\( \rho_{a2} \) — Mass concentration of component A in mixture 2 (kg/m³)
\( \pi \) — Archimedes' constant (approximately 3.1416)

Explanation: This equation calculates the mass transfer rate through a spherical shell based on Fick's law of diffusion, accounting for the spherical geometry.

3. Importance of Mass Diffusion Calculation

Details: Accurate calculation of mass diffusing rate is crucial for designing separation processes, predicting reaction rates, and analyzing transport phenomena in various engineering applications.

4. Using the Calculator

Tips: Enter all values in appropriate units. Ensure outer radius is greater than inner radius. All values must be positive, with concentration values non-negative.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the spherical geometry in this formula?
A: The spherical geometry affects the diffusion area, which varies with radius, making the calculation different from planar diffusion.

Q2: What are typical units for mass diffusing rate?
A: Mass diffusing rate is typically measured in kilograms per second (kg/s) in SI units.

Q3: When is this formula applicable?
A: This formula applies to steady-state diffusion through a spherical shell with constant diffusion coefficient and concentration difference.

Q4: What are the limitations of this equation?
A: This equation assumes constant diffusion coefficient, steady-state conditions, and no chemical reactions occurring during diffusion.

Q5: How does temperature affect mass diffusion?
A: Temperature significantly affects diffusion coefficients, with higher temperatures generally increasing diffusion rates according to the Arrhenius equation.