General Rate Equation of Mass Transfer Calculator

General Rate Equation Formula:

\[ r''''_A = \frac{1}{\left(\frac{1}{k_{Ag} \cdot a} + \frac{H_A}{k_{Al} \cdot a \cdot E} + \frac{H_A}{k \cdot f_l \cdot C_{Bl}}\right)} \cdot p_A \]

Gas Phase Mass Transfer Coefficient (k_Ag):

m/s

Interfacial Area (a):

1/m

Henry Law Constant (H_A):

mol/(m³·Pa)

Liquid Phase Mass Transfer Coefficient (k_Al):

m/s

Liquid Film Enhancement Factor (E):

Rate Constant for Fluid Reactions (k):

mol/(m³·s)

Fraction of Liquid (f_l):

Concentration of Liquid B (C_Bl):

mol/m³

Partial Pressure of Reactant A (p_A):

Rate based on Volume of Contactor (r''''_A):

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1. What is the General Rate Equation of Mass Transfer?

Definition: This equation calculates the overall rate of mass transfer in gas-liquid systems considering resistances in both phases and chemical reaction.

Purpose: It helps chemical engineers design and analyze gas-liquid contactors like absorbers, strippers, and reactors.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r''''_A = \frac{1}{\left(\frac{1}{k_{Ag} \cdot a} + \frac{H_A}{k_{Al} \cdot a \cdot E} + \frac{H_A}{k \cdot f_l \cdot C_{Bl}}\right)} \cdot p_A \]

Where:

\( r''''_A \) — Rate based on volume of contactor (mol/(m³·s))
\( k_{Ag} \) — Gas phase mass transfer coefficient (m/s)
\( a \) — Interfacial area per unit volume (1/m)
\( H_A \) — Henry's law constant (mol/(m³·Pa))
\( k_{Al} \) — Liquid phase mass transfer coefficient (m/s)
\( E \) — Liquid film enhancement factor (dimensionless)
\( k \) — Rate constant for fluid-fluid reactions (mol/(m³·s))
\( f_l \) — Fraction of liquid (dimensionless)
\( C_{Bl} \) — Concentration of liquid B (mol/m³)
\( p_A \) — Partial pressure of reactant A (Pa)

Explanation: The equation combines resistances from gas film, liquid film, and chemical reaction to determine the overall mass transfer rate.

3. Importance of Mass Transfer Rate Calculation

Details: Accurate rate calculation is crucial for designing efficient contactors, optimizing reaction conditions, and predicting system performance.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. Default values are provided for reference. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical meaning of the enhancement factor (E)?
A: The enhancement factor accounts for how chemical reaction increases the mass transfer rate beyond pure physical absorption.

Q2: How do I determine the interfacial area (a)?
A: This depends on the contactor type and can be estimated from equipment specifications or correlations.

Q3: When can I neglect the reaction term in the denominator?
A: When the reaction is very fast compared to mass transfer (k → ∞), the reaction term becomes negligible.

Q4: What's a typical range for Henry's law constant?
A: H_A varies widely (10^-5 to 10³ mol/(m³·Pa)) depending on the gas and solvent.

Q5: How does temperature affect the calculation?
A: Temperature affects k_Ag, k_Al, H_A, and k. Use values appropriate for your operating temperature.