Rate Equation of Reactant A at Extreme B Calculator

Reaction Rate Formula:

\[ rA''' = -\frac{1}{\left(\frac{1}{k_{Ag}a_i} + \frac{H_A}{k_{Al}a_i} + \frac{H_A}{k_{Ac}a_c} + \frac{H_A}{k_A'''C_{Bl,d}\xi_A f_s}\right)} p_{Ag} \]

Gas Phase Mass Transfer Coefficient (k_Ag):

m/s

Inner Area of Particle (a_i):

1/m

Henry Law Constant (H_A):

mol/(m³·Pa)

Liquid Phase Mass Transfer Coefficient (k_Al):

m/s

Film Coefficient of Catalyst on A (k_Ac):

m/s

External Area of Particle (a_c):

m²

Rate Constant of A (k_A'''):

1/s

Diffused Concentration of Total Reactant B (C_Bl,d):

mol/m³

Effectiveness Factor of Reactant A (ξ_A):

Solid Loading into Reactors (f_s):

Pressure of Gaseous A (p_Ag):

Reaction Rate of Reactant A (r_A'''):

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1. What is the Rate Equation of Reactant A at Extreme B?

Definition: This equation calculates the reaction rate of reactant A in a gas-liquid-solid catalytic system where reactant B is in excess (extreme B conditions).

Purpose: It helps chemical engineers determine the reaction rate in multiphase catalytic systems, accounting for mass transfer resistances in all phases.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ rA''' = -\frac{1}{\left(\frac{1}{k_{Ag}a_i} + \frac{H_A}{k_{Al}a_i} + \frac{H_A}{k_{Ac}a_c} + \frac{H_A}{k_A'''C_{Bl,d}\xi_A f_s}\right)} p_{Ag} \]

Where:

\( rA''' \) — Reaction rate of A per unit volume (mol/(m³·s))
\( k_{Ag} \) — Gas phase mass transfer coefficient (m/s)
\( a_i \) — Inner area of particle (1/m)
\( H_A \) — Henry's law constant (mol/(m³·Pa))
\( k_{Al} \) — Liquid phase mass transfer coefficient (m/s)
\( k_{Ac} \) — Film coefficient of catalyst on A (m/s)
\( a_c \) — External area of particle (m²)
\( k_A''' \) — Rate constant of A (1/s)
\( C_{Bl,d} \) — Diffused concentration of total reactant B (mol/m³)
\( \xi_A \) — Effectiveness factor of reactant A
\( f_s \) — Solid loading into reactors
\( p_{Ag} \) — Pressure of gaseous A (Pa)

Explanation: The formula accounts for resistances in gas film, liquid film, catalyst film, and reaction kinetics.

3. Importance of Reaction Rate Calculation

Details: Accurate reaction rate calculation is crucial for reactor design, process optimization, and scaling up chemical processes.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. Default values are provided for reference but should be adjusted based on your specific system.

5. Frequently Asked Questions (FAQ)

Q1: What does "extreme B" mean in this context?
A: It means reactant B is present in such excess that its concentration remains essentially constant during the reaction.

Q2: How do I determine the Henry's Law constant for my system?
A: The Henry's Law constant can be found in chemical engineering handbooks or determined experimentally for your specific gas-liquid system.

Q3: What's the difference between inner and external area of particle?
A: Inner area refers to the surface within pores, while external area is the outer surface of the catalyst particle.

Q4: How does solid loading affect the reaction rate?
A: Higher solid loading (more catalyst) typically increases reaction rate, but too much can cause mass transfer limitations.

Q5: What if my system doesn't have all these resistances?
A: For simpler systems, set the corresponding terms to very large numbers (effectively eliminating their resistance).