Reactant Concentration for Second Order Reaction for Plug Flow or Infinite Reactors Calculator

Reactant Concentration Formula:

\[ C = \frac{C_0}{1 + (C_0 \cdot k'' \cdot \tau_p)} \]

Initial Reactant Concentration (C₀):

mol/m³

Rate Constant for Second Order Reaction (k''):

m³/(mol·s)

Space Time for Plug Flow Reactor (τₚ):

seconds

Reactant Concentration (C):

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1. What is Reactant Concentration for Second Order Reaction in Plug Flow Reactors?

Definition: This calculator determines the concentration of a reactant remaining after a second-order reaction occurs in a plug flow reactor (PFR) or infinite series of continuous stirred-tank reactors (CSTRs).

Purpose: It helps chemical engineers design reactors and predict reaction outcomes for second-order kinetics.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ C = \frac{C_0}{1 + (C_0 \cdot k'' \cdot \tau_p)} \]

Where:

\( C \) — Final reactant concentration (mol/m³)
\( C_0 \) — Initial reactant concentration (mol/m³)
\( k'' \) — Second-order rate constant (m³/(mol·s))
\( \tau_p \) — Space time for plug flow reactor (seconds)

Explanation: The formula accounts for the second-order reaction kinetics where the rate depends on the square of the reactant concentration.

3. Importance of Reactant Concentration Calculation

Details: Accurate prediction of reactant concentration helps in reactor sizing, process optimization, and ensuring desired conversion rates are achieved.

4. Using the Calculator

Tips: Enter the initial concentration, rate constant, and space time. All values must be positive numbers. The rate constant is typically determined experimentally.

5. Frequently Asked Questions (FAQ)

Q1: What is a plug flow reactor (PFR)?
A: A PFR is a reactor where fluid flows through with no mixing in the axial direction but complete mixing in the radial direction.

Q2: How does second-order reaction differ from first-order?
A: In second-order reactions, the reaction rate depends on the square of the reactant concentration, while first-order depends linearly on concentration.

Q3: What is space time in reactor design?
A: Space time (τ) is the time required to process one reactor volume of feed at specified conditions.

Q4: Can this calculator be used for batch reactors?
A: No, this specific formula applies to plug flow reactors or infinite series of CSTRs. Batch reactors have different design equations.

Q5: What are typical units for second-order rate constants?
A: For second-order reactions, rate constants typically have units of m³/(mol·s) or L/(mol·s).