Rate Constant for Second Order Reaction for Mixed Flow Calculator

Formula Used:

\[ k''_{MixedFlow} = \frac{1}{\tau_{MFR} \cdot C_{0,MFR}} \times \frac{X_{MFR}(1 + (\epsilon \cdot X_{MFR}))^2}{(1 - X_{MFR})^2} \]

Space Time in MFR (τ):

Initial Reactant Concentration (C₀):

mol/m³

Reactant Conversion (X):

Fractional Volume Change (ε):

Rate Constant (k''):

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1. What is Rate Constant for Second Order Reaction for Mixed Flow?

Definition: This calculator determines the rate constant for a second-order reaction occurring in a mixed flow reactor (MFR) based on space time, initial concentration, reactant conversion, and volume change.

Purpose: It helps chemical engineers and researchers analyze reaction kinetics in continuous stirred-tank reactors (CSTRs).

2. How Does the Calculator Work?

The calculator uses the formula:

\[ k''_{MixedFlow} = \frac{1}{\tau \cdot C_0} \times \frac{X(1 + \epsilon X)^2}{(1 - X)^2} \]

Where:

\( k'' \) — Rate constant for 2nd order reaction (m³/mol·s)
\( \tau \) — Space time in MFR (s)
\( C_0 \) — Initial reactant concentration (mol/m³)
\( X \) — Reactant conversion (decimal between 0 and 1)
\( \epsilon \) — Fractional volume change in reactor

Explanation: The formula accounts for the reaction kinetics and volume changes in a mixed flow reactor system.

3. Importance of Rate Constant Calculation

Details: Accurate determination of rate constants is essential for reactor design, process optimization, and scaling up chemical reactions.

4. Using the Calculator

Tips: Enter space time (τ) in seconds, initial concentration (C₀) in mol/m³, conversion (X) as decimal (0-1), and fractional volume change (ε). All values must be valid (τ > 0, C₀ > 0, 0 ≤ X < 1).

5. Frequently Asked Questions (FAQ)

Q1: What is space time in a MFR?
A: Space time is the time required to process one reactor volume of feed at entrance conditions.

Q2: What does a negative ε value mean?
A: Negative ε indicates a decrease in volume during the reaction (more products than reactants).

Q3: How does conversion affect the rate constant?
A: Higher conversions typically result in higher calculated rate constants for the same space time and concentration.

Q4: What are typical units for second-order rate constants?
A: For second-order reactions, rate constants typically have units of m³/mol·s.

Q5: When would I use this calculation?
A: This is used when analyzing second-order reactions in continuous stirred-tank reactors with potential volume changes.