Initial Reactant Concentration for Second Order Reaction for Mixed Flow Calculator

Formula Used:

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

Space Time in MFR:

Rate Constant for Second Order Reaction:

m³/(mol·s)

Reactant Conversion in MFR:

(0 to 1)

Fractional Volume Change in Reactor:

Initial Reactant Concentration (mol/m³):

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1. What is Initial Reactant Concentration for Second Order Reaction in MFR?

Definition: This calculator determines the initial concentration of reactant needed for a second-order reaction in a Mixed Flow Reactor (MFR) based on space time, rate constant, conversion, and volume change.

Purpose: It helps chemical engineers design reactors and determine operating conditions for second-order reactions.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( C_{0,MFR} \) — Initial reactant concentration (mol/m³)
\( \tau_{MFR} \) — Space time in MFR (seconds)
\( k''_{MFR} \) — Rate constant for second order reaction (m³/(mol·s))
\( X_{MFR} \) — Reactant conversion in MFR (0 to 1)
\( \epsilon \) — Fractional volume change in reactor

Explanation: The formula accounts for the reaction kinetics, conversion rate, and potential volume changes in the reactor.

3. Importance of This Calculation

Details: Accurate calculation of initial reactant concentration is crucial for reactor design, process optimization, and ensuring desired conversion rates.

4. Using the Calculator

Tips:

Enter space time in seconds
Enter second-order rate constant in m³/(mol·s)
Conversion must be between 0 and 1 (0% to 100%)
Fractional volume change can be positive, negative, or zero

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 under entrance conditions.

Q2: How does second-order reaction differ from first-order?
A: The reaction rate depends on the square of reactant concentration for second-order, versus directly proportional for first-order.

Q3: What does fractional volume change represent?
A: It accounts for volume expansion or contraction during reaction (ε > 0 for expansion, ε < 0 for contraction).

Q4: Can conversion be 1 (100%) in this calculation?
A: No, the formula becomes undefined at 100% conversion. Enter values between 0 and 0.999.

Q5: How does MFR differ from PFR in this context?
A: MFR (Mixed Flow Reactor) has uniform composition throughout, while PFR (Plug Flow Reactor) has concentration gradients along its length.