Initial Reactant Concentration for Second Order Reaction using Space Time for Mixed Flow Calculator

Formula Used:

\[ C_0 = \frac{X_{mfr}}{(1-X_{mfr})^2 \times \tau_{mixed} \times k_{mixed}} \]

Reactant Conversion in Mixed Flow:

(0 to 1)

Space Time in Mixed Flow:

seconds

Rate Constant for Second Order in Mixed Flow:

m³/(mol·s)

Initial Reactant Concentration:

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

Definition: This calculator determines the initial concentration of reactant needed for a second-order reaction in a mixed flow reactor, based on conversion, space time, and rate constant.

Purpose: It helps chemical engineers design reactors and understand reaction kinetics for second-order reactions in continuous stirred-tank reactors (CSTR).

2. How Does the Calculator Work?

The calculator uses the formula:

\[ C_0 = \frac{X_{mfr}}{(1-X_{mfr})^2 \times \tau_{mixed} \times k_{mixed}} \]

Where:

\( C_0 \) — Initial reactant concentration (mol/m³)
\( X_{mfr} \) — Reactant conversion in mixed flow (0 to 1)
\( \tau_{mixed} \) — Space time in mixed flow (seconds)
\( k_{mixed} \) — Rate constant for second order reaction (m³/(mol·s))

Explanation: The formula relates the initial concentration to the achieved conversion, reactor residence time, and reaction rate constant.

3. Importance of This Calculation

Details: Accurate calculation of initial reactant concentration is crucial for reactor sizing, process optimization, and achieving desired product yields in chemical processes.

4. Using the Calculator

Tips:

Enter conversion as a decimal between 0 and 1 (e.g., 0.75 for 75% conversion)
Space time must be > 0 seconds
Rate constant must be > 0 m³/(mol·s)

5. Frequently Asked Questions (FAQ)

Q1: What is space time in a mixed flow reactor?
A: Space time is the time required to process one reactor volume of feed at entrance conditions, calculated as reactor volume divided by volumetric flow rate.

Q2: How does conversion affect the initial concentration?
A: Higher conversions require higher initial concentrations (or longer space times) to achieve the same reaction extent.

Q3: What's a typical range for second-order rate constants?
A: Rate constants vary widely depending on the reaction, but common values range from 10^-6 to 10 m³/(mol·s).

Q4: Can this be used for first-order reactions?
A: No, this formula is specific to second-order reactions. First-order reactions have a different relationship.

Q5: What assumptions does this calculation make?
A: It assumes perfect mixing, isothermal conditions, constant density, and a single irreversible second-order reaction.