Product Concentration for First Order Reaction for Mixed Flow Reactor Calculator

Product Concentration Formula:

\[ C_S = \frac{C_{A0} \cdot k_1 \cdot k_2 \cdot (\tau_m^2)}{(1 + (k_1 \cdot \tau_m)) \cdot (1 + (k_2 \cdot \tau_m))} \]

Initial Reactant Concentration (CA0):

mol/m³

Rate Constant First Step (k₁):

1/s

Rate Constant Second Step (k₂):

1/s

Space Time (τₘ):

Final Product Concentration (Cs): mol/m³

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1. What is Product Concentration for First Order Reaction in MFR?

Definition: This calculator determines the final concentration of the desired product in a two-step first-order irreversible reaction series in a mixed flow reactor.

Purpose: It helps chemical engineers design and optimize reactors for multi-step reactions, predicting product yields under given conditions.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ C_S = \frac{C_{A0} \cdot k_1 \cdot k_2 \cdot (\tau_m^2)}{(1 + (k_1 \cdot \tau_m)) \cdot (1 + (k_2 \cdot \tau_m))} \]

Where:

\( C_S \) — Final product concentration (mol/m³)
\( C_{A0} \) — Initial reactant concentration (mol/m³)
\( k_1 \) — Rate constant for first step (1/s)
\( k_2 \) — Rate constant for second step (1/s)
\( \tau_m \) — Space time for mixed flow reactor (s)

Explanation: The formula accounts for the sequential first-order reactions and the continuous stirred-tank reactor (CSTR) behavior.

3. Importance of Product Concentration Calculation

Details: Accurate prediction of product concentration is crucial for reactor design, process optimization, and economic evaluation of chemical processes.

4. Using the Calculator

Tips: Enter the initial reactant concentration, both rate constants, and space time. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is space time in a mixed flow reactor?
A: Space time (τₘ) is the time required to process one reactor volume of feed under specified conditions.

Q2: How do I determine the rate constants?
A: Rate constants are typically determined experimentally or from literature data for specific reactions and conditions.

Q3: Does this formula work for batch reactors?
A: No, this specific formula is designed for continuous mixed flow reactors (CSTRs).

Q4: What if my reaction has more than two steps?
A: This calculator is specifically for two-step reactions. More complex models are needed for additional steps.

Q5: How does temperature affect the calculation?
A: Temperature affects the rate constants (k₁ and k₂) through the Arrhenius equation. Use rate constants appropriate for your operating temperature.