Initial Reactant Concentration for Two Steps First Order Irreversible Reaction in Series Calculator

Formula:

\[ C_{A0} = \frac{C_R \times (k_2 - k_I)}{k_I \times (e^{-k_I \times \tau} - e^{-k_2 \times \tau})} \]

Intermediate Concentration (C_R):

mol/m³

Rate Constant Second Step (k₂):

1/s

Rate Constant First Step (k_I):

1/s

Space Time for PFR (τ):

Initial Reactant Concentration (C_A0): mol/m³

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Initial Reactant Concentration for Series Reactions?

Definition: This calculator determines the initial concentration of reactant needed to achieve a specific intermediate concentration in a two-step first-order irreversible reaction series in a PFR.

Purpose: It helps chemical engineers design and analyze plug flow reactors for consecutive reactions.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ C_{A0} = \frac{C_R \times (k_2 - k_I)}{k_I \times (e^{-k_I \times \tau} - e^{-k_2 \times \tau})} \]

Where:

\( C_{A0} \) — Initial reactant concentration (mol/m³)
\( C_R \) — Intermediate concentration (mol/m³)
\( k_I \) — Rate constant for first step (1/s)
\( k_2 \) — Rate constant for second step (1/s)
\( \tau \) — Space time for PFR (s)

Explanation: The formula calculates the required initial concentration based on reaction kinetics and reactor residence time.

3. Importance of This Calculation

Details: Accurate calculation ensures proper reactor design, optimal yields, and efficient use of reactants in consecutive reaction systems.

4. Using the Calculator

Tips: Enter the intermediate concentration, both rate constants, and space time. Default values are provided for typical cases.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for the rate constants?
A: Rate constants vary widely but typically range from 0.001 to 10 1/s depending on temperature and reaction nature.

Q2: How does space time affect the calculation?
A: Longer space times generally allow more complete reaction but may lead to over-reaction of intermediates.

Q3: What if I get extremely large values?
A: This may indicate the desired intermediate concentration is too high for the given kinetics and space time.

Q4: Can this be used for batch reactors?
A: Yes, if τ is replaced with reaction time, though the dynamics differ slightly.

Q5: What assumptions does this formula make?
A: It assumes isothermal operation, first-order kinetics for both steps, and ideal plug flow.