Intermediate Concentration for Two Steps First Order Irreversible Reaction in Series Calculator

Intermediate Concentration Formula:

\[ C_R = C_{A0} \times \left( \frac{k_1}{k_2 - k_1} \right) \times \left( e^{-k_1 \tau} - e^{-k_2 \tau} \right) \]

Initial Reactant Concentration (CA0):

mol/m³

Rate Constant for First Step (k1):

1/s

Rate Constant for Second Step (k2):

1/s

Space Time for PFR (τ):

Intermediate Concentration (CR):

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1. What is Intermediate Concentration for Series Reactions?

Definition: This calculator determines the concentration of the intermediate product (R) in a two-step first-order irreversible reaction series in a Plug Flow Reactor (PFR).

Purpose: It helps chemical engineers and researchers predict the intermediate product concentration at different reaction conditions.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ C_R = C_{A0} \times \left( \frac{k_1}{k_2 - k_1} \right) \times \left( e^{-k_1 \tau} - e^{-k_2 \tau} \right) \]

Where:

\( C_R \) — Intermediate 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)
\( \tau \) — Space time for PFR (s)

Explanation: The formula accounts for the formation and consumption of the intermediate product in consecutive reactions.

3. Importance of Intermediate Concentration Calculation

Details: Accurate prediction of intermediate concentrations is crucial for reactor design, optimization, and understanding reaction kinetics.

4. Using the Calculator

Tips: Enter all positive values with CA0 > 0, k1 > 0, k2 > 0, τ > 0, and k2 ≠ k1. The calculator will compute the intermediate concentration.

5. Frequently Asked Questions (FAQ)

Q1: What if k1 equals k2?
A: The formula becomes indeterminate. A different approach is needed when rate constants are equal.

Q2: What units should I use?
A: Use consistent units: mol/m³ for concentrations, 1/s for rate constants, and seconds for space time.

Q3: Does this apply to batch reactors?
A: The formula is derived for PFRs, but similar principles apply to batch reactors with time instead of space time.

Q4: How does space time affect the result?
A: Longer space times generally lead to higher conversion but may reduce intermediate concentration at certain points.

Q5: Can I use this for reversible reactions?
A: No, this calculator is specifically for irreversible first-order reactions in series.