Initial Reactant Concentration for Zero Order Reaction for Plug Flow Calculator

Formula Used:

\[ C_{0,PFR} = \frac{k_0 \times \tau_{PFR}}{X_{A,PFR}} \]

Rate Constant for Zero Order Reaction (k₀):

mol/m³·s

Space Time in PFR (τ_PFR):

seconds

Reactant Conversion in PFR (X_A,PFR):

(0 to 1)

Initial Reactant Concentration (C₀,PFR): mol/m³

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1. What is Initial Reactant Concentration for Zero Order Reaction in PFR?

Definition: This calculator determines the initial concentration of reactant needed in a Plug Flow Reactor (PFR) for a zero-order reaction based on the rate constant, space time, and desired conversion.

Purpose: It helps chemical engineers design PFR systems by calculating the required initial reactant concentration to achieve a specific conversion.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ C_{0,PFR} = \frac{k_0 \times \tau_{PFR}}{X_{A,PFR}} \]

Where:

\( C_{0,PFR} \) — Initial reactant concentration (mol/m³)
\( k_0 \) — Rate constant for zero-order reaction (mol/m³·s)
\( \tau_{PFR} \) — Space time in PFR (seconds)
\( X_{A,PFR} \) — Reactant conversion in PFR (decimal between 0 and 1)

Explanation: For zero-order reactions, the reaction rate is independent of reactant concentration. The initial concentration is directly proportional to the rate constant and space time, and inversely proportional to conversion.

3. Importance of Initial Concentration Calculation

Details: Accurate initial concentration calculation ensures proper reactor design, optimal reaction conditions, and desired product yields in chemical processes.

4. Using the Calculator

Tips: Enter the rate constant (k₀), space time (τ_PFR), and desired conversion (X_A,PFR as a decimal). All values must be positive, with conversion between 0 and 1.

5. Frequently Asked Questions (FAQ)

Q1: What is a zero-order reaction?
A: A reaction where the rate is independent of the reactant concentration. The rate is constant and equal to k₀.

Q2: What is space time in a PFR?
A: The time required to process one reactor volume of feed at entrance conditions (τ = V/v₀).

Q3: How does conversion affect the calculation?
A: Higher conversion requires higher initial concentration for the same space time and rate constant.

Q4: What are typical units for k₀ in zero-order reactions?
A: Common units are mol/m³·s or mol/L·s, depending on concentration units used.

Q5: When is this formula not applicable?
A: For non-zero-order reactions or when other factors like backmixing or temperature gradients are significant.