Rate Constant for Second Order Reaction using Reactant Concentration for Plug Flow Calculator

Formula Used:

\[ k'' = \frac{C_{oBatch} - C_{Batch}}{\tau_{Batch} \times C_{oBatch} \times C_{Batch}} \]

Initial Reactant Concentration in Batch Reactor:

mol/m³

Reactant Conc at any Time in Batch Reactor:

mol/m³

Space Time in Batch Reactor:

Rate Constant for Second Order in Batch Reactor:

m³/(mol·s)

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1. What is Rate Constant for Second Order Reaction?

Definition: The rate constant for a second-order reaction is a proportionality constant that relates the reaction rate to the concentrations of the reactants.

Purpose: This calculator determines the rate constant for a second-order reaction in a batch reactor using reactant concentrations and space time.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ k'' = \frac{C_{oBatch} - C_{Batch}}{\tau_{Batch} \times C_{oBatch} \times C_{Batch}} \]

Where:

\( k'' \) — Rate constant for second order reaction (m³/(mol·s))
\( C_{oBatch} \) — Initial reactant concentration (mol/m³)
\( C_{Batch} \) — Reactant concentration at any time (mol/m³)
\( \tau_{Batch} \) — Space time in batch reactor (s)

Explanation: The formula calculates how quickly reactants are being consumed in a second-order reaction based on concentration changes over time.

3. Importance of Rate Constant Calculation

Details: Knowing the rate constant helps in reactor design, process optimization, and predicting reaction behavior under different conditions.

4. Using the Calculator

Tips: Enter the initial reactant concentration, current reactant concentration, and space time. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is a second-order reaction?
A: A reaction whose rate depends on the concentration of one reactant raised to the second power or two reactants each raised to the first power.

Q2: What are typical units for second-order rate constants?
A: For reactions in solution, typical units are m³/(mol·s) or L/(mol·s).

Q3: How does temperature affect the rate constant?
A: Rate constants typically increase with temperature according to the Arrhenius equation.

Q4: What is space time in a batch reactor?
A: It's the time required to process one reactor volume of feed under specified conditions.

Q5: Can this calculator be used for flow reactors?
A: This specific formula is for batch reactors. Different equations apply for continuous flow reactors.