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Definition: The rate constant for a second-order reaction quantifies the speed at which reactants are converted to products in a reaction where the rate depends on the concentration of two reactants or the square of one reactant's concentration.
Purpose: This calculator determines the rate constant using space time, initial concentration, and reactant conversion in a batch reactor.
The calculator uses the formula:
Where:
Explanation: The formula relates the rate constant to the space time, initial concentration, and the extent of reaction conversion.
Details: Knowing the rate constant is essential for reactor design, process optimization, and predicting reaction behavior under different conditions.
Tips: Enter the space time (τ) in seconds, initial concentration (C₀) in mol/m³, and conversion (X_A) as a decimal between 0 and 1. All values must be positive, and conversion must be less than 1.
Q1: What is space time in a batch reactor?
A: Space time is the time required to process one reactor volume of feed under specified conditions.
Q2: How does conversion affect the rate constant?
A: Higher conversion values typically result in higher calculated rate constants, as the relationship is nonlinear.
Q3: What are typical units for second-order rate constants?
A: For second-order reactions, rate constants typically have units of m³/(mol·s) or L/(mol·s).
Q4: Can I use this for continuous reactors?
A: This specific formula is for batch reactors. Different equations apply for continuous flow reactors.
Q5: What if my conversion is very close to 1?
A: As conversion approaches 1, the denominator (1-X_A) approaches 0, making the rate constant approach infinity. This reflects the mathematical relationship at complete conversion.