1. What is Rate Constant for First Order Reaction?

Definition: The Rate Constant for First Order Reaction is defined as the rate of the reaction divided by the concentration of the reactant.

Purpose: This calculator determines the rate constant for first-order reactions in plug flow or infinite reactors.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( k' \) — Rate Constant for First Order Reaction (1/s)
• \( \tau_p \) — Space Time for Plug Flow Reactor (seconds)
• \( C_o \) — Initial Reactant Concentration (mol/m³)
• \( C \) — Reactant Concentration (mol/m³)

Explanation: The natural logarithm of the concentration ratio is divided by the space time to determine the rate constant.

3. Importance of Rate Constant Calculation

Details: Accurate rate constant determination is crucial for reactor design, process optimization, and reaction kinetics analysis.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is space time in a plug flow reactor?
A: Space time is the time taken by the amount of fluid to either completely enter or completely exit the plug flow reactor.

Q2: What units should I use for concentrations?
A: The calculator uses mol/m³, but any consistent concentration units can be used as long as Co and C are in the same units.

Q3: Why is the natural logarithm used in this formula?
A: The natural logarithm (ln) is the inverse function of the natural exponential function and is used to solve first-order kinetics equations.

Q4: Can this calculator be used for batch reactors?
A: Yes, the same formula applies to batch reactors where space time would be replaced by reaction time.

Q5: What does a higher rate constant indicate?
A: A higher rate constant means the reaction proceeds faster at a given reactant concentration.