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

Formula Used:

\[ k_{batch} = \frac{1}{\tau_{Batch}} \times \ln\left(\frac{C_{o\,Batch}}{C_{Batch}}\right) \]

Space Time in Batch Reactor:

seconds

Initial Reactant Concentration:

mol/m³

Reactant Concentration at Time t:

mol/m³

Rate Constant (1/s):

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1. What is Rate Constant for First Order Reaction?

Definition: The rate constant for a first-order reaction in a batch reactor determines how quickly the reactant concentration decreases over time.

Purpose: This calculator helps chemical engineers and researchers determine the reaction rate constant based on concentration measurements.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ k_{batch} = \frac{1}{\tau_{Batch}} \times \ln\left(\frac{C_{o\,Batch}}{C_{Batch}}\right) \]

Where:

\( k_{batch} \) — Rate constant (1/s)
\( \tau_{Batch} \) — Space time in batch reactor (seconds)
\( C_{o\,Batch} \) — Initial reactant concentration (mol/m³)
\( C_{Batch} \) — Reactant concentration at time t (mol/m³)

Explanation: The natural log of the concentration ratio divided by the space time gives the first-order rate constant.

3. Importance of Rate Constant Calculation

Details: Accurate rate constants are essential for reactor design, process optimization, and predicting reaction behavior.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is space time in a batch reactor?
A: Space time is the time required to process one reactor volume of feed under entrance conditions.

Q2: How does temperature affect the rate constant?
A: Rate constants typically increase with temperature according to the Arrhenius equation.

Q3: What units should I use for concentrations?
A: The calculator uses mol/m³, but any consistent concentration units can be used as long as they're the same for both concentrations.

Q4: Can I use this for second-order reactions?
A: No, this calculator is specifically for first-order reactions.

Q5: What if my current concentration is higher than initial?
A: This would give a negative rate constant, which is physically impossible - check your measurements.