Space Time for First Order Reaction using Reactant Concentration for Plug Flow Calculator

Space Time Formula:

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

Rate Constant (k_batch):

1/s

Initial Concentration (C_{o batch}):

mol/m³

Current Concentration (C_batch):

mol/m³

Space Time (τ_batch): s

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1. What is Space Time in Batch Reactor?

Definition: Space Time in a Batch Reactor is the time necessary to process the volume of reactor fluid at the entrance conditions for a first-order reaction.

Purpose: It helps chemical engineers determine the required reaction time to achieve a specific conversion in a batch reactor.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( \tau_{batch} \) — Space Time in Batch Reactor (seconds)
\( k_{batch} \) — Rate Constant for First Order in Batch Reactor (1/s)
\( C_{o\,batch} \) — Initial Reactant Concentration (mol/m³)
\( C_{batch} \) — Reactant Concentration at any Time (mol/m³)

Explanation: The natural logarithm of the concentration ratio divided by the rate constant gives the space time required for the reaction.

3. Importance of Space Time Calculation

Details: Accurate space time calculation ensures optimal reactor design, proper reaction control, and efficient process scaling.

4. Using the Calculator

Tips: Enter the rate constant (must be > 0), initial reactant concentration, and current reactant concentration. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical meaning of space time?
A: Space time represents the time needed to process one reactor volume of feed under entrance conditions.

Q2: How does rate constant affect space time?
A: Higher rate constants result in shorter required space times for the same conversion.

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 both concentrations are in the same units.

Q4: Can this be used for non-first-order reactions?
A: No, this specific formula is only valid for first-order reactions.

Q5: What if my current concentration is higher than initial?
A: This would give a negative result, which is physically meaningless. Current concentration must be less than initial.