Space Time for First Order Reaction for Vessel i using Reaction Rate Calculator

Space Time Formula:

\[ \tau_i = \frac{C_0 \times (X_{i-1} - X_i)}{r_i} \]

Initial Reactant Concentration (C₀):

mol/m³

Reactant Conversion of Vessel i-1 (X_i-1):

Reactant Conversion of Vessel i (X_i):

Reaction Rate for Vessel i (r_i):

mol/m³·s

Space Time (τ_i):

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1. What is Space Time for First Order Reaction?

Definition: Space time (τ) is the time required to process one reactor volume of feed at specified conditions.

Purpose: It helps chemical engineers determine the residence time needed for a given conversion in a continuous stirred-tank reactor (CSTR).

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \tau_i = \frac{C_0 \times (X_{i-1} - X_i)}{r_i} \]

Where:

\( \tau_i \) — Space time for vessel i (seconds)
\( C_0 \) — Initial reactant concentration (mol/m³)
\( X_{i-1} \) — Conversion from previous vessel (dimensionless)
\( X_i \) — Conversion in current vessel (dimensionless)
\( r_i \) — Reaction rate in vessel i (mol/m³·s)

Explanation: The formula calculates the time needed to achieve the specified conversion based on the reaction kinetics.

3. Importance of Space Time Calculation

Details: Proper space time calculation ensures optimal reactor design, efficient conversion rates, and cost-effective chemical processes.

4. Using the Calculator

Tips: Enter the initial concentration, conversions (as decimals between 0-1), and reaction rate. Ensure X_i-1 ≥ X_i.

5. Frequently Asked Questions (FAQ)

Q1: What units should I use for concentration and reaction rate?
A: Use consistent units (mol/m³ for concentration and mol/m³·s for reaction rate) for accurate results.

Q2: How do I determine the reaction rate?
A: Reaction rate can be determined experimentally or from kinetic studies of the specific reaction.

Q3: What if my conversion decreases between vessels?
A: This calculator assumes X_i-1 ≥ X_i. If conversion decreases, check your system for errors.

Q4: Can this be used for batch reactors?
A: No, this formula is specifically for continuous flow reactors (CSTRs).

Q5: How does temperature affect the calculation?
A: Temperature effects are captured in the reaction rate value (r_i), which should be determined at the operating temperature.