Reaction Rate for Vessel i using Space Time Calculator

Reaction Rate Formula:

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

Initial Reactant Concentration (C₀):

mol/m³

Reactant Conversion of Vessel i-1 (Xᵢ₋₁):

Reactant Conversion of Vessel i (Xᵢ):

Space Time for Vessel i (τᵢ):

seconds

Reaction Rate for Vessel i (rᵢ):

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1. What is Reaction Rate for Vessel i?

Definition: This calculator determines the reaction rate in a specific vessel (i) of a series based on reactant concentrations and space time.

Purpose: It helps chemical engineers analyze and optimize reaction kinetics in continuous stirred-tank reactors (CSTRs) in series.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( r_i \) — Reaction rate in vessel i (mol/m³·s)
\( C_0 \) — Initial reactant concentration (mol/m³)
\( X_{i-1} \) — Reactant conversion from previous vessel (dimensionless, 0-1)
\( X_i \) — Reactant conversion in current vessel (dimensionless, 0-1)
\( \tau_i \) — Space time for vessel i (seconds)

Explanation: The formula calculates how fast reactants are being converted to products in a specific vessel of a series reactor system.

3. Importance of Reaction Rate Calculation

Details: Accurate reaction rate determination is crucial for reactor design, process optimization, and ensuring product quality in chemical manufacturing.

4. Using the Calculator

Tips: Enter the initial concentration, conversion values (between 0 and 1), and space time. Conversion in vessel i should be ≤ conversion in vessel i-1.

5. Frequently Asked Questions (FAQ)

Q1: What is space time in reactor design?
A: Space time (τ) is the time required to process one reactor volume of feed, calculated as reactor volume divided by volumetric flow rate.

Q2: How does conversion change between vessels?
A: In series reactors, conversion typically increases with each vessel (Xᵢ > Xᵢ₋₁) as more reactant is converted to product.

Q3: What are typical units for reaction rate?
A: Reaction rate is typically expressed in mol/m³·s or similar molar concentration per time units.

Q4: When would reaction rate decrease between vessels?
A: Reaction rate may decrease if the reaction is approaching completion (most reactant already converted) or if conditions become less favorable.

Q5: How does initial concentration affect reaction rate?
A: Higher initial concentrations generally lead to higher reaction rates, all else being equal, as there are more reactant molecules available.