Rate Constant for First Order Reaction in Vessel i Calculator

Formula Used:

\[ k' = \frac{C_{i-1} - C_i}{C_i \times \tau_i} \]

Reactant Concentration in Vessel i-1:

mol/m³

Reactant Concentration in Vessel i:

mol/m³

Space Time for Vessel i:

seconds

Rate Constant for First Order Reaction (1/s):

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1. What is Rate Constant for First Order Reaction in Vessel i?

Definition: The rate constant for a first-order reaction in a vessel represents how quickly the reaction proceeds, relating the reaction rate to the reactant concentration.

Purpose: This calculator helps chemical engineers and researchers determine the reaction rate constant in continuous flow systems with multiple vessels.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ k' = \frac{C_{i-1} - C_i}{C_i \times \tau_i} \]

Where:

\( k' \) — Rate constant for first order reaction (1/s)
\( C_{i-1} \) — Reactant concentration in previous vessel (mol/m³)
\( C_i \) — Reactant concentration in current vessel (mol/m³)
\( \tau_i \) — Space time for current vessel (seconds)

Explanation: The formula calculates the rate constant based on the concentration difference between vessels and the residence time in the current vessel.

3. Importance of Rate Constant Calculation

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

4. Using the Calculator

Tips: Enter the reactant concentrations in adjacent vessels and the space time for the current vessel. All values must be positive numbers.

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: What are typical units for first-order rate constants?
A: First-order rate constants have units of reciprocal time (1/s, 1/min, etc.).

Q3: How does this differ from batch reactor calculations?
A: This formula is specifically for continuous flow systems with multiple vessels in series.

Q4: What if my concentrations are increasing between vessels?
A: This would suggest an error in measurement, as concentrations should typically decrease as reaction proceeds.

Q5: Can I use this for non-first-order reactions?
A: No, this formula is specifically derived for first-order reaction kinetics.