Space Time for Second Order Reaction using Reactant Concentration for Mixed Flow Calculator

Space Time Formula:

\[ \tau_{mixed} = \frac{C_0 - C}{(k_{mixed} \times C^2)} \]

Initial Reactant Concentration (C₀):

mol/m³

Reactant Concentration at Time (C):

mol/m³

Rate Constant (k_mixed):

m³/(mol·s)

Space Time (τ_mixed):

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1. What is Space Time for Second Order Reaction in Mixed Flow?

Definition: Space time (τ_mixed) is the time required to process one reactor volume of feed based on entrance conditions for a second-order reaction in a mixed flow reactor.

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

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \tau_{mixed} = \frac{C_0 - C}{(k_{mixed} \times C^2)} \]

Where:

\( \tau_{mixed} \) — Space time in mixed flow (seconds)
\( C_0 \) — Initial reactant concentration (mol/m³)
\( C \) — Reactant concentration at given time (mol/m³)
\( k_{mixed} \) — Rate constant for second order reaction (m³/(mol·s))

Explanation: The formula calculates the time needed to achieve a specific concentration change in a CSTR for a second-order reaction.

3. Importance of Space Time Calculation

Details: Accurate space time calculation ensures proper reactor sizing, optimal reaction conditions, and efficient process design in chemical engineering.

4. Using the Calculator

Tips: Enter the initial concentration (must be greater than final concentration), final concentration, and rate constant. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a mixed flow reactor?
A: A mixed flow reactor (or CSTR) is a reactor where contents are perfectly mixed and have uniform composition throughout.

Q2: Why is space time important?
A: Space time helps determine reactor volume needed for a given conversion and flow rate.

Q3: What are typical units for rate constant?
A: For second-order reactions, the rate constant has units of m³/(mol·s).

Q4: Can initial concentration be less than final?
A: No, for this calculation C₀ must be greater than C as concentration decreases over time in normal reactions.

Q5: How does this differ from plug flow reactors?
A: The space time calculation differs because mixing patterns affect reaction rates differently in CSTRs vs PFRs.