Space Time for Second Order Reaction for Mixed Flow Calculator

Space Time Formula:

\[ \tau_{mixed} = \frac{X_{mfr}}{(1-X_{mfr})^2 \times k_{mixed} \times C_0} \]

Reactant Conversion in Mixed Flow:

(0 to 1)

Rate Constant for Second Order:

m³/mol·s

Initial Reactant Concentration:

mol/m³

Space Time in Mixed Flow (s):

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

Definition: Space time is the time required to process one reactor volume of feed at specified conditions for a second-order reaction in a mixed flow reactor.

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

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \tau_{mixed} = \frac{X_{mfr}}{(1-X_{mfr})^2 \times k_{mixed} \times C_0} \]

Where:

\( \tau_{mixed} \) — Space time in mixed flow (seconds)
\( X_{mfr} \) — Reactant conversion in mixed flow (0 to 1)
\( k_{mixed} \) — Rate constant for second order reaction (m³/mol·s)
\( C_0 \) — Initial reactant concentration (mol/m³)

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

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 reactant conversion (between 0 and 1), rate constant (must be > 0), and initial concentration (must be > 0). The calculator will compute the required space time.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical range for second-order rate constants?
A: Second-order rate constants vary widely but typically range from 10⁻⁶ to 10³ m³/mol·s depending on the reaction.

Q2: Why does the conversion need to be less than 1?
A: The formula becomes undefined at 100% conversion (X=1) due to division by zero in the denominator.

Q3: How does space time relate to reactor volume?
A: Space time is directly proportional to reactor volume for a given flow rate (τ = V/Q).

Q4: What's the difference between space time and residence time?
A: Space time is calculated from inlet conditions while residence time is the actual time fluid spends in the reactor.

Q5: Can this be used for first-order reactions?
A: No, this calculator is specifically for second-order reactions. First-order reactions use a different formula.