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

Space Time Formula:

\[ \tau_{mixed} = \frac{1}{k'} \times \left( \frac{C_0 - C}{C} \right) \]

Rate Constant for First Order Reaction:

1/s

Initial Reactant Concentration:

mol/m³

Reactant Concentration at Time:

mol/m³

Space Time in Mixed Flow (s):

Unit Converter ▲

Unit Converter ▼

From:	To:

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

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

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

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \tau_{mixed} = \frac{1}{k'} \times \left( \frac{C_0 - C}{C} \right) \]

Where:

\( \tau_{mixed} \) — Space time in mixed flow (seconds)
\( k' \) — Rate constant for first order reaction (1/s)
\( C_0 \) — Initial reactant concentration (mol/m³)
\( C \) — Reactant concentration at given time (mol/m³)

Explanation: The formula relates the space time to the reaction rate constant and the fractional conversion of reactant.

3. Importance of Space Time Calculation

Details: Proper space time calculation ensures optimal reactor design, efficient reaction conversion, and cost-effective operation.

4. Using the Calculator

Tips: Enter the rate constant (must be > 0), initial reactant concentration, and current reactant concentration. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between space time and residence time?
A: Space time is based on inlet conditions, while residence time is the actual time fluid elements spend in the reactor.

Q2: How does space time affect conversion?
A: Higher space time generally leads to higher conversion, but the relationship depends on reaction kinetics.

Q3: What are typical units for the rate constant?
A: For first-order reactions, the rate constant has units of 1/s (reciprocal seconds).

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

Q5: What if my reactant concentration is zero?
A: The formula becomes undefined when C=0, which corresponds to 100% conversion (infinite space time theoretically required).