1. What is Space Time for First Order Reaction?

Definition: Space time (τ) is the time required to process one reactor volume of feed at specified conditions.

Purpose: It helps chemical engineers determine the residence time needed for a first-order reaction in a continuous stirred-tank reactor (CSTR).

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \tau_i \) — Space time for vessel i (seconds)
• \( V_i \) — Volume of reactor vessel i (cubic meters)
• \( C_0 \) — Initial reactant concentration (mol/m³)
• \( F_0 \) — Molar feed rate (mol/s)

Explanation: The formula calculates how long it takes for one reactor volume of feed to pass through the reactor under steady-state conditions.

3. Importance of Space Time Calculation

Details: Proper space time calculation ensures optimal reactor design, reaction completion, and efficient use of resources in chemical processes.

4. Using the Calculator

Tips: Enter the reactor volume in m³, initial reactant concentration in mol/m³, and molar feed rate in mol/s. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between space time and residence time?
A: Space time is a design parameter based on feed conditions, while residence time is the actual time fluid elements spend in the reactor.

Q2: How does this relate to conversion in a first-order reaction?
A: For a first-order reaction, conversion X = 1 - exp(-kτ), where k is the rate constant.

Q3: What units should I use for the inputs?
A: The calculator uses SI units: m³ for volume, mol/m³ for concentration, and mol/s for flow rate.

Q4: Can this be used for batch reactors?
A: No, space time is specifically for continuous flow reactors like CSTRs.

Q5: How does temperature affect the calculation?
A: Temperature affects reaction rate but not the space time calculation itself, unless it changes feed density or flow rate.