1. What is Rate Constant for First Order Reaction?

Definition: The rate constant for a first-order reaction in a batch reactor quantifies how quickly reactants are converted to products.

Purpose: This calculation helps chemical engineers design and optimize batch reactors for first-order reactions.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( k_{batch} \) — Rate constant (1/second)
• \( \tau_{batch} \) — Space time in batch reactor (seconds)
• \( X_{A\,batch} \) — Reactant conversion (0 to 1)

Explanation: The natural logarithm term accounts for the exponential nature of first-order reactions, while space time represents the reactor's processing capacity.

3. Importance of Rate Constant Calculation

Details: Accurate rate constants are essential for reactor sizing, predicting reaction times, and optimizing process conditions.

4. Using the Calculator

Tips: Enter the space time in seconds and reactant conversion (as a decimal between 0 and 1). Space time must be > 0 and conversion must be ≥ 0 and < 1.

5. Frequently Asked Questions (FAQ)

Q1: What is space time in a batch reactor?
A: Space time is the time required to process one reactor volume of feed under entrance conditions.

Q2: Why is the conversion limited to less than 1?
A: At 100% conversion (X=1), the equation becomes undefined as ln(1/0) approaches infinity.

Q3: How does this differ from continuous reactors?
A: Batch reactors have different dynamics than continuous flow reactors, though the first-order rate expression is similar.

Q4: What units should I use for space time?
A: Always use seconds for consistency with the rate constant units (s⁻¹).

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