1. What is Reaction Time for First Order Irreversible Reaction?

Definition: This calculator determines the time required to achieve a certain reactant conversion in a first-order irreversible chemical reaction.

Purpose: It helps chemical engineers and researchers estimate reaction times for process design and optimization.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( t \) — Reaction time (seconds)
• \( X_A \) — Reactant conversion (0 to 1)
• \( k \) — Rate constant (1/second)

Explanation: The formula derives from the integrated rate law for first-order reactions, using base-10 logarithm for convenience.

3. Importance of Reaction Time Calculation

Details: Accurate reaction time estimation is crucial for reactor design, process optimization, and ensuring complete conversion in chemical processes.

4. Using the Calculator

Tips: Enter the reactant conversion (between 0 and 1) and the rate constant (must be positive). The calculator will compute the required reaction time.

5. Frequently Asked Questions (FAQ)

Q1: Why is the logarithm negative in the formula?
A: The negative sign accounts for the fact that (1 - X_A) decreases as conversion increases, ensuring positive time values.

Q2: What's a typical rate constant value?
A: Rate constants vary widely depending on the reaction and conditions. Values typically range from 10^-6 to 10³ s^-1.

Q3: Why 2.303 in the formula?
A: 2.303 is the conversion factor between natural logarithm (ln) and base-10 logarithm (log₁₀), since 2.303 = ln(10).

Q4: What if my conversion is 100% (X_A = 1)?
A: The formula becomes undefined at 100% conversion as log₁₀(0) is undefined. In practice, reactions approach but never truly reach 100% completion.

Q5: Does this work for reversible reactions?
A: No, this calculator is specifically for irreversible first-order reactions. Reversible reactions require different equations.