1. What is Time at Maximum Intermediate Concentration?

Definition: This is the instant of time at which the maximum concentration of intermediate is achieved in a two-step first order irreversible reaction in series.

Purpose: It helps chemical engineers and researchers determine the optimal time to measure intermediate concentrations in consecutive reactions.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \tau_{R,max} \) — Time at maximum intermediate concentration (seconds)
• \( k_2 \) — Rate constant for second step (1/s)
• \( k_I \) — Rate constant for first step (1/s)

Explanation: The natural logarithm of the ratio of rate constants divided by their difference gives the time when intermediate concentration peaks.

3. Importance of This Calculation

Details: Knowing this time helps in reaction optimization, intermediate isolation, and process design for consecutive chemical reactions.

4. Using the Calculator

Tips: Enter both rate constants in 1/s units. The values must be positive and cannot be equal (k₂ ≠ k₁).

5. Frequently Asked Questions (FAQ)

Q1: What happens when k₁ = k₂?
A: The formula becomes indeterminate. In practice, a limiting case approach is used when rate constants are nearly equal.

Q2: How do I obtain the rate constants?
A: Rate constants are typically determined experimentally from reaction kinetics studies.

Q3: Does this apply to reversible reactions?
A: No, this formula is specifically for irreversible consecutive first-order reactions.

Q4: What units should I use?
A: Consistent time units must be used (typically seconds) for both rate constants.

Q5: Can this be used for higher order reactions?
A: No, this formula is only valid for first-order consecutive reactions.