Concentration of Product C in First Order Consecutive Reaction Calculator

Concentration Formula:

\[ [C] = A_0 \times \left(1 - \frac{1}{k_2 - k_1} \times \left(k_2 e^{-k_1 t} - k_1 e^{-k_2 t}\right)\right) \]

Initial Concentration of A:

mol/m³

Rate Constant k₁:

s⁻¹

Rate Constant k₂:

s⁻¹

Reaction Time:

seconds

Concentration of C (mol/m³):

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1. What is the Concentration of Product C Calculator?

Definition: This calculator determines the concentration of product C in a consecutive first-order reaction A → B → C.

Purpose: It helps chemists and chemical engineers predict product concentrations over time in consecutive reactions.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ [C] = A_0 \times \left(1 - \frac{1}{k_2 - k_1} \times \left(k_2 e^{-k_1 t} - k_1 e^{-k_2 t}\right)\right) \]

Where:

\( [C] \) — Concentration of product C (mol/m³)
\( A_0 \) — Initial concentration of reactant A (mol/m³)
\( k_1 \) — Rate constant for A → B (s⁻¹)
\( k_2 \) — Rate constant for B → C (s⁻¹)
\( t \) — Reaction time (seconds)

Explanation: The formula accounts for the sequential transformation of A to B and then B to C, with both steps following first-order kinetics.

3. Importance of the Calculation

Details: Understanding product concentrations helps optimize reaction conditions, predict yields, and design chemical processes.

4. Using the Calculator

Tips: Enter the initial concentration of A, both rate constants (k₁ and k₂), and the reaction time. All rate constants must be positive and distinct.

5. Frequently Asked Questions (FAQ)

Q1: What if k₁ equals k₂?
A: The formula becomes indeterminate. A different equation is needed when rate constants are equal.

Q2: What units should I use?
A: Use consistent units - mol/m³ for concentrations, s⁻¹ for rate constants, and seconds for time.

Q3: How do I determine the rate constants?
A: Rate constants are typically determined experimentally from kinetic studies.

Q4: Does this work for non-first-order reactions?
A: No, this formula is specific for consecutive first-order reactions.

Q5: What's the maximum time I can enter?
A: Theoretically unlimited, but extremely large times will approach the final equilibrium concentration.