Maximum Intermediate Concentration in First Order followed by Zero Order Reaction Calculator

Formula Used:

\[ C_{R,max} = C_{A0} \times \left(1 - \left(\frac{k_0}{C_{A0} \times k_I} \times \left(1 - \ln\left(\frac{k_0}{C_{A0} \times k_I}\right)\right)\right)\right) \]

Initial Reactant Concentration (CA0):

mol/m³

Zero Order Rate Constant (k0):

mol/m³·s

First Order Rate Constant (kI):

1/s

Maximum Intermediate Concentration (CR,max): mol/m³

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1. What is Maximum Intermediate Concentration?

Definition: This is the highest concentration of intermediate product achieved in a two-step reaction where the first step is first order and the second step is zero order.

Purpose: It helps chemical engineers and researchers determine the optimal conditions for maximizing intermediate product yield in consecutive reactions.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ C_{R,max} = C_{A0} \times \left(1 - \left(\frac{k_0}{C_{A0} \times k_I} \times \left(1 - \ln\left(\frac{k_0}{C_{A0} \times k_I}\right)\right)\right)\right) \]

Where:

\( C_{R,max} \) — Maximum intermediate concentration (mol/m³)
\( C_{A0} \) — Initial reactant concentration (mol/m³)
\( k_0 \) — Zero order rate constant (mol/m³·s)
\( k_I \) — First order rate constant for first step (1/s)

Explanation: The formula calculates the peak concentration of the intermediate product R in a consecutive reaction scheme A → R → S.

3. Importance of This Calculation

Details: Knowing the maximum intermediate concentration helps in designing reactors and optimizing reaction conditions when the intermediate is the desired product.

4. Using the Calculator

Tips: Enter the initial reactant concentration, zero order rate constant, and first order rate constant. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What types of reactions does this apply to?
A: This applies specifically to consecutive reactions where the first step is first order and the second step is zero order.

Q2: How do I determine the rate constants?
A: Rate constants are typically determined experimentally through kinetic studies of the individual reaction steps.

Q3: What if my reaction has different orders?
A: Different formulas apply for different reaction orders. This calculator is specific to first→zero order consecutive reactions.

Q4: What units should I use?
A: Use consistent units: mol/m³ for concentrations, mol/m³·s for zero order rate constant, and 1/s for first order rate constant.

Q5: Can this be used for batch or flow reactors?
A: The formula applies to ideal batch reactors or plug flow reactors where there's no back-mixing.