Calculator
Use the method that best matches your data. The page supports direct rate-law evaluation, Arrhenius estimation, first-order decay fitting, and correction of observed constants for diffusion limits.
Example Data Table
| Method | Example inputs | Example output | Units |
|---|---|---|---|
| Rate law | rate = 0.012, A = 0.40, B = 0.20, orders = 1 and 1 | k = 0.15 | L mol^-1 s^-1 |
| Arrhenius | A = 2.5e10, Ea = 75 kJ/mol, T = 350 K | k ≈ 0.1605 | same units as A |
| First-order decay | C0 = 0.80, Ct = 0.30, t = 120 s | k ≈ 0.00816 | s^-1 |
| Corrected observed | kobs = 0.12, η = 0.65 | k ≈ 0.18462 | same units as observed k |
Formula Used
1. General intrinsic rate law
For a reaction written as r = k CAα CBβ CCγ,
the intrinsic rate constant is:
k = r / (C_A^α × C_B^β × C_C^γ)
2. Arrhenius relationship
When activation energy and temperature are known:
k = A × exp(-E_a / (R × T))
3. First-order integrated form
For first-order decay based on concentration change over time:
k = ln(C_0 / C_t) / t
4. Correcting an observed constant
If diffusion or pore resistance suppresses the observed value:
k_intrinsic = k_observed / η
In catalytic chemistry, “intrinsic” usually means the true kinetic constant after minimizing or correcting transport limitations. Always confirm the method matches your experiment, mechanism, and unit system.
How to Use This Calculator
- Choose the calculation method that matches your laboratory or reactor data.
- Enter all values in a consistent unit system, especially concentration, time, and temperature.
- Submit the form to display the result panel directly above the calculator.
- Review the summary cards and the Plotly chart to understand how the constant behaves.
- Use the CSV or PDF buttons to save a clean copy of the result for reports or lab notes.
FAQs
1. What is an intrinsic rate constant?
It is the kinetic constant that reflects the true chemical reaction rate, ideally free from external film resistance, pore diffusion, and other transport limitations.
2. When should I use the rate-law method?
Use it when you already know the reaction orders and have a measured rate with concentrations for the active reactants at the same condition.
3. When is the Arrhenius method best?
Use Arrhenius when you know the pre-exponential factor, activation energy, and temperature, or when your model is based on temperature-driven kinetic estimation.
4. Can this page handle non-integer reaction orders?
Yes. Fractional and other real-valued orders are accepted, which is useful for empirical rate laws and mechanistic fits from experimental data.
5. Why does the unit of k sometimes change?
The unit depends on the overall reaction order. First-order reactions give s^-1, while higher or lower orders change the concentration dependence.
6. What does the effectiveness factor represent?
It measures how strongly diffusion or internal transport reduces the observed reaction compared with the ideal intrinsic kinetic behavior.
7. Why is my first-order calculation rejected?
For decay-style first-order fitting, the final concentration must be lower than the initial concentration and all values must remain positive.
8. Are the exported files suitable for reports?
Yes. The CSV provides structured numeric output, and the PDF creates a concise summary that is convenient for lab notebooks or technical appendices.