Calculator Inputs
Use the intermediate mechanism R → I, I → R, and I → P. The calculator assumes a steady intermediate balance and also reports a transient concentration at a chosen time.
Formula Used
Mechanism: R → I with k1, I → R with k−1, and I → P with k2.
Intermediate balance: d[I]/dt = k1[R] − (k−1 + k2)[I]
Steady-state condition: d[I]/dt ≈ 0
Steady intermediate concentration: [I]ss = k1[R] / (k−1 + k2)
Product formation rate: rP = k2[I]ss = (k1k2[R]) / (k−1 + k2)
Intermediate lifetime: τ = 1 / (k−1 + k2)
Transient profile: [I](t) = [I]ss + ([I]0 − [I]ss)e−(k−1 + k2)t
The validity check compares the intermediate size against the reactant pool and also checks whether intermediate removal is substantially faster than intermediate generation.
How to Use This Calculator
- Enter the bulk reactant concentration feeding the intermediate step.
- Provide kinetic constants for formation, reverse loss, and product formation.
- Set an initial intermediate concentration if a transient estimate is needed.
- Choose a time point for the concentration profile calculation.
- Press Calculate to show results below the header and above the form.
- Review the assumption verdict before using the simplified rate law in design or analysis.
- Download the result as CSV or PDF for reports, lab records, or teaching notes.
Example Data Table
These sample rows illustrate how kinetic ratios change the steady-state result and the quality of the approximation.
| Case | [R] (mol/L) | k1 (s⁻¹) | k−1 (s⁻¹) | k2 (s⁻¹) | [I]ss (mol/L) | rP (mol·L⁻¹·s⁻¹) | Assessment |
|---|---|---|---|---|---|---|---|
| Fast removal | 0.100 | 1.50 | 12.00 | 30.00 | 0.00357 | 0.10714 | Strong steady-state region |
| Moderate removal | 0.080 | 2.20 | 4.50 | 7.00 | 0.01530 | 0.10710 | Reasonable approximation |
| Slow removal | 0.120 | 3.50 | 1.20 | 2.10 | 0.12727 | 0.26727 | Weak approximation |
Use the example cases to compare whether your mechanism is removal-controlled or formation-controlled.
Frequently Asked Questions
1. What does the steady-state approximation mean?
It assumes the reactive intermediate forms and disappears so quickly that its concentration stays nearly constant over the time window being analyzed.
2. When is this approximation usually valid?
It works best when intermediate consumption is much faster than intermediate formation, and when the intermediate concentration remains much smaller than the reactant concentration.
3. Why does the calculator report a validity ratio?
The ratio [I]ss/[R] helps flag whether the intermediate remains small. Smaller values support the approximation and reduce the chance of major modeling error.
4. What is the purpose of the transient concentration result?
It shows how the intermediate approaches the steady value at a selected time. This helps compare short-time behavior with the long-time approximation.
5. Can I use this for catalytic mechanisms?
Yes, if your catalytic cycle contains a short-lived intermediate that is formed and consumed rapidly compared with the observable reactant pool.
6. What units should I use?
Enter concentrations in mol/L and rate constants in s⁻¹ for this model. Keeping units consistent ensures meaningful intermediate concentrations and rates.
7. Does the calculator solve all kinetic mechanisms?
No. It is tailored to a simple intermediate mechanism with one formation path and two loss paths. Complex networks need broader kinetic modeling.
8. Why might a full differential equation model still matter?
If the intermediate becomes appreciable, or if early-time dynamics matter strongly, solving the full system can provide more accurate concentration profiles.