Chemistry and reaction planning
Stoichiometry Sensitivity Calculator
Recalculate expected product mass under one-at-a-time changes to reactant amount, purity, and yield while preserving limiting-reagent switches.
CURRENT STOICHIOMETRIC MODEL
Enter the chemical assumptions
For experiment planning and review when users need to see which entered assumption most changes predicted product.
LIVE DECISION VIEW
Which assumption moves product mass most?
The centered tornado chart plots signed low and high product-mass changes; the ledger records the limiting reagent on each side.
| Quantity | Formula path | Current value | Interpretation |
|---|
HOW TO USE
Use Stoichiometry Sensitivity Calculator without hiding assumptions
- Enter gross reactant masses, assays, molar masses, and coefficients from one balanced reaction.
- Set a relative perturbation no larger than 50% and review the baseline before comparing scenarios.
- Use the signed bars to identify direction and the ledger to identify limiting-reagent switches.
- Pair mathematical leverage with actual measurement uncertainty and control cost before changing an experiment.
CURRENT CALCULATION PROCESS
Formula, substitution, intermediate steps and final check
extent = min[m_A(p_A/100)/(M_A a), m_B(p_B/100)/(M_B b)]; m_P,0 = extent c M_P(Y/100); S_i(low/high) = 100[m_P(x_i changed by +/-delta)-m_P,0]/m_P,0.
Calculate one baseline, then change reactant A mass, A purity, B mass, B purity, and expected yield separately. Recalculate both reagent capacities for every case; cap purity and yield high cases at 100%.
Waiting for valid inputs.
MODEL EXPLANATION
Sensitivity is not uncertainty
One-at-a-time sensitivity measures response around the entered baseline but assigns no likelihood, covariance, or confidence interval.
Near a stoichiometric tie, changing one reactant can move the reaction to the other reagent's capacity, creating an asymmetric response.
SYMBOLS AND VARIABLES
Read the formula before relying on the result
| Symbol | Unit or range | Meaning |
|---|---|---|
| m_A, m_B | g | gross baseline masses of reactants A and B |
| p_A, p_B | % | reactant assays entered as percentages |
| M_A, M_B, M_P | g/mol | molar masses of both reactants and the product |
| a, b, c | coefficient | positive whole-number balanced-equation coefficients |
| extent | mol | minimum purity-corrected stoichiometric capacity |
| Y | % | entered expected isolated yield |
| delta | fraction | entered perturbation divided by 100 |
| S_i(low/high) | % | signed product response when driver x_i is changed alone |
WORKED EXAMPLE
Default near-tie sensitivity
- The defaults give A capacity 0.098 mol and B capacity 0.095 mol, so B limits and expected product mass is 8.8825 g at 85% yield.
- A 10% low case for A mass or A purity lowers A capacity to 0.0882 mol, switches the limit to A, and gives 8.2467 g product.
- A mass and purity each have a maximum swing of about 7.158%. B mass, B purity, and expected yield each reach 10.000% at displayed precision; the unrounded model returns Expected yield as the summary label.
CHEMISTRY FOUNDATIONS
Reading the tornado chart
- A longer span means greater modeled leverage for the selected perturbation, not necessarily greater real-world uncertainty.
- Unequal left and right spans reveal a 100% cap or a change in which reactant limits product formation.
- A zero reactant span means the other reagent controls every tested case in that direction.
- B mass, B purity, and expected yield tie at 10.000% under the defaults, although unrounded floating-point values make the summary card report Expected yield.
DEEPER ANALYSIS
Choosing a method beyond local screening
- Use joint scenarios when operating assumptions move together.
- Use distributions and covariance for measurement-uncertainty propagation.
- Use global sensitivity when the plausible domain is too wide for one local perturbation.
- Add kinetic or equilibrium models when stoichiometric extent alone cannot describe product formation.
REAL-WORLD CASE
Case: deciding what to assay more carefully
A trial reaction sits close to a limiting-reagent switch, and product forecasts vary across raw-material lots.
The team compares equal relative changes first, then combines that leverage ranking with each assay's observed variation and testing cost.
This separates a useful data-collection priority from an unsupported claim about process capability.
TERMS
Page-specific chemistry vocabulary
- Baseline
- Current input set used as the comparison point.
- Perturbation
- Controlled relative low or high change applied to one driver.
- Local sensitivity
- Output response near one entered baseline.
- Driver
- Input varied while all other baseline entries are held fixed.
- Limiting switch
- Change in which reactant sets the reaction extent.
LIMITS AND DISCLAIMER
Where this model stops
- One-at-a-time cases do not represent simultaneous changes or correlations.
- Rankings can change with the baseline and perturbation size.
- Purity and expected-yield high cases stop at their physical 100% ceiling.
- The model excludes kinetics, equilibrium, side reactions, workup losses beyond entered yield, and measurement quality.
- The summary reports one unrounded top value and has no tie band; compare displayed swings before prioritizing work.
Scenario-planning tool only; do not treat its deterministic bars as a validated operating range, safety limit, or statistical uncertainty estimate.
Frequently asked questions
Why can one side of a bar be shorter?
A 100% cap or a limiting-reagent switch can truncate one side of the local response.
Does the largest bar prove causation?
No. It reports model response when one entered value changes and all other values stay fixed.
Why does a reactant show zero sensitivity?
Its capacity may remain above the other reactant's capacity throughout that tested direction.
Can I combine all low cases?
Not in this ledger. Combining them creates a joint scenario with a different interpretation.
Is 10% always the right perturbation?
No. Select a locally plausible change and compare it with observed assay or measurement variation.
What should I do when two drivers tie?
Treat both as equally responsive at the displayed precision, then compare uncertainty, cost, and controllability.
SOURCES