Reaction Kinetics Calculator
Arrhenius equation: compute rate constant k from A and Ea, or determine Ea and A from k at two temperatures. Arrhenius plot and 1st order conversion vs time
This free online reaction kinetics calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Supports both metric (SI) and imperial units with built-in unit selection dropdowns on every input field, so you can work in whatever units your problem provides. Designed for engineering students and professionals working through coursework, design projects, or quick reference calculations.
Arrhenius Parameters
Arrhenius Plot: ln(k) vs 1000/T (K⁻¹)
Arrhenius Data Table
| 1000/T (K⁻¹) | ln(k) |
|---|---|
| 3.6610 | -5.2936 |
| 3.6161 | -4.8618 |
| 3.5723 | -4.4405 |
| 3.5296 | -4.0292 |
| 3.4879 | -3.6276 |
| 3.4471 | -3.2355 |
| 3.4073 | -2.8524 |
| 3.3684 | -2.4780 |
| 3.3304 | -2.1121 |
| 3.2932 | -1.7544 |
| 3.2568 | -1.4045 |
| 3.2213 | -1.0623 |
| 3.1865 | -0.7275 |
| 3.1524 | -0.3999 |
| 3.1191 | -0.0792 |
| 3.0864 | 0.2348 |
| 3.0545 | 0.5423 |
| 3.0232 | 0.8436 |
| 2.9925 | 1.1386 |
| 2.9625 | 1.4278 |
| 2.9330 | 1.7112 |
| 2.9041 | 1.9891 |
| 2.8758 | 2.2615 |
| 2.8481 | 2.5286 |
| 2.8208 | 2.7907 |
| 2.7941 | 3.0478 |
| 2.7679 | 3.3000 |
| 2.7422 | 3.5476 |
| 2.7169 | 3.7906 |
| 2.6921 | 4.0292 |
| 2.6678 | 4.2635 |
| 2.6439 | 4.4935 |
| 2.6204 | 4.7195 |
| 2.5973 | 4.9415 |
| 2.5746 | 5.1596 |
| 2.5524 | 5.3740 |
| 2.5305 | 5.5846 |
| 2.5089 | 5.7917 |
| 2.4878 | 5.9953 |
| 2.4670 | 6.1955 |
| 2.4465 | 6.3924 |
| 2.4264 | 6.5860 |
| 2.4066 | 6.7765 |
| 2.3871 | 6.9638 |
| 2.3680 | 7.1482 |
| 2.3491 | 7.3297 |
| 2.3306 | 7.5082 |
| 2.3123 | 7.6840 |
| 2.2943 | 7.8571 |
| 2.2766 | 8.0274 |
| 2.2592 | 8.1952 |
| 2.2420 | 8.3604 |
| 2.2251 | 8.5231 |
| 2.2084 | 8.6834 |
| 2.1920 | 8.8413 |
| 2.1758 | 8.9969 |
| 2.1599 | 9.1502 |
| 2.1442 | 9.3012 |
| 2.1287 | 9.4501 |
| 2.1135 | 9.5969 |
1st Order Conversion vs Time
Conversion Data Table
| t (s) | X |
|---|---|
| 0.0000 | 0.000000 |
| 0.9560 | 0.087989 |
| 1.9120 | 0.168236 |
| 2.8679 | 0.241422 |
| 3.8239 | 0.308169 |
| 4.7799 | 0.369043 |
| 5.7359 | 0.424560 |
| 6.6919 | 0.475193 |
| 7.6478 | 0.521370 |
| 8.6038 | 0.563484 |
| 9.5598 | 0.601893 |
| 10.5158 | 0.636922 |
| 11.4718 | 0.668869 |
| 12.4278 | 0.698005 |
| 13.3837 | 0.724577 |
| 14.3397 | 0.748811 |
| 15.2957 | 0.770913 |
| 16.2517 | 0.791070 |
| 17.2077 | 0.809454 |
| 18.1636 | 0.826220 |
| 19.1196 | 0.841511 |
| 20.0756 | 0.855456 |
| 21.0316 | 0.868174 |
| 21.9876 | 0.879774 |
| 22.9435 | 0.890352 |
| 23.8995 | 0.900000 |
| 24.8555 | 0.908799 |
| 25.8115 | 0.916824 |
| 26.7675 | 0.924142 |
| 27.7234 | 0.930817 |
| 28.6794 | 0.936904 |
| 29.6354 | 0.942456 |
| 30.5914 | 0.947519 |
| 31.5474 | 0.952137 |
| 32.5033 | 0.956348 |
| 33.4593 | 0.960189 |
| 34.4153 | 0.963692 |
| 35.3713 | 0.966887 |
| 36.3273 | 0.969800 |
| 37.2833 | 0.972458 |
| 38.2392 | 0.974881 |
| 39.1952 | 0.977091 |
| 40.1512 | 0.979107 |
| 41.1072 | 0.980945 |
| 42.0632 | 0.982622 |
| 43.0191 | 0.984151 |
| 43.9751 | 0.985546 |
| 44.9311 | 0.986817 |
| 45.8871 | 0.987977 |
| 46.8431 | 0.989035 |
| 47.7990 | 0.990000 |
Theory
Arrhenius: k = A · exp(−Ea / RT)
Linearized: ln(k) = ln(A) − Ea/(R·T)
Two-temperature: ln(k₂/k₁) = −(Ea/R)·(1/T₂ − 1/T₁)
1st order half-life: t₁/₂ = ln(2)/k
1st order conversion: X(t) = 1 − exp(−k·t)
How to Use This Calculator
Enter your input values
Fill in all required input fields for the Reaction Kinetics Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.
Review your inputs
Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.
Read the results
The Reaction Kinetics Calculator instantly computes the output and displays results with units clearly labeled. All calculations happen in your browser — no loading time and no data sent to a server.
Explore parameter sensitivity
Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.
Formula Reference
Reaction Kinetics Calculator Formula
See calculator inputs for the governing equation
Variables: All variables and their units are labeled in the calculator interface above. Input fields accept values in multiple unit systems — select your preferred unit from the dropdown next to each field.
When to Use This Calculator
- •Use the Reaction Kinetics Calculator when solving homework or exam problems that require quick numerical verification of your hand calculations — instant feedback helps identify arithmetic errors before they propagate.
- •Use it during the early design phase to rapidly iterate on parameters and narrow down feasible configurations before committing time to detailed finite element simulations or full design packages.
- •Use it when reviewing a colleague's calculation or checking a vendor's data sheet for plausibility — a quick sanity check can prevent costly downstream errors.
- •Use it to generate reference data for a technical report or presentation without manual computation, ensuring consistent, reproducible numbers throughout the document.
- •Use it in the field when a quick estimate is needed and a full engineering software package is not available.
About This Calculator
The Reaction Kinetics Calculator is a precision engineering calculation tool designed for students, engineers, and technical professionals. Arrhenius equation: compute rate constant k from A and Ea, or determine Ea and A from k at two temperatures. Arrhenius plot and 1st order conversion vs time All calculations are performed using established engineering formulas from the relevant scientific literature and standards. Inputs support both metric (SI) and imperial unit systems, with unit conversion handled automatically — simply select your preferred unit from the dropdown next to each field. Results are computed instantly in the browser without sending data to a server, ensuring both speed and privacy. This calculator is intended as a supplementary tool for learning and design exploration; always verify results against authoritative references for safety-critical applications.
The Theory Behind It
Reaction kinetics describes the rate at which chemical reactions proceed. For a reaction A → products, the rate law is r = −dC_A/dt = k·C_A^n, where k is the rate constant (with units depending on n), C_A is the reactant concentration, and n is the reaction order with respect to A. The Arrhenius equation gives the temperature dependence of k: k = A·exp(−E_a/(RT)), where A is the pre-exponential factor, E_a is the activation energy, R is the gas constant, and T is absolute temperature. Plot ln(k) vs 1/T gives a straight line with slope −E_a/R. Typical activation energies: 10-200 kJ/mol for most reactions. Each 10°C rise in temperature typically doubles the rate (for E_a ≈ 50 kJ/mol around room temperature) — the 'rule of thumb' for organic reactions. Reaction order (0, 1, or 2 commonly) is determined by fitting rate data to different integrated rate laws. Zero-order: C = C₀ − k·t. First-order: C = C₀·e^(−k·t). Second-order: 1/C = 1/C₀ + k·t. Half-life for first-order: t₁/₂ = ln(2)/k. For non-elementary reactions, order may not match stoichiometry and must be measured experimentally. The calculator computes rate constants, activation energies, and conversions using Arrhenius-fit data.
Real-World Applications
- •Batch reactor design: compute residence time needed to achieve target conversion at specific temperature for a known rate law.
- •Catalyst evaluation: compare the activity of different catalysts by measuring reaction rates under identical conditions.
- •Scale-up from laboratory to industrial reactor: ensure rate constants and activation energies hold across the scale difference.
- •Stability and shelf-life prediction: Arrhenius extrapolation from elevated temperature tests to room temperature gives pharmaceutical and food shelf life.
- •Temperature sensitivity analysis: determine how reactor performance changes with temperature variation for process control and safety.
Frequently Asked Questions
What's the Arrhenius equation?
k = A·exp(−E_a/(RT)), where k is the rate constant, A is the pre-exponential factor (captures collision frequency and orientation), E_a is the activation energy (the barrier molecules must overcome to react), R is the gas constant, and T is absolute temperature. Higher T means more molecules have enough energy to react, so k increases exponentially with T.
How do I find activation energy from experimental data?
Measure k at several temperatures. Plot ln(k) vs 1/T. The slope of the best-fit line equals −E_a/R, so E_a = −R × slope. Make sure to use absolute temperature (K) and consistent units. Well-behaved reactions give a straight line; deviation from linearity indicates changing mechanism or other complications.
What's reaction order?
The exponent of concentration in the rate law. For r = k·C^n: n = 0 (rate independent of C), n = 1 (rate proportional to C), n = 2 (rate proportional to C²). Order is determined experimentally and may not match the stoichiometric coefficient. For elementary reactions, order = stoichiometric coefficient; for multi-step mechanisms, order depends on the rate-limiting step.
How does temperature affect reaction rate?
Exponentially. The Arrhenius equation gives k = A·exp(−E_a/(RT)). For E_a = 50 kJ/mol at room temperature, a 10°C increase doubles the rate. For E_a = 100 kJ/mol, the factor is about 4. Strong temperature dependence (high E_a) means precise temperature control matters; weak dependence (low E_a) means less critical.
What's the difference between rate constant and rate?
Rate constant k is a material property depending on temperature but not on concentration. It characterizes the reaction's intrinsic speed. Rate is the actual rate at a given time, depending on both k and current concentration: rate = k·C^n. Rate changes as concentration changes during the reaction; rate constant stays fixed at constant temperature.
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