The rate law calculator determines reaction order (0, 1, or 2) and rate constant k from experimental concentration vs time data. It fits data to all three integrated rate laws, calculates R² for each, and identifies the best fit with a Chart.js scatter plot.
Concentration vs Time Data
| Time (s) | [A] (M) |
|---|
Reaction Order Determination
| Plot | R² | Order |
|---|---|---|
| [A] vs t | — | Zero |
| ln[A] vs t | — | First |
| 1/[A] vs t | — | Second |
Best-Fit Plot
How to Use the Rate Law Calculator
The rate law calculator analyzes concentration vs time data to determine reaction order and rate constant k. It's the standard method used in physical chemistry labs to characterize kinetics.
Step 1: Enter Data Points
Enter time (in seconds) and corresponding concentration [A] (in mol/L) measurements. You need at least 3 data points; 5-8 gives better accuracy. The N₂O₅ preset loads a classic first-order decomposition example.
Step 2: Interpret the R² Values
The calculator plots data three ways: [A] vs t (zero order), ln[A] vs t (first order), and 1/[A] vs t (second order). The linearization with the highest R² identifies the reaction order. R² ≥ 0.99 indicates excellent agreement.
Step 3: Read the Results
The rate constant k equals the slope magnitude of the best-fit line. Units are: M/s (zero order), s⁻¹ (first order), M⁻¹·s⁻¹ (second order). The half-life is calculated from the order-specific formula.
Worked Example: N₂O₅ Decomposition
N₂O₅ decomposes as 2N₂O₅ → 4NO₂ + O₂. At 65°C, typical data: t=0, [A]=0.100 M; t=200s, [A]=0.0775 M; t=400s, [A]=0.0600 M; t=600s, [A]=0.0465 M; t=800s, [A]=0.0360 M. Plotting ln[A] vs t gives R²=0.999, confirming first order. Slope = -k ≈ -0.00139 s⁻¹, so t½ = 0.693/0.00139 ≈ 499 s ≈ 8.3 minutes.
Common Applications
Reaction kinetics are used in pharmaceuticals (drug degradation rates), food science (shelf life modeling), environmental chemistry (pollutant decay), and chemical engineering (reactor design). First-order kinetics apply to radioactive decay, many biological processes, and simple decomposition reactions. Second-order kinetics appear in bimolecular reactions where two molecules collide.
FAQ
How do you determine reaction order from concentration-time data?
Plot three graphs: [A] vs t (zero order), ln[A] vs t (first order), and 1/[A] vs t (second order). The plot that gives the best straight line (highest R²) indicates the reaction order. The slope of the best-fit line gives the rate constant k.
What are the integrated rate laws?
Zero order: [A] = [A]₀ - kt. First order: ln[A] = ln[A]₀ - kt (or [A] = [A]₀e^(-kt)). Second order: 1/[A] = 1/[A]₀ + kt. The integrated rate law lets you calculate concentration at any time, or find when a specific concentration is reached.
How is half-life related to reaction order?
Half-life depends on reaction order: Zero order: t½ = [A]₀/2k (depends on initial concentration). First order: t½ = ln(2)/k ≈ 0.693/k (constant, independent of concentration). Second order: t½ = 1/(k[A]₀) (depends on initial concentration).
What is the rate constant k?
The rate constant k determines how fast a reaction proceeds at a given temperature. Units depend on reaction order: k for zero order = M/s, first order = 1/s (or s⁻¹), second order = 1/(M·s) or L/(mol·s). Higher k means faster reaction.
Is this rate law calculator free?
Yes, completely free with no signup required. All calculations and plots run in your browser.
What is R-squared and why does it matter?
R² (coefficient of determination) measures how well the data fits a straight line. R² = 1 means perfect linear fit. For rate law determination, the order with R² closest to 1 is the best fit. R² > 0.99 indicates excellent linearity and confident order determination.
What is the N₂O₅ decomposition example?
The decomposition of N₂O₅ (dinitrogen pentoxide) is a classic first-order reaction: 2N₂O₅ → 4NO₂ + O₂. The concentration decreases exponentially, giving a straight line when ln[N₂O₅] is plotted vs time. The rate constant k ≈ 0.00139 s⁻¹ at 65°C.