How to find the rate law from experimental data

You need experimental data consisting of at least two trials for each reactant, where the concentration of one reactant changes while all others remain constant. The general rate law is written as $ext{Rate} = k[A]^m[B]^n\dots$, where the orders $m, n, \dots$ must be determined experimentally.

1. Select two trials where the concentration of one reactant changes while the concentrations of all other reactants are held constant.
2. Set up a ratio of the rate laws for these two trials: $\frac{ ext{Rate}_2}{ ext{Rate}_1} = \frac{k[A]_2^m[B]_2^n}{k[A]_1^m[B]_1^n}$.
3. Cancel the rate constant $k$ and the constant concentration terms.
4. Solve the resulting equation for the exponent (the reaction order) of the varied reactant. Often this can be done by inspection; otherwise, use logarithms.
5. Repeat steps 1-4 for each remaining reactant.
6. Write the final rate law using the determined orders.
7. To find the rate constant $k$, substitute the concentrations and rate from any single trial into the complete rate law and solve for $k$.

To verify the rate law and the value of $k$, plug the reactant concentrations from a different trial into the calculated rate law. The computed rate should match the experimental rate for that trial within experimental error.

• Assuming reaction orders match stoichiometric coefficients from the balanced equation. Orders must be found experimentally.
• Forgetting to include units for the rate constant $k$. The units of $k$ depend on the overall reaction order.
• Selecting two trials where multiple concentrations change simultaneously, making it impossible to isolate the effect of a single reactant.