Introduction to Rate Law — AP Chemistry
1. Core Definition of a Rate Law ★★☆☆☆ ⏱ 2 min
A rate law (or rate equation) is a mathematical relationship that connects the instantaneous rate of a chemical reaction to the concentration of reactants (and rarely catalysts, which are not commonly tested in introductory problems).
A key AP-exam tested distinction: rate laws are *exclusively experimentally derived*. You cannot determine a rate law from the balanced reaction stoichiometry alone. This topic is the foundation of all kinetics, which makes up 7-9% of total AP Chemistry exam score, with rate law questions appearing regularly in both MCQ and FRQ sections.
2. Rate Law Structure and Reaction Order ★★☆☆☆ ⏱ 4 min
For a general overall reaction $aA + bB \rightarrow cC$, the general form of the rate law is:
\text{rate} = k [A]^m [B]^n
- $\text{rate}$ = instantaneous reaction rate, with units $\text{M} \cdot \text{time}^{-1}$ (most commonly $\text{M} \cdot \text{s}^{-1}$)
- $k$ = rate constant: a proportionality constant unique to the reaction at a specific temperature. $k$ does not change with reactant concentration, only with temperature or catalyst addition.
- $[A], [B]$ = molar concentrations of gaseous/aqueous reactants (pure solids/liquids are omitted, as their concentration is constant)
- $m, n$ = individual reaction orders with respect to $A$ and $B$, almost always 0, 1, or 2 on the AP exam. Overall reaction order is the sum $m + n$.
Reaction order describes how changing a reactant's concentration impacts overall rate: zero order means concentration change has no effect, first order means rate is directly proportional to concentration, second order means rate is proportional to the square of concentration. Critically, individual orders do not need to match the stoichiometric coefficients of the balanced overall reaction.
Exam tip: When asked for units of $k$, always match the time units given in the problem. The general formula for units of $k$ is $M^{-(\text{overall order} -1)} \text{time}^{-1}$.
3. Method of Initial Rates ★★★☆☆ ⏱ 5 min
The method of initial rates is the primary experimental technique tested on the AP exam to determine a rate law from raw experimental data. Initial rate is the instantaneous rate measured immediately after the reaction starts, before any significant change in reactant concentration occurs. Data is provided as a table of multiple reaction runs, each with different starting concentrations and a measured initial rate.
To find the order for a reactant, compare two runs where only that reactant's concentration changes, and all other concentrations are held constant, using the relationship:
\frac{\text{rate}_2}{\text{rate}_1} = \left( \frac{[A]_2}{[A]_1} \right)^m
On the AP exam, ratios almost always result in whole-number orders that can be solved by inspection, no logarithms required. Once all orders are found, substitute data from any run to calculate $k$, then write the final rate law.
Exam tip: Always verify your $k$ value by checking with data from another run. A consistent $k$ (within rounding) confirms your reaction orders are correct.
4. Zero-Order Rate Laws ★★★☆☆ ⏱ 3 min
A zero-order reaction with respect to a reactant means changing that reactant's concentration has no effect on the overall reaction rate. This is most common for saturated enzyme-catalyzed reactions and heterogeneous reactions catalyzed on solid surfaces.
Since any value raised to the power of zero equals 1, a zero-order reactant is omitted from the final rate law expression. If all reactants are zero order, the rate is simply equal to $k$, so rate is constant regardless of concentration.
Exam tip: If changing a reactant's concentration leaves rate unchanged, immediately assign order 0 and omit it from the final rate law, unless explicitly asked to write the full general form.
Common Pitfalls
Why: Students assume coefficients translate directly to exponents, as they do for equilibrium constants and elementary reactions, so they skip the experimental ratio step.
Why: Mixing up which run is which when comparing leads to incorrect order calculations.
Why: Units of $k$ change with overall reaction order and depend on the time unit given in the problem.
Why: Students remember to omit these from equilibrium expressions but forget the same rule applies to rate laws, as their concentration is constant.
Why: Students learn $k$ is constant for a set of initial rate experiments, so incorrectly extend this to all conditions.