Rate laws and orders - Chemistry AP Study Notes

Rate laws describe the mathematical relationship between reaction rate and reactant concentrations. The rate equation takes the form: rate = k[A]^m[B]^n, where k is the rate constant, [A] and [B] are reactant concentrations, and m and n are the orders of reaction with respect to each reactant.

Order of reaction indicates how the rate changes when a reactant's concentration changes. A zero-order reaction (m=0) means rate is independent of that reactant's concentration. A first-order reaction (m=1) means rate is directly proportional to concentration—doubling [A] doubles the rate. A second-order reaction (m=2) means rate is proportional to concentration squared—doubling [A] quadruples the rate.

The overall order is the sum of all individual orders (m+n). Important: orders must be determined experimentally, NOT from the balanced equation's stoichiometric coefficients.

The rate constant (k) has units that depend on overall order:

• Zero order: mol dm⁻³ s⁻¹
• First order: s⁻¹
• Second order: mol⁻¹ dm³ s⁻¹

Units calculation: Rearrange rate equation to k = rate/[A]^m[B]^n, then substitute units.

Key Cambridge Definition: "The rate equation shows the relationship between the rate of a chemical reaction and the concentrations of the reactants raised to appropriate powers."

Initial rates method: By comparing experiments where one reactant's concentration changes while others stay constant, we can deduce individual orders by examining how rate changes proportionally.

Think of rate laws like recipe sensitivity. Imagine baking where ingredients affect cooking speed differently. Sugar (zero-order) doesn't change baking time whether you use 100g or 200g—the oven temperature controls it. Yeast (first-order) directly affects rise time—double the yeast, halve the rising time. Baking powder (second-order) has exponential effects—double it, and reactions happen four times faster.

Real-world application: Pharmaceutical stability. Drug manufacturers use rate laws to determine shelf life. Aspirin hydrolysis follows first-order kinetics—knowing the rate constant allows calculation of expiry dates. Temperature affects k (via Arrhenius equation), explaining why medicines must be stored correctly.

Industrial catalysis: The Haber process (N₂ + 3H₂ → 2NH₃) operates at specific conditions because rate laws reveal which reactant concentrations most affect ammonia production. Engineers optimize [H₂] and [N₂] based on their reaction orders to maximize yield efficiently.

Environmental chemistry: Ozone depletion by CFCs follows complex rate laws. Understanding that some reactions are first-order in [CFC] but zero-order in [O₃] helps atmospheric scientists predict ozone layer recovery times after CFC bans.

Analogy for rate constant: k is like a speed multiplier in video games. Higher k means faster base reaction speed. Temperature increases k (molecules have more kinetic energy), just as power-ups increase game character speed. The orders (m, n) are like sensitivity settings—they determine HOW MUCH each reactant's concentration affects the overall rate.