Rate Laws
If reaction rate is the speedometer, the rate law is the owner’s manual that explains what controls the speed. The rate law is a mathematical equation that relates the reaction rate to the concentrations of the reactants. It is the single most important equation in this chapter.
The Rate Constant (k)
The rate constant k is a proportionality constant that is specific to a particular reaction at a particular temperature. A larger k means a faster reaction. Two key facts about k:
- k changes with temperature. Increase the temperature and k increases (the reaction gets faster). This relationship is described by the Arrhenius equation, which we cover in Section 5.7.
- k does not change with concentration. For a given reaction at a fixed temperature, k is truly constant regardless of how much reactant you add.
Reaction Orders
The exponents x and y in the rate law are called the reaction orders. They tell you how sensitive the rate is to changes in each reactant’s concentration.
- Order 0: Rate is independent of that reactant’s concentration. Doubling [A] has no effect on rate.
- Order 1: Rate is directly proportional to concentration. Double [A], double the rate.
- Order 2: Rate is proportional to the square of concentration. Double [A], quadruple the rate.
The overall reaction order is the sum of all individual orders. For rate = k[A]²[B]¹, the overall order is 2 + 1 = 3 (third-order overall).
Two Exceptions Where Orders Match Coefficients
There are exactly two situations where the orders in the rate law match the stoichiometric coefficients:
- The reaction occurs in a single elementary step. If the balanced equation represents the actual molecular event, then the coefficients are the orders.
- You are given the mechanism and told which step is rate-determining. The coefficients of the reactants in the slow step become the orders.
In every other case, the rate law must be determined experimentally.
Rate Law vs. Equilibrium Expression
This is one of the most common traps on the MCAT. The rate law and the equilibrium expression look similar but mean completely different things.
| Rate Law | Equilibrium Expression | |
|---|---|---|
| Includes | Reactants only | Both reactants AND products |
| Exponents from | Experiment (or mechanism) | Balanced equation coefficients |
| Tells you | How fast the reaction goes | Where the reaction ends up |
| Symbol | k (rate constant) | Keq (equilibrium constant) |
Units of k
The units of k depend on the overall reaction order. This is because the rate always has units of M/s, so k must have whatever units are needed to make the math work.
| Overall Order | Rate Law | Units of k |
|---|---|---|
| 0 | rate = k | M/s (or M·s⁻¹) |
| 1 | rate = k[A] | s⁻¹ |
| 2 | rate = k[A]² | M⁻¹·s⁻¹ |
| 3 | rate = k[A]²[B] | M⁻²·s⁻¹ |