Rate Law Formula
The rate law formula rate = k[A]^n describes how reactant concentration affects reaction speed.
Learn chemical kinetics with examples.
The Formula
The rate law describes how the speed of a chemical reaction depends on the concentrations of the reactants. Each reactant's concentration is raised to a power called the order of the reaction with respect to that reactant.
The rate constant k is specific to each reaction and depends on temperature. Unlike equilibrium expressions, rate law exponents are NOT determined from the balanced equation — they must be found experimentally.
The overall reaction order is the sum of all the individual exponents (m + n). This determines how the rate changes when all concentrations are scaled equally.
Variables
| Symbol | Meaning |
|---|---|
| Rate | Reaction rate (measured in mol/(L·s) or M/s) |
| k | Rate constant (units depend on overall reaction order) |
| [A], [B] | Molar concentrations of reactants (mol/L) |
| m, n | Reaction orders with respect to each reactant (determined experimentally) |
Common Reaction Orders
- Zero order (n = 0): Rate = k — rate is independent of concentration
- First order (n = 1): Rate = k[A] — rate doubles when concentration doubles
- Second order (n = 2): Rate = k[A]² — rate quadruples when concentration doubles
Example 1
For the reaction 2NO + O₂ → 2NO₂, experiments show: when [NO] doubles (with [O₂] constant), the rate quadruples. When [O₂] doubles (with [NO] constant), the rate doubles. If k = 7,100 M⁻²s⁻¹, [NO] = 0.020 M, and [O₂] = 0.010 M, what is the rate?
From the data: rate quadruples when [NO] doubles → order = 2 for NO
Rate doubles when [O₂] doubles → order = 1 for O₂
Rate law: Rate = k[NO]²[O₂]
Rate = 7,100 × (0.020)² × 0.010
Rate = 7,100 × 4.0 × 10⁻⁴ × 0.010 = 7,100 × 4.0 × 10⁻⁶
Rate = 2.84 × 10⁻² M/s
Example 2
A first-order reaction has a rate constant of k = 0.045 s⁻¹. If the initial concentration of reactant A is 0.80 M, what is the initial rate?
For a first-order reaction: Rate = k[A]
Rate = 0.045 × 0.80
Rate = 0.036 M/s
When to Use It
Use the rate law to analyze and predict reaction speeds.
- Determining how fast a reaction proceeds under given conditions
- Predicting how concentration changes affect reaction speed
- Designing industrial processes for optimal reaction rates
- Calculating the rate constant from experimental data
- Understanding enzyme kinetics and drug metabolism rates