What you'll be able to do: Determine reaction orders and the rate constant from initial-rate data, and state the correct units of k.
Best after: Reaction Rates and How They Are Measured
A rate law is an experimental fact, not something you can read off a balanced equation. The method of initial rates finds it by changing one concentration at a time and watching what the rate does.
These are recommended, not required. You can start this lesson at any time.
A rate law states how the instantaneous rate depends on concentrations at that moment. The exponents are the reaction orders, and they are found by experiment. They are frequently whole numbers, but fractional and negative orders exist.
rate = k[A]ᵐ[B]ⁿ
For 2 N₂O₅ → 4 NO₂ + O₂ the rate law is first order in N₂O₅, not second order, even though the coefficient is 2. Coefficients describe the overall stoichiometry; orders describe the slowest step of the mechanism, which the overall equation hides.
Find two experiments in which one concentration changes and all others are held constant. Take the ratio of the rates and the ratio of the concentrations. The order is the exponent that connects them: if the concentration ratio is 2 and the rate ratio is 4, then 2ᵐ = 4 and m = 2.
rate2/rate1 = ([A]2/[A]1)ᵐ
Doubling a concentration and finding no rate change means zero order in that species. Double the rate means first order. Four times the rate means second order. Tripling a concentration and getting nine times the rate is also second order.
Substitute one full set of experimental data into the rate law and solve for k. The units follow from the overall order: zero order M/s, first order 1/s, second order 1/(M s), third order 1/(M² s). Quoting k without units is an incomplete answer.
units of k = M¹ - overall order) s⁻¹
An experimentally determined equation giving rate as a function of concentrations.
The exponent on a concentration term in the rate law.
The sum of the individual orders, which sets the units of the rate constant.
Compare experiments in which only one concentration differs, otherwise two effects are mixed together.
The rate constant is constant only at fixed temperature; raising the temperature raises k.
rate = k[A]ᵐ[B]ⁿ
m = ln(rate2/rate1) / ln([A]2/[A]1)
For A + B → C: Exp 1, [A] = 0.10, [B] = 0.10, rate = 2.0 × 10⁻³ M/s. Exp 2, [A] = 0.20, [B] = 0.10, rate = 4.0 × 10⁻³ M/s. Exp 3, [A] = 0.10, [B] = 0.20, rate = 8.0 × 10⁻³ M/s. Find the rate law and k.
Try it first: Pick the pair of experiments where only [A] changes, then the pair where only [B] changes.
0 of 4 steps revealed.
Doubling [X] leaves the rate unchanged. What is the order in X, and what does that mean physically?
0 of 2 steps revealed.
A reaction has rate law rate = k[A]². The rate is 0.024 M/s when [A] = 0.20 M. Find k and predict the rate at [A] = 0.50 M.
0 of 2 steps revealed.
Why it's wrong: Overall stoichiometry says nothing about the slowest step, which is what controls the rate.
Check instead: Determine every order from experimental data unless the equation is stated to be a single elementary step.
Why it's wrong: The units of k depend on the overall order, so a bare number is ambiguous.
Check instead: Use M¹ - overall order) s⁻¹ and state it every time.
Why it's wrong: The two effects are combined, so neither order can be isolated.
Check instead: Choose a pair with exactly one concentration different, or handle the algebra with logarithms.
Why it's wrong: k depends on temperature and catalyst only, not on how much reactant is left.
Check instead: Attribute the slowing rate to the falling concentration term.
No practice questions are available for this topic yet. You can still practice the whole unit.
The rate law rate = k[A]ᵐ[B]ⁿ links rate to concentration through orders that must be measured. Comparing two experiments in which only one concentration changes isolates that order: doubling a concentration doubles the rate for first order, quadruples it for second order and leaves it unchanged for zero order. The overall order is the sum of the individual orders, and it fixes the units of k, which are M¹⁻overall order) per second.
Chemistry 2e, OpenStax, Rice University, licensed CC BY 4.0. License