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 a multistep reaction, the experimentally measured orders reflect the mechanism as a whole. A slow step can help explain the rate, but its reactant coefficients alone do not always give the observed overall rate law, especially when earlier equilibria or intermediates are involved. Only for a single elementary step can its reactant coefficients be used directly as exponents in that step’s rate expression.
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
In rate = k[A]ᵐ[B]ⁿ, changing A by a factor f multiplies the rate by fᵐ; changing B by g multiplies it by gⁿ. A zero-order reactant still participates in the overall reaction but its concentration does not affect the measured rate in the observed regime. Combine independent factors only after applying each exponent.
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.
For rate = k[A]²[B]⁰, [A] is halved while [B] is doubled. What happens to rate?
Try it first: Calculate a factor for each concentration separately.
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Why it's wrong: The overall equation gives net stoichiometry, not the sequence of elementary steps. For a multistep mechanism, measured orders can depend on several steps and intermediates.
Check instead: Determine orders from initial-rate data unless the prompt explicitly identifies a single elementary step; then compare the proposed mechanism with the measured rate law.
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: At fixed temperature and reaction medium, k does not change just because reactant concentrations fall. Changing temperature, solvent or medium, or catalyst can change the observed rate constant.
Check instead: Hold temperature, solvent or medium, and catalyst conditions fixed when treating k as constant.
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The rate law rate = k[A]ᵐ[B]ⁿ relates rate to concentrations through orders established experimentally. Comparing experiments where only one concentration changes isolates that order. For multistep reactions, the observed orders reflect the mechanism as a whole; only an elementary step lets you read exponents directly from its reactant coefficients. Overall order sets the units of k. At fixed reaction conditions, k stays constant as concentrations change.
Chemistry 2e, OpenStax, Rice University, licensed CC BY 4.0. License