Physical chemistry
Reaction rate, reaction order
Measuring how fast concentrations change, and how the empirical order of a reaction is read from its concentration–time behaviour.
IntuitionIntuition: counting how fast molecules disappear
Chemistry is invisible, but its pace is not: a glowing splint flares in oxygen, milk sours in days, and a cut apple browns in minutes. The reaction rate is simply a bookkeeping of how quickly concentrations change. Its dependence on the amounts present — the reaction order — turns out to be a fingerprint of the microscopic events producing the change.
SchoolSchool: rate, rate law, order
Definition: Rate and reaction order
The rate v of a reaction is the change of concentration per unit time, weighted by stoichiometric coefficient. The empirical rate law v = k[A]^m[B]^n defines orders m and n; the overall order m + n must be found experimentally and need not equal the stoichiometric coefficients. Order 0: rate independent of amount; order 1: proportional; order 2: quadratic.
Each order integrates to a signature curve. Zero order: [A] = [A]₀ − kt, a straight line ending at depletion. First order: [A] = [A]₀e^(−kt), an exponential with constant half-life t½ = ln 2/k. Second order: 1/[A] = 1/[A]₀ + kt, which falls hyperbolically and lingers longest at low concentration.
| Order | Integrated law | Linear plot | t½ |
|---|---|---|---|
| 0 | [A] = [A]₀ − kt | [A] vs t | [A]₀/2k |
| 1 | ln[A] = ln[A]₀ − kt | ln[A] vs t | ln 2/k |
| 2 | 1/[A] = 1/[A]₀ + kt | 1/[A] vs t | 1/(k[A]₀) |
Example: Identifying the order from data
For the decomposition of N₂O₅ at 318 K, the concentration drops from 0.50 to 0.25 mol L⁻¹ in the first 30 s, and from 0.25 to 0.125 mol L⁻¹ in the next 30 s. What is the order, and what is k?
Solution
Each half-life is 30 s regardless of starting concentration: this is the signature of first order, since only t½ = ln 2/k is concentration-independent. Then k = ln 2/30 ≈ 0.0231 s⁻¹.
UndergraduateUniversity: from collisions to rate laws
Collision theory counts encounters per unit volume and weights them by the Boltzmann factor for crossing the activation barrier: only collisions with enough energy along the reactive coordinate succeed, and geometry further reduces the odds through a steric factor. For an elementary step the rate law mirrors molecularity — a bimolecular elementary step gives v = k[A][B] — but for an overall reaction this is only a starting hypothesis.
The initial-rates method is the workhorse for finding orders: repeat the experiment changing one concentration at a time; the way the initial rate responds (unchanged, doubled, quadrupled when the concentration doubles) gives each order directly. The isolation method achieves the same by flooding the mixture with all reagents but one, so only one concentration changes appreciably (pseudo-first-order kinetics).
Example: Doubling experiments
For A + B → products, doubling [A] at fixed [B] doubles the initial rate; doubling [B] at fixed [A] leaves the rate unchanged; doubling both doubles the rate. Write the rate law and the overall order.
Solution
Rate ∝ [A]¹[B]⁰ = k[A]: first order in A, zero order in B, overall order 1. The independence from [B] tells us B is not involved in (or is far in excess around) the rate-determining events.
AdvancedAdvanced: what a rate law hides
A measured order is evidence, not proof, of mechanism. Fractional orders hint at equilibria preceding the slow step or dissociation of a reagent; inhibition terms like v = k[A]/(1 + K[B]) signal competition for a surface or an intermediate sink. The same overall stoichiometry can also correspond to very different microscopic routes — gas-phase H₂ + I₂ was long believed bimolecular but actually proceeds through a complex mechanism.
References
- Chemical Kinetics · K. J. Laidler, 1987