Chemical kinetics

Rate and rate law

Reaction rate = change in concentration per unit time. Instantaneous rate is the tangent to a concentration–time curve.

Rate law = k[A]^m[B]^n where m, n are orders determined experimentally — not always equal to stoichiometric coefficients. Overall order = m + n.

Molecularity is for elementary steps only (number of molecules colliding in one step). A balanced equation can hide a multi-step mechanism.

Integrated rate equations

Zero order: [A] = [A]₀ − kt. First order: ln[A] = ln[A]₀ − kt or k = (2.303/t) log([A]₀/[A]). Second order (simple): 1/[A] = 1/[A]₀ + kt when rate = k[A]².

Half-life: t½ = [A]₀/2k (zero); t½ = 0.693/k (first order — independent of [A]₀). Plot shape distinguishes orders: first order gives straight ln[A] vs t.

Arrhenius equation

k = A e^(−E_a/RT). ln k = ln A − E_a/RT. Plot ln k vs 1/T gives slope −E_a/R.

Activation energy E_a is the barrier; A is pre-exponential factor. Catalyst lowers E_a by offering an alternative path — more molecules have enough energy to react.

Collision theory

Rate ∝ frequency of effective collisions. Effective means sufficient energy (≥ E_a) and correct orientation for bimolecular steps.

Temperature increases rate mainly by increasing fraction of molecules with E ≥ E_a, not just collision frequency.