Chemical Kinetics

Rate law expresses reaction rate in terms of concentrations:

Rate = k · [A]^m · [B]^n

Order of reaction = m + n. Determined experimentally — has nothing to do with stoichiometry.

Molecularity = number of molecules colliding in the rate-determining elementary step. Always a small integer (1, 2, rarely 3). Has to do with mechanism.

They differ for multi-step reactions. Example: 2N₂O₅ → 4NO₂ + O₂ is overall first order (rate = k[N₂O₅]) even though stoichiometry suggests bimolecular.

Integrated rate equations:

Zero order: [A] = [A]₀ − kt. Half-life: t₁/₂ = [A]₀ / (2k).

First order: ln[A] = ln[A]₀ − kt, or [A] = [A]₀ · e^(−kt). Half-life: t₁/₂ = 0.693 / k. Independent of [A]₀ — this is the hallmark of first-order.

Second order (rate = k[A]²): 1/[A] − 1/[A]₀ = kt. Half-life: t₁/₂ = 1 / (k[A]₀).

Identifying order from half-life data:

• t₁/₂ constant as concentration drops → first order
• t₁/₂ doubles as concentration halves → second order
• t₁/₂ halves as concentration halves → zero order

Arrhenius equation: k = A · e^(−Ea/RT). Taking log: ln k = ln A − Ea/(RT). A plot of ln k vs 1/T is a straight line with slope −Ea/R.

Worked example. A first-order reaction has k = 0.1 min⁻¹. How long for 75% to react?

[A]/[A]₀ = 0.25. Using ln(0.25) = −kt: −1.386 = −0.1 · t → t = 13.86 min.