Chemical Kinetics

Concept overview

Chemical kinetics studies reaction rates and how they depend on concentration, temperature and catalyst. The rate law for a reaction is an empirical expression of the form rate = k[A]^m[B]^n, where m and n are the orders with respect to A and B — determined by experiment, not by stoichiometry. The overall order is m + n.

The most-tested case is the first-order reaction, for which rate = k[A], and the integrated law gives [A] = [A]₀ e^(−kt), or equivalently ln([A]₀/[A]) = kt. First-order half-life is independent of concentration: t_½ = 0.693/k. This is why radioactive decay and many biological processes have well-defined half-lives.

The Arrhenius equation k = A e^(−E_a/RT) captures temperature dependence. Taking logs: ln k = ln A − E_a/(RT), which is a linear plot of ln k versus 1/T with slope −E_a/R. The magnitude of E_a determines how sensitive the rate is to temperature; a rule of thumb — often tested in JEE — is that rate roughly doubles for every 10 K increase near room temperature, corresponding to E_a in the range 50–100 kJ/mol.

Molecularity refers to how many species collide in a single elementary step and is always a small positive integer; order is empirical and can be zero or fractional. Confusing these two is the single most common JEE mistake.

Key formulas & concepts

• Rate law: rate = k [A]^m [B]^n (m, n determined experimentally)
• First-order integrated: ln([A]₀/[A]) = kt
• First-order half-life: t_½ = 0.693 / k (independent of [A]₀)
• Second-order integrated: 1/[A] − 1/[A]₀ = kt
• Zero-order integrated: [A]₀ − [A] = kt
• Arrhenius: k = A e^(−E_a/RT)
• Arrhenius ln form: ln(k₂/k₁) = (E_a/R)(1/T₁ − 1/T₂)

Common mistakes to avoid

• Assuming the order equals the stoichiometric coefficient — order is experimental; molecularity matches stoichiometry only for elementary steps.
• Computing k in the wrong units — first-order k is s⁻¹, second-order is L/(mol·s), zero-order is mol/(L·s).
• Using the temperature ratio T₂/T₁ instead of 1/T₁ − 1/T₂ in Arrhenius.
• Forgetting that catalysts change E_a but not ΔH — so both forward and reverse rates increase equally.

JEE Main relevance

JEE Main asks 2 kinetics problems every paper: one integrated-rate-law or half-life numerical, and one Arrhenius-equation problem comparing rates at two temperatures. The chapter has 4 clean archetypes and no more.

JEE Advanced relevance

Advanced kinetics problems combine order determination from data — given a table of concentrations versus time, decide whether the reaction is 0, 1st or 2nd order — with Arrhenius temperature dependence, sometimes further linked to thermodynamics via the pre-exponential factor A. Pseudo-first-order approximations (like acid hydrolysis of an ester with water in large excess) are also standard Advanced patterns.

Previous-year questions (PYQ)

The PYQ bank has ~890 kinetics-tagged problems. First-order half-life alone accounts for roughly a third of them — practise those in one focused session before moving to Arrhenius.