Physical · Chemical Kinetics

Chemical Kinetics

CSIR-NET Chemical Sciences revision note · 9 sections · about 612 words · free to read in full

Exam-focused revision notes on Chemical Kinetics for CSIR-NET Chemical Sciences, GATE Chemistry and IIT-JAM — the core concepts, the formulas worth memorising, the traps that cost marks, and a quick-recall table.

The core idea

Kinetics is about how fast a reaction goes and by what pathway — not whether it is thermodynamically favourable. Rate is measured as the change in concentration per unit time, and it depends on concentration through the rate law, which must be found experimentally.

Rate of reaction

For a A + b B → c C + d D, the unique rate is:

rate = −(1/a) d[A]/dt = −(1/b) d[B]/dt = +(1/c) d[C]/dt = +(1/d) d[D]/dt

Divide each rate by its stoichiometric coefficient so all species give the same rate value.

Rate law, order & molecularity

Rate law: rate = k[A]^m[B]ⁿ. The exponents m, n are the orders (found by experiment, not from the balanced equation).
Overall order = m + n.
Molecularity = number of species colliding in an elementary step; always a positive integer (1, 2, rarely 3).
Order can be zero, fractional or negative; molecularity cannot.
k = rate constant; its units depend on overall order.

Integrated rate laws

Zero order:

[A] = [A]₀ − kt t_½ = [A]₀ / 2k

First order:

ln[A] = ln[A]₀ − kt → [A] = [A]₀ e^−kt t_½ = 0.693 / k (constant)

Second order (single reactant, rate = k[A]²):

1/[A] = 1/[A]₀ + kt t_½ = 1 / (k[A]₀)

First-order half-life is independent of concentration — the signature of first-order (e.g. radioactive decay).

Arrhenius equation & activation energy

k = A e^−E_a/RT → ln k = ln A − E_a/(RT)

A = pre-exponential (frequency) factor; E_a = activation energy.
Plot ln k vs 1/T → straight line, slope = −E_a/R, intercept = ln A.
Two-temperature form: ln(k₂/k₁) = −(E_a/R)(1/T₂ − 1/T₁).

Effect of temperature & catalyst

Raising T increases the fraction of molecules with energy ≥ E_a → k rises (rule of thumb: rate roughly doubles per 10 K, though this is only approximate).
A catalyst provides an alternative pathway with lower E_a, speeding both forward and reverse reactions equally — it does not change ΔG or the position of equilibrium.

Rate-determining step (RDS)

In a multi-step mechanism, the slowest step controls the overall rate.
The observed rate law reflects the RDS (using pre-equilibria / the steady-state approximation to eliminate intermediates).
This is why order need not match stoichiometry — it mirrors the mechanism, not the overall equation.

⚠️ Common traps students miss

Order ≠ molecularity. Order is experimental for the overall reaction; molecularity applies only to an elementary step.
Never read the order off the balanced equation (only valid for a genuinely elementary reaction).
Units of k change with order — a common numeric slip. Zero: mol L⁻¹ s⁻¹; first: s⁻¹; second: L mol⁻¹ s⁻¹.
Only first-order t_½ is concentration-independent; zero- and second-order half-lives depend on [A]₀.
A catalyst lowers E_a but does not shift equilibrium or make a non-spontaneous reaction spontaneous.

30-second recall table

Order	Integrated law	t_½	Units of k
Zero	[A] = [A]₀ − kt	[A]₀ / 2k	mol L⁻¹ s⁻¹
First	ln[A] = ln[A]₀ − kt	0.693 / k	s⁻¹
Second	1/[A] = 1/[A]₀ + kt	1 / (k[A]₀)	L mol⁻¹ s⁻¹

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