Chemical Kinetics for JEE: Rate Laws, Order, and Half-Life Complete Guide

Order is determined experimentally from rate law and can be zero, fractional, or negative. Molecularity is the number of molecules in the elementary step and is always a whole number. Molecularity ≥ 1, while order can be any value.

Use the initial rates method: compare rates at different initial concentrations. If doubling [A] doubles rate, it is first order in A. If doubling [A] quadruples rate, it is second order in A.

The half-life of a first-order reaction is t½ = 0.693/k. It is independent of initial concentration. This means it takes the same time to go from 1M to 0.5M as from 0.5M to 0.25M.

The Arrhenius equation k = Ae^(-Ea/RT) relates rate constant to temperature and activation energy. It is used to: (1) calculate Ea from rate constants at two temperatures, (2) predict rate at different temperatures, (3) understand catalysts (lower Ea, higher rate).

Units of k depend on order: Zero order: mol L⁻¹ s⁻¹. First order: s⁻¹. Second order: L mol⁻¹ s⁻¹. General formula: (mol L⁻¹)^(1-n) s⁻¹ where n is order.

Plot concentration vs time graphs: if [A] vs t is linear → zero order. If ln[A] vs t is linear → first order. If 1/[A] vs t is linear → second order. The straight-line plot determines the order.

Rate depends on concentration: Rate = k[A]^n. Rate constant k is independent of concentration but depends on temperature, catalyst, and nature of reaction. Rate changes with time, k is constant at constant temperature.

Rate approximately doubles for every 10°C rise in temperature. This is due to the Arrhenius equation: k = Ae^(-Ea/RT). More molecules cross the activation energy barrier at higher temperature.

Activation energy (Ea) is the minimum energy required for a reaction to occur. It is the energy barrier between reactants and products. A catalyst lowers Ea, increasing the rate without being consumed.

A reaction that is second order overall but appears first order because one reactant is in large excess. Example: hydrolysis of ester in excess water: CH₃COOC₂H₅ + H₂O → CH₃COOH + C₂H₅OH. Water concentration is effectively constant.

A catalyst provides an alternative pathway with lower activation energy. This increases the rate constant k (and hence rate) without changing the equilibrium position or ΔG of the reaction.

Molecularity is the number of molecules that collide in an elementary step. It is always a whole number (1, 2, 3). Unimolecular: one molecule. Bimolecular: two molecules. Termolecular: three molecules (rare).

The Arrhenius factor A represents the frequency of collisions with correct orientation. It has the same units as k and depends on the frequency factor and steric factor (orientation probability).

In consecutive reactions A → B → C, the intermediate B reaches a maximum concentration then decreases. The slowest step is the rate-determining step. The overall rate is governed by the slowest step.