2.1 Rate of Reaction and Its Measurement

The rate of reaction expresses how fast concentrations change per unit time. It is always reported as a positive quantity. The average rate over an interval $\Delta t$ is $-\Delta[A]/\Delta t$; the instantaneous rate is the slope of the $[A]$ vs $t$ curve at a specific point. Stoichiometric coefficients must be used when expressing the rate in terms of different species to obtain a single, unambiguous rate for the reaction.

NEET focus: Reading graphs of concentration vs time to identify instantaneous rate by drawing a tangent.

2.2 Factors Affecting Rate

2.3 Rate Law and Rate Constant

Rate law $= k[A]^m[B]^n$ is always experimentally determined. The rate constant $k$ depends only on temperature (via Arrhenius); changing concentration does not change $k$. Units of $k$ are derived from the requirement that $\text{rate} = k[\text{concentration}]^n$, giving units $(mol\,L^{-1})^{1-n}\,s^{-1}$.

2.4 Integrated Rate Laws

Zero order: $[A] = [A]_0 - kt$; linear $[A]$ vs $t$ plot.

First order: $\ln[A] = \ln[A]_0 - kt$; linear $\ln[A]$ vs $t$ plot; $t_{1/2} = 0.693/k$.

Second order: $1/[A] = 1/[A]_0 + kt$; linear $1/[A]$ vs $t$ plot; $t_{1/2} = 1/(k[A]_0)$.

NEET graph questions typically ask you to identify the order from the shape of the linear plot.

2.5 Half-Life Comparisons

The key NEET fact: first-order $t_{1/2}$ is concentration-independent, making it unique and directly calculable from $k$ alone. Zero-order $t_{1/2}$ is directly proportional to $[A]_0$; second-order $t_{1/2}$ is inversely proportional to $[A]_0$.

2.6 Pseudo First-Order Reactions

Any bimolecular reaction can behave as first-order if one reactant is in large excess. This is important for reactions in aqueous solution (water is the solvent and its concentration barely changes). The experimentally measured $k'$ (pseudo rate constant) equals $k[\text{excess reactant}]$.

2.7 Arrhenius Equation and Activation Energy

The Arrhenius equation connects $k$ to temperature and $E_a$. The slope of an $\ln k$ vs $1/T$ graph $= -E_a/R$, so $E_a = -\text{slope} \times R$. The two-temperature form is used in numerical problems. Temperature must always be in Kelvin.

2.8 Energy Profile and Catalysis

The energy profile shows reactants, transition state (energy maximum), and products. The height of the barrier from reactants to the transition state is $E_a(\text{forward})$; from products it is $E_a(\text{backward})$. Their difference equals $\Delta H$. A catalyst lowers both barriers by the same amount; the energy difference $\Delta H$ is unchanged.

2.9 Order vs Molecularity (Conceptual)

This subtopic is a perennial NEET conceptual question. Remember: molecularity can never be zero or fractional; order can. Molecularity is a property of an elementary step; overall reaction order is derived from experiment or from the mechanism's rate-determining step.