Chemical Kinetics

2.1 Core concepts

• Rate of a reaction is the change in concentration of a reactant or product in unit time; expressed as −Δ[R]/Δt (disappearance of reactant) or +Δ[P]/Δt (appearance of product); the negative sign keeps the rate positive (NCERT §3.1, p. 62).
• The units of rate are concentration·time⁻¹ — typically mol L⁻¹ s⁻¹; for gaseous reactions, when concentration is expressed as partial pressure, the units become atm s⁻¹ (NCERT §3.1, p. 63).
• Average rate = Δ[R]/Δt over a finite time interval; instantaneous rate = −d[R]/dt = d[P]/dt at a specific instant, obtained graphically as the slope of the tangent to a concentration-vs-time curve (NCERT §3.1, p. 64).
• For a reaction with unequal stoichiometric coefficients (e.g. 2HI → H₂ + I₂), the rate is the rate of disappearance/appearance divided by the stoichiometric coefficient: Rate = −(1/2)·Δ[HI]/Δt = Δ[H₂]/Δt = Δ[I₂]/Δt (NCERT §3.1, p. 65).
• The rate of a reaction depends on the experimental conditions — concentration of reactants (pressure for gases), temperature and catalyst (NCERT §3.2, p. 66).
• The rate law (or rate expression) relates rate to molar concentrations of reactants, each raised to some power: Rate = k[A]^x [B]^y. The exponents x and y are determined experimentally and may or may not equal the stoichiometric coefficients (NCERT §3.2.2, p. 67).
• The rate constant (k) is the proportionality constant in the rate law; it is independent of concentration but depends on temperature and the presence of a catalyst (NCERT §3.2.2, p. 67).
• Order of a reaction = sum of the powers of concentration terms in the experimentally determined rate law; can be 0, 1, 2, 3 or a fraction; a zero-order reaction has a rate independent of reactant concentration (NCERT §3.2.3, p. 68).
• Units of k depend on order: zero order → mol L⁻¹ s⁻¹; first order → s⁻¹; second order → mol⁻¹ L s⁻¹ (NCERT Table 3.3, p. 69).
• Molecularity = number of reacting species that must collide simultaneously in an elementary reaction; can be 1 (unimolecular), 2 (bimolecular) or 3 (termolecular, very rare); cannot be zero or fractional; defined only for elementary reactions (NCERT §3.2.4, p. 69–70).
• For a complex reaction the rate-determining step is the slowest step; order of the overall reaction equals molecularity of this slowest step (NCERT §3.2.4, p. 70–71).
• Integrated rate equation, zero order: [R] = −kt + [R]₀, so k = ([R]₀ − [R])/t; plot of [R] vs t is a straight line of slope −k; half-life t₁/₂ = [R]₀/2k (depends on initial concentration). Examples: decomposition of NH₃ on hot Pt, thermal decomposition of HI on gold (NCERT §3.3.1, p. 71–72).
• Integrated rate equation, first order: ln[R] = −kt + ln[R]₀, or k = (2.303/t)·log([R]₀/[R]); plot of ln[R] vs t (or log[R]₀/[R] vs t with slope k/2.303) is a straight line; half-life t₁/₂ = 0.693/k (independent of [R]₀). Examples: hydrogenation of ethene, all radioactive decay, decomposition of N₂O₅ and N₂O (NCERT §3.3.2 & 3.3.3, p. 72–77).
• For a first-order gas-phase reaction A(g) → B(g) + C(g): k = (2.303/t)·log[p_i/(2p_i − p_t)], where p_i is initial pressure of A and p_t is total pressure at time t (NCERT §3.3.2, p. 74–75).
• Pseudo first-order reactions are higher-order reactions which appear first order because one reactant is in large excess and its concentration is effectively constant — e.g. acid hydrolysis of ethyl acetate, inversion of cane sugar (NCERT §3.3.3, p. 78).
• Temperature dependence: rate constant nearly doubles for every 10 K rise in temperature; quantified by the Arrhenius equation k = A·e^(−Ea/RT) where A is the frequency/pre-exponential factor, Ea is activation energy and R is the gas constant (NCERT §3.4, p. 78–79).
• The activated complex is the unstable high-energy intermediate; Ea is the energy required to form it from reactants. A plot of ln k vs 1/T is a straight line of slope −Ea/R and intercept ln A (NCERT §3.4, p. 79–80).
• The two-temperature form: log(k₂/k₁) = (Ea/2.303R)·[(T₂ − T₁)/(T₁T₂)] — used to find Ea from rate constants at two temperatures (NCERT eq. 3.22, p. 81).
• Maxwell–Boltzmann distribution: the fraction of molecules with energy E plotted against E peaks at the most probable kinetic energy; raising temperature shifts the peak to higher energy and broadens the curve, doubling the fraction of molecules with E ≥ Ea for a 10 K rise (NCERT §3.4, p. 79–80, Fig. 3.8 & 3.9).
• Catalyst increases the rate without itself being consumed; it provides an alternate path with lower activation energy. A catalyst does not change ΔG, does not catalyse non-spontaneous reactions and does not alter the equilibrium constant — it only helps equilibrium be reached faster (NCERT §3.4.1, p. 82).
• Collision theory treats molecules as hard spheres reacting on collision; the collision frequency Z is the number of collisions per second per unit volume; Rate = Z_AB·e^(−Ea/RT) (NCERT §3.5, p. 82–83).
• Not all collisions yield products — only effective collisions with sufficient kinetic energy (≥ threshold energy) and proper orientation succeed. The steric (probability) factor P accounts for orientation, giving Rate = P·Z_AB·e^(−Ea/RT) (NCERT §3.5, p. 83).
• Threshold energy = Activation energy + energy possessed by reacting species (NCERT footnote, p. 83).

2.2 Definitions to memorise

2.3 Diagrams / processes to remember

• Fig. 3.1 (p. 63): Concentration of R and P vs time — slope of secant = average rate; slope of tangent = instantaneous rate.
• Fig. 3.2 (p. 64): Instantaneous rate of hydrolysis of butyl chloride C₄H₉Cl, obtained by drawing the tangent at t = 600 s.
• Fig. 3.3 (p. 72): [R] vs t straight line for a zero-order reaction; slope = −k, intercept = [R]₀.
• Fig. 3.4 (p. 74): ln[R] vs t for first-order reaction; straight line, slope = −k.
• Fig. 3.5 (p. 74): log([R]₀/[R]) vs t; slope = k/2.303.
• Fig. 3.6–3.7 (p. 79): Formation of HI via an intermediate; potential energy vs reaction coordinate showing reactants → activated complex (peak, Ea) → products.
• Fig. 3.8 (p. 79): Maxwell–Boltzmann distribution — fraction of molecules vs kinetic energy, peak at most probable energy.
• Fig. 3.9 (p. 80): Distribution at T and T + 10 K — curve shifts right and broadens; the area beyond Ea (fraction of energetic molecules) roughly doubles.
• Fig. 3.10 (p. 80): ln k vs 1/T straight-line plot — slope = −Ea/R, intercept = ln A.
• Fig. 3.11 (p. 82): Effect of a catalyst on the potential-energy profile — catalyst provides an alternative path with a lower energy barrier.
• Fig. 3.12 (p. 83): Orientation of colliding molecules — proper orientation leads to product, improper orientation only causes bounce-back.

2.4 Common confusions / NTA trap points

• Order vs molecularity. Order is experimental, can be 0 or fractional, defined for both elementary and complex reactions. Molecularity is theoretical, must be a positive integer (1–3), defined only for elementary reactions (NCERT p. 70).
• Rate vs rate constant. Rate depends on concentration and changes during a reaction; the rate constant k depends only on temperature (and catalyst) — not on concentration. NTA likes to phrase distractors that swap these.
• Half-life behaviour. For a zero-order reaction t₁/₂ ∝ [R]₀; for a first-order reaction t₁/₂ is independent of [R]₀. Students often reverse these (NCERT p. 76).
• Units of k. Zero order → mol L⁻¹ s⁻¹; first order → s⁻¹; second order → mol⁻¹ L s⁻¹. A favorite NTA question identifies order from the units of k (NCERT Table 3.3, p. 69).
• Catalyst does NOT change ΔG, K_eq, or the position of equilibrium. It lowers Ea (forward and backward equally) so equilibrium is reached faster, not shifted (NCERT p. 82).
• Threshold energy ≠ activation energy. Threshold energy = Ea + energy already with the molecules (NCERT footnote p. 83).
• Arrhenius factor A. A relates to collision frequency Z (not to Ea or temperature directly). Higher A or lower Ea both raise k.
• Temperature coefficient. For most reactions, rate (or k) becomes 2–3 times for every 10 K rise — NTA sometimes paraphrases this as "doubles per °C" which is wrong.
• Pseudo first order. The reactant in large excess behaves as a constant; the apparent k is k′ = k[excess]. Inversion of cane sugar and ester hydrolysis with water are the two NCERT examples (p. 79).

2.5 Quick reference — kinetics at a glance