Kinetics

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Kinetics — Key Facts for JEE Advanced

Rate Laws:

• Rate = k[A]^m[B]^n (for reaction: mA + nB → products)
• k = rate constant (units depend on order)
• m, n = partial orders (determined experimentally, NOT from stoichiometry)
• Overall order = m + n

Units of Rate Constant:

Order	Units
Zero	mol L⁻¹ s⁻¹
First	s⁻¹
Second	L mol⁻¹ s⁻¹
Third	L² mol⁻² s⁻¹

Integrated Rate Laws:

• Zero order: [A]_t = [A]_0 − kt
• First order: log [A]_t = log [A]_0 − kt/2.303
• First order half-life: t½ = 0.693/k (independent of initial concentration)
• Second order: 1/[A]_t = 1/[A]_0 + kt

Arrhenius Equation: k = A × e^(−Ea/RT) Taking log: log k = log A − Ea/(2.303RT) Slope = −Ea/(2.303R), Intercept = log A Activation energy Ea = 2.303 R × (log k₂/k₁) × (T₁T₂/(T₂−T₁))

⚡ Exam Tip: In half-life problems, if the order is not given, try first order first because it has the unique property of t½ independent of [A]₀. This is the most commonly tested trick in JEE.

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🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Kinetics — Chemistry Study Guide

Rate Expression and Order Determination:

For a general reaction: aA + bB → products Rate = k[A]^x[B]^y x and y are determined experimentally

Method of initial rates: Run experiments at different initial concentrations, measure initial rates. Example: For reaction A + B → products Expt 1: [A] = a, [B] = b, rate = r₁ Expt 2: [A] = 2a, [B] = b, rate = r₂ If r₂ = 2r₁, then x = 1 (first order in A) Expt 3: [A] = a, [B] = 2b, rate = r₃ If r₃ = r₁, then y = 0 (zero order in B)

Isolation method (Ostwald’s isolation method): Keep one reactant in large excess, study pseudo-order with respect to the other. If [B] >> [A]: Rate ≈ k’[A]^x where k’ = k[B]^y (pseudo-order)

Order of Reaction from Time Data:

For first order, log [A]_t vs time gives straight line with slope = −k/2.303 For zero order, [A]_t vs time gives straight line with slope = −k

Half-life method: t½ ∝ [A]₀^(1−n) where n is the order

• Zero order: t½ = [A]₀/(2k) → proportional to [A]₀
• First order: t½ = 0.693/k → independent of [A]₀
• Second order: t½ = 1/(k[A]₀) → inversely proportional to [A]₀

Molecularity vs Order:

Molecularity: Number of molecules/ions that collide to produce the reaction Order: Sum of exponents in rate law (experimental quantity)

Reaction	Molecularity	Order
unimolecular decomposition	1	may be 1 or different
Termolecular elementary step	3	always 3 (but rarely observed)

Complex reactions (multi-step) often have order ≠ molecularity of any step.

Arrhenius Parameters:

k = A × e^(−Ea/RT)

A = pre-exponential factor (frequency factor) Ea = activation energy (in J mol⁻¹) R = 8.314 J mol⁻¹ K⁻¹

Physical meaning of A: Represents collision frequency and orientation factor. Physical meaning of Ea: Minimum energy required for reaction to occur.

Two-point form of Arrhenius: log(k₂/k₁) = (Ea/2.303R) × (T₂ − T₁)/(T₁T₂)

⚡ Exam Tip: When k doubles, the reaction rate doesn’t necessarily double — it depends on the order! However, for first order, doubling k does double the rate. Know your rate law.

Rate-Determining Step (RDS) and Reaction Mechanism:

A reaction mechanism consists of elementary steps. The slowest step is the rate-determining step.

Example: 2NO + O₂ → 2NO₂ Mechanism: Step 1 (slow, RDS): 2NO ⇌ N₂O₂ (fast equilibrium) Step 2 (fast): N₂O₂ + O₂ → 2NO₂

Rate from RDS: rate = k[NO]² But experimentally observed order = 3 (because [N₂O₂] = K[NO]² and substituting gives rate ∝ [NO]²[O₂])

Types of Reactions Based on Rate:

Parallel reactions: A → products A → byproducts

Rate of disappearance of A: −d[A]/dt = (k₁ + k₂)[A] Effective rate constant: k_eff = k₁ + k₂ t½ = 0.693/(k₁ + k₂)

Relative amounts: [Product₁]/[Product₂] = k₁/k₂ (at any time)

Consecutive reactions: A → B → C

For A → B (first order, k₁): [A] = [A]₀e^(−k₁t) For B → C (first order, k₂): [B] = [A]₀ × k₁/(k₂−k₁) × (e^(−k₁t) − e^(−k₂t)) Maximum B concentration occurs at t_max = ln(k₂/k₁)/(k₂−k₁)

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Kinetics — Comprehensive Chemistry Notes

Collision Theory of Reaction Rates:

For a reaction to occur, two conditions must be met:

1. Collision frequency (number of collisions per unit time per unit volume)
2. Collision energy must exceed activation energy (Ea)
3. Proper orientation of colliding molecules

Rate = Z_AB × f × P where Z_AB = collision frequency, f = fraction with Ea, P = steric factor

Z_AB ∝ (σ_AB) × √(8πkT/μ) × N_A × [A][B] where σ_AB is collision cross-section and μ is reduced mass

f = e^(−Ea/RT) (Boltzmann factor)

P accounts for proper orientation (e.g., in SN2 reactions, backside attack orientation)

Transition State Theory (Activated Complex Theory):

Reactants ⇌ [Activated Complex]‡ → Products

Activated complex: Highest energy, unstable configuration at the saddle point

For elementary reaction: A + BC ⇌ [ABC]‡ → products k = (k_B T/h) × e^(−ΔG‡/RT) where k_B is Boltzmann constant, h is Planck’s constant, ΔG‡ is free energy of activation

ΔG‡ = ΔH‡ − TΔS‡

Interpretation:

• High ΔH‡ (high Ea): Slow reaction (energetic barrier)
• High ΔS‡ (positive): Faster reaction (more disorder favorable)
• For reactions in solution: ΔS‡ dominates
• For reactions in gas phase: ΔH‡ dominates

Order Greater Than 3:

Third order reactions are possible in gas phase (e.g., 2NO + O₂ → 2NO₂ is third order overall) Third order requires termolecular elementary steps (3-body collisions), which are statistically rare in gas phase but do occur in atmospheric chemistry.

Fourth and higher orders: Extremely rare; usually seen in chain reactions where the order refers to the overall reaction rate law not reflecting the elementary step.

Pseudo-Order Reactions:

When one reactant is in large excess: For reaction: A + B + C → products If [B]₀ >> [A]₀ and [C]₀ >> [A]₀: Rate = k[A][B][C] ≈ k’ [A] where k’ = k[B][C] Pseudo-first order in A

Applications:

• Hydrolysis of esters: CH₃COOC₂H₅ + H₂O → CH₃COOH + C₂H₅OH Rate = k[ester][H₂O] → pseudo-first order (water in large excess)
• Acid catalyzed inversion of cane sugar: water present in large excess

Half-Life in Complex Reactions:

n-th order reaction (excluding n=1): t½ = [A]₀^(1−n) / [(n−1)k] (for n ≠ 1)

For n > 1: t½ decreases as [A]₀ increases (concentrated reactions die out faster) For n < 1: t½ increases as [A]₀ increases

Temperature Jump (T-jump) Methods:

Real-world kinetics: Not all reactions follow simple first/second order at all temperatures. Above a certain temperature (T₁), the rate increases significantly.

For Arrhenius-type reactions: log k vs 1/T is linear (straight line) Deviations from linearity indicate:

• Change in mechanism
• Non-Arrhenius behavior (quantum tunneling at low T)
• Competing reactions with different Ea

Chain Reactions:

Hydrogen-bromine reaction: H₂ + Br₂ → 2HBr Rate law: d[HBr]/dt = k[H₂][Br₂]^½ / (1 + k’[HBr]/[Br₂])

Mechanism (classical chain reaction): Initiation: Br₂ → 2Br• (homolytic cleavage, requires UV light or heat) Propagation: Br• + H₂ → HBr + H• (slow) and H• + Br₂ → HBr + Br• (fast) Termination: 2Br• → Br₂, H• + Br• → HBr, H• + H• → H₂

The half-order arises from the termination step involving Br atoms.

Catalysis:

Homogeneous catalysis: Catalyst in same phase as reactants Example: Decomposition of H₂O₂ catalyzed by I⁻: 2H₂O₂ → 2H₂O + O₂ Mechanism: I⁻ oxidized to IO₃⁻ or other intermediates The I⁻ is regenerated, acts in cycle

Heterogeneous catalysis: Catalyst in different phase Examples:

• Haber process: Fe catalyst (solid) + N₂ + H₂ (gases)
• Contact process: V₂O₅ catalyst (solid) + SO₂ + O₂ (gases)
• catalytic converters: Pt/Rh on alumina

Mechanism of heterogeneous catalysis:

1. Diffusion of reactants to surface
2. Adsorption of reactants on active sites
3. Reaction on surface
4. Desorption of products
5. Diffusion of products away

Adsorption isotherms: Langmuir: θ = KP/(1 + KP) where θ is fraction covered Freundlich: x/m = KP^n (empirical)

Enzyme Kinetics (Michaelis-Menten):

E + S ⇌ ES → E + P where E = enzyme, S = substrate, ES = enzyme-substrate complex, P = product

Rate equation: v = v_max[S] / (K_M + [S]) where v_max = k_cat[E]total and K_M = (k{-1} + k_cat)/k_1

When [S] << K_M (first order region): v ∝ [S] When [S] >> K_M (zero order region): v = v_max (saturated)

Lineweaver-Burk plot (double reciprocal): 1/v = (K_M/v_max) × (1/[S]) + 1/v_max Slope = K_M/v_max, y-intercept = 1/v_max, x-intercept = −1/K_M

⚡ Exam Tip: Enzyme kinetics is NOT covered in JEE Advanced syllabus directly but has appeared as application of kinetics in competitive problems. Focus on the Michaelis-Menten equation and Lineweaver-Burk plot.

Photochemical Reactions:

Primary photochemical process: After absorption of photon (hν) JEE-relevant photochemical processes:

Photosynthesis: 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂ (Not a simple photochemical reaction, involves complex electron transport chain)

Bleaching of color: In presence of light, colored compounds decompose Hydrogen-chlorine reaction: H₂ + Cl₂ → 2HCl (initiated by hν)

Quantum yield = Number of molecules reacted / Number of photons absorbed If quantum yield > 1: chain reaction (e.g., H₂ + Cl₂ has quantum yield ~10⁵ due to chain propagation)

Radioactive Decay Kinetics:

First order kinetics applies: N = N₀ × e^(−λt) t½ = 0.693/λ λ = decay constant (unique to each isotope)

Applications in dating:

• Carbon-14 dating: t½ = 5730 years
• Potassium-Argon dating: t½ = 1.25 × 10⁹ years
• Uranium-Lead dating: t½ = 4.5 × 10⁹ years

Instantaneous vs Average Rate:

Average rate over time interval Δt: r_avg = −Δ[A]/Δt Instantaneous rate at time t: r_inst = d[A]/dt = limit as Δt→0 of r_avg In calculus terms: rate = −d[C]/dt (for disappearance of reactant C) Rate = +d[P]/dt (for appearance of product P)

For stoichiometry: If 2A → B then −(1/2)(d[A]/dt) = d[B]/dt

⚡ Exam Tip: JEE often uses the convention Rate = −(1/a)(d[A]/dt) = +(1/b)(d[B]/dt) = … for reaction aA + bB → products. Always write rate expression in terms of stoichiometric coefficients.

Effect of Catalyst on Kinetics:

A catalyst:

• Provides alternative pathway with lower Ea
• Does NOT change ΔG of reaction (does not affect equilibrium)
• Does NOT change reaction quotient or equilibrium constant
• Increases both forward and reverse rates equally
• Is consumed in one step, regenerated in another (not consumed overall)

Illustration: Without catalyst: Ea = 100 kJ/mol, k₁ With catalyst: Ea = 60 kJ/mol, k₂ Ratio: k₂/k₁ = e^[(100−60)/RT] = e^(40/RT) At 298 K: ratio = e^(40/8.314×298) ≈ e^(16.2) ≈ 10⁷

The catalyst works because it provides an alternative reaction surface or mechanism with lower activation energy. Even a small reduction in Ea dramatically increases the rate.

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