Kinetics

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Kinetics — Quick Facts

Chemical kinetics is the branch of chemistry that studies the rates of chemical reactions and the factors that affect them. For NEET, the rate law expression and half-life calculations are the most frequently tested concepts.

Rate and Rate Law:

• Rate of reaction = (1/α) × (Δ[C]/Δt) where α is the stoichiometric coefficient
• Rate law: Rate = k[A]^m[B]^n where k is the rate constant, m and n are reaction orders
• Order is experimentally determined — never from stoichiometric coefficients
• Molecularity is the number of molecules colliding in an elementary step; order can be zero, fractional, or negative

Key Formulas to Memorise:

• First-order kinetics: k = (2.303/t) × log₁₀([A]₀/[A]ₜ)
• Half-life for first order: t₁/₂ = 0.693/k (independent of initial concentration)
• Zero-order half-life: t₁/₂ = [A]₀/2k (depends on initial concentration)
• Rate constant units: for zero order (mol L⁻¹ s⁻¹), first order (s⁻¹), second order (L mol⁻¹ s⁻¹)

⚡ Exam tip: NEET 2022 asked a direct numerical on first-order half-life — if k = 0.0693 min⁻¹, then t₁/₂ = 10 minutes. Always check units of k to confirm order.

⚡ Common mistake: Students confuse order and molecularity. Molecularity must be a whole number (1, 2, or 3); order can be any value including zero and fractions.

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🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Kinetics — NEET/JEE Study Guide

Collision Theory of Reaction Rates: For a reaction to occur, molecules must collide with sufficient energy (activation energy, Eₐ) and proper orientation. The fraction of molecules with energy ≥ Eₐ is given by the Maxwell-Boltzmann distribution: f = e^(−Eₐ/RT).

The Arrhenius equation relates rate constant to temperature: $$k = A \cdot e^{-E_a/RT}$$ Taking logarithms: log k = log A − Eₐ/(2.303RT)

A plot of log k vs 1/T gives a straight line with slope = −Eₐ/(2.303R).

Integrated Rate Equations:

Order	Rate Law	Integrated Form	Half-life
0	Rate = k[A]⁰	[A]ₜ = [A]₀ − kt	[A]₀/2k
1	Rate = k[A]¹	ln[A]ₜ = ln[A]₀ − kt	0.693/k
2	Rate = k[A]²	1/[A]ₜ = 1/[A]₀ + kt	1/([A]₀·k)

Effect of Catalyst: A catalyst provides an alternate pathway with lower activation energy (Eₐ). It increases rate without being consumed. The rate constant changes exponentially with Eₐ — even a small decrease in Eₐ causes a large increase in k.

Pseudo-first-order reactions: When one reactant is in vast excess (e.g., hydrolysis of sucrose where water is solvent), the reaction appears first order. For A + B → products with [B]₀ >> [A]₀: Rate = k’[A] where k’ = k[B]₀.

Half-life in Radioactive Decay: The same first-order kinetics applies: t₁/₂ = 0.693/λ where λ is the decay constant. This is directly tested in NEET physics section too.

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Kinetics — Comprehensive Notes

Derivation of First-Order Integrated Rate Law: For a reaction A → products, Rate = −d[A]/dt = k[A] Rearranging: d[A]/[A] = −k dt Integrating from t=0 to t=t: ∫[A]₀^[A]ₜ d[A]/[A] = −∫₀^t k dt ln[A]ₜ − ln[A]₀ = −kt ln([A]ₜ/[A]₀) = −kt [A]ₜ = [A]₀ e^(−kt) Converting to base-10: log₁₀([A]ₜ/[A]₀) = −kt/2.303

Half-life Derivation: At t = t₁/₂, [A]ₜ = [A]₀/2 log₁₀([A]₀/2 / [A]₀) = −kt₁/₂/2.303 log₁₀(1/2) = −kt₁/₂/2.303 −0.3010 = −kt₁/₂/2.303 t₁/₂ = 0.693/k ✓

Arrhenius Equation Derivation (from collision theory): k = PZ · e^(−Eₐ/RT) where P is the steric factor (orientation probability), Z is the collision frequency. The temperature dependence of k comes entirely from the exponential term.

Two-point form of Arrhenius: log(k₂/k₁) = (Eₐ/2.303R) × (1/T₁ − 1/T₂)

Order Determination Methods:

1. Initial rate method: Conduct experiments at different [A]₀ and measure initial rates. If doubling [A]₀ doubles rate → first order. If doubling [A]₀ quadruples rate → second order.

2. Integrated method: Plot different functions of [A] vs time. The plot that gives a straight line indicates the correct order:

   • [A] vs t (linear) → zero order
   • ln[A] vs t (linear) → first order
   • 1/[A] vs t (linear) → second order

Complex Reactions:

• Parallel reactions: When a reactant can form multiple products simultaneously. k₁ and k₂ compete. The branching ratio is k₁/k₂.

• Consecutive reactions: A → B → C. The intermediate B builds up then decays. Rate-determining step (RDS) controls overall rate.

• NEET Pattern: Questions often give concentration-time data and ask to determine order. Always check which integrated form gives a straight line.

Temperature Jump (Effect of Temperature): Roughly, for every 10°C rise, reaction rate approximately doubles (van’t Hoff rule). More precisely, use Arrhenius: if T rises from 298K to 308K, k₂/k₁ = e^(−Eₐ/R) × (1/298 − 1/308).

⚡ NEET 2023 Qn: A reaction is 50% complete in 2 hours and 75% complete in 4 hours. What is the order? Answer: First order (half-life is constant).

⚡ JEE 2022 Qn: For the reaction 2NO(g) + Br₂(g) → 2NOBr(g), rate = k[NO]²[Br₂]. If [NO] is doubled and [Br₂] halved, the rate becomes 2× the original.