Chemical Kinetics

Concept Core

Rate, order, molecularity, half-life, and temperature dependence — the kinetics framework.

Rate Law & Order of Reaction

For aA + bB → products, the rate law is:

Rate = k [A]ˣ [B]ʸ

x, y = order with respect to A, B (determined experimentally, NOT from stoichiometry). Overall order = x + y.

k = rate constant. Units of k depend on order: zero order: mol L⁻¹s⁻¹; first order: s⁻¹; second order: L mol⁻¹s⁻¹.

Integrated Rate Laws

Order	Integrated Law	Half-life
Zero	[A] = [A]₀ − kt	t₁/₂ = [A]₀/2k
First	ln[A] = ln[A]₀ − kt	t₁/₂ = 0.693/k
Second	1/[A] = 1/[A]₀ + kt	t₁/₂ = 1/(k[A]₀)

First-Order Reaction — Key Features

Most important for EAPCET. Half-life is independent of initial concentration:

t₁/₂ = 0.693/k = ln 2/k

Radioactive decay, many drug eliminations are first-order.

After n half-lives: [A] = [A]₀ × (1/2)ⁿ

Arrhenius Equation — Temperature Dependence

k = A e^(−Eₐ/RT) ln k = ln A − Eₐ/(RT) log k₂/k₁ = Eₐ/(2.303R) × (1/T₁ − 1/T₂)

A = frequency/pre-exponential factor. Eₐ = activation energy (J/mol). Higher Eₐ = more temperature sensitive. Catalyst lowers Eₐ.

Molecularity vs Order

Molecularity	Order
Theoretical — how many molecules collide in elementary step	Experimental — from rate law
Always whole number (1,2,3)	Can be 0, fraction, or negative
Only for elementary reactions	For overall reactions too

Collision Theory & Activation Energy

Reaction occurs when molecules collide with: (1) sufficient energy ≥ Eₐ, and (2) correct orientation.

Rate = frequency × orientation factor × energy factor Rate ∝ e^(−Eₐ/RT)

A catalyst provides an alternative path with lower Eₐ. It speeds up the reaction without being consumed.

Formula Vault

All chemical kinetics formulas for EAPCET.

Rate Law

Rate = k[A]ˣ[B]ʸ

Orders determined experimentally

Zero Order t₁/₂

t₁/₂ = [A]₀/2k

Depends on initial concentration

First Order Integrated

ln[A] = ln[A]₀ − kt

Or: [A] = [A]₀ e^(−kt)

First Order t₁/₂

t₁/₂ = 0.693/k

Independent of [A]₀

After n Half-Lives

[A] = [A]₀ × (½)ⁿ

n = number of half-lives elapsed

Second Order t₁/₂

t₁/₂ = 1/(k[A]₀)

Depends on [A]₀

Arrhenius Equation

k = A e^(−Eₐ/RT)

A = pre-exponential factor

Arrhenius (Two Temps)

log(k₂/k₁) = Eₐ(T₂−T₁)/(2.303RT₁T₂)

Find Eₐ or rate at new T

Units of k

k units = (mol/L)^(1−n) / s

n = overall order

Threshold Energy

Eₐ = E_threshold − E_reactants

Min energy to overcome barrier

Worked Examples

5 problems — rate law, half-life, Arrhenius, and order determination.

EasyA first-order reaction has k = 0.693 min⁻¹. Find half-life.▾

Find the half-life of a first-order reaction with k = 0.693 min⁻¹.

t₁/₂ = 0.693/k = 0.693/0.693 = 1 min

✓ t₁/₂ = 1 min

EasyAfter 3 half-lives of a first-order reaction, what fraction remains?▾

What fraction of a reactant remains after 3 half-lives of a first-order reaction?

After n half-lives: fraction remaining = (1/2)ⁿ = (1/2)³ = 1/8

So 87.5% has reacted, 12.5% remains.

✓ Fraction remaining = 1/8 (12.5%)

MediumFind order from experimental data: doubling [A] doubles rate▾

Experiment 1: [A]=0.1M, Rate=0.02 mol/Ls. Experiment 2: [A]=0.2M, Rate=0.04 mol/Ls. Find order w.r.t. A.

Rate = k[A]ˣ. Divide: Rate₂/Rate₁ = ([A]₂/[A]₁)ˣ

0.04/0.02 = (0.2/0.1)ˣ → 2 = 2ˣ → x = 1 (first order)

✓ Order w.r.t. A = 1 (first order)

EAPCET LevelArrhenius: find k at 50°C given k at 25°C and Ea▾

A reaction has Eₐ = 50 kJ/mol. Rate constant k = 2×10⁻³ s⁻¹ at 25°C. Find k at 50°C. (R = 8.314 J/mol/K)

T₁ = 298 K, T₂ = 323 K, Eₐ = 50000 J/mol

log(k₂/k₁) = Eₐ(T₂−T₁)/(2.303×R×T₁×T₂)

= 50000×25/(2.303×8.314×298×323) = 1250000/1838500 ≈ 0.680

k₂/k₁ = 10^0.680 ≈ 4.79

k₂ = 4.79 × 2×10⁻³ ≈ 9.6×10⁻³ s⁻¹

✓ k₂ ≈ 9.6×10⁻³ s⁻¹ (rate nearly 5× faster at 50°C)

Trap QuestionOrder = molecularity for any reaction — True or False?▾

A student states: 'For the reaction 2H₂ + O₂ → 2H₂O, molecularity = 3 and order = 3.' Evaluate.

The trap: Molecularity and order are the same ONLY for elementary reactions.

2H₂ + O₂ → 2H₂O is an overall reaction, not an elementary step.

Molecularity applies only to elementary steps (single collision events). This reaction proceeds through multiple steps.

The order of the overall reaction must be determined experimentally — it might be first order, second order, or anything else.

✓ False — order ≠ molecularity for complex reactions; order is always experimental

Mistake DNA

4 chemical kinetics errors from EAPCET distractor analysis.

🔢

Writing Rate Law Exponents from Stoichiometry

The order of reaction is determined experimentally, NOT from the balanced equation.

❌ Wrong

2A+B→C: Rate = k[A]²[B] ✗ (stoichiometric coefficients ≠ orders)

✓ Correct

Order from experiment ✓ Might be Rate = k[A][B]⁰ ✓ or any other combination determined by data

Stoichiometric coefficients give molecularity (for elementary steps) not order. Always determine order from experimental rate data (doubling/tripling concentrations).

⏱️

First Order t₁/₂ Depends on Concentration

A key feature of first-order reactions is that the half-life is CONSTANT — independent of starting concentration.

❌ Wrong

1st order: 2nd half-life is twice the first ✗ (that's zero order!)

✓ Correct

1st order: t₁/₂ = 0.693/k ✓ Same regardless of [A]₀ ✓ Each half-life = same duration

Zero-order half-life depends on [A]₀. First-order half-life is constant. This distinction is a favourite EAPCET fact question.

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Arrhenius: Using Celsius Instead of Kelvin

R and T in the Arrhenius equation require T in Kelvin. Using Celsius gives completely wrong answers.

❌ Wrong

log(k₂/k₁) = Eₐ(T₂−T₁)/(2.303R×25×50) ✗ (°C used instead of K)

✓ Correct

T₁=298K, T₂=323K ✓ use K everywhere in Arrhenius calculations ✓

Arrhenius: k = Ae^(−Eₐ/RT). R = 8.314 J/mol/K. T must be in Kelvin. This is non-negotiable.

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Catalyst Changes K (Equilibrium Constant)

A catalyst lowers the activation energy and speeds up the reaction, but it doesn't change ΔG or K.

❌ Wrong

Catalyst → products form faster → K increases ✗

✓ Correct

Catalyst: lowers Eₐ ✓ Speeds up both forward and reverse equally ✓ K unchanged ✓

A catalyst provides an alternative pathway with lower Eₐ. It speeds up BOTH forward and reverse reactions by the same factor. The ratio of rate constants (= K) is unchanged.

Chapter Intelligence

Chemical kinetics is heavily numerical — mastering rate law and Arrhenius calculations is essential.

EAPCET Weightage (2019–2024)

First-order reactions & half-life

Determining order from data

Arrhenius equation calculations

Integrated rate laws

Molecularity vs order

High-Yield PYQ Patterns

Calculate t₁/₂ from k (first order)Find order from two rate experimentsFraction remaining after n half-livesk at new T using ArrheniusUnits of rate constant for nth orderOrder from concentration-time graph

Exam Strategy

First-order t₁/₂ = 0.693/k. Memorise this. If the question says 'half-life is constant', it's first-order.
Determining order: double [A], observe rate. Rate doubles → first order. Rate quadruples → second order. Rate unchanged → zero order.
Arrhenius calculations: ALWAYS convert T to Kelvin. Use the two-temperature formula log(k₂/k₁) = Eₐ(T₂−T₁)/(2.303RT₁T₂).
Units of k: for nth order, units = (mol/L)^(1−n) / s. Zero: mol/L/s. First: s⁻¹. Second: L/mol/s. This is a direct EAPCET question.
Kinetics connects to Equilibrium (rates forward and reverse determine K) and Thermodynamics (Eₐ and ΔH are different — knowing ΔH doesn't tell you Eₐ).

Concept Core

Formula Vault

Worked Examples

Mistake DNA

Chapter Intelligence

💡 Suggestions & Feedback

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