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.
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?
1
After n half-lives: fraction remaining = (1/2)ⁿ = (1/2)³ = 1/8
2
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.
1
Rate = k[A]ˣ. Divide: Rate₂/Rate₁ = ([A]₂/[A]₁)ˣ
2
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)
1
T₁ = 298 K, T₂ = 323 K, Eₐ = 50000 J/mol
2
log(k₂/k₁) = Eₐ(T₂−T₁)/(2.303×R×T₁×T₂)
3
= 50000×25/(2.303×8.314×298×323) = 1250000/1838500 ≈ 0.680
5
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.
1
The trap: Molecularity and order are the same ONLY for elementary reactions.
2
2H₂ + O₂ → 2H₂O is an overall reaction, not an elementary step.
3
Molecularity applies only to elementary steps (single collision events). This reaction proceeds through multiple steps.
4
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.
🌡️
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.
🧮
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~8 Determining order from data~7 Arrhenius equation calculations~6 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).