Module 01
Introduction to Chemical Kinetics
Chemical Kinetics is the branch of physical chemistry that deals with the rate of chemical reactions, the factors that influence the rate, and the mechanism by which a reaction proceeds.
Thermodynamics tells us whether a reaction will occur; kinetics tells us how fast it will occur. A thermodynamically spontaneous reaction may be kinetically very slow (e.g., diamond → graphite).
Illustration – Scope of Chemical Kinetics
Fast Reactions
Ionic reactions in solution — milliseconds (e.g., AgNO₃ + NaCl)
Slow Reactions
Rusting of iron, radioactive decay — hours to years
Moderate
Decomposition of H₂O₂, esterification — minutes to hours
Scope
Predicts time for drugs to work, industrial reactor design
Module 02
Rate of a Reaction
The rate of reaction is the change in concentration of a reactant or product per unit time. It is always positive.
Average Rate
📐 Average Rate — General Formula
For: aA + bB → cC + dD
Rate = -1/a · Δ[A]/Δt = -1/b · Δ[B]/Δt
= +1/c · Δ[C]/Δt = +1/d · Δ[D]/Δt
Rate = -1/a · Δ[A]/Δt = -1/b · Δ[B]/Δt
= +1/c · Δ[C]/Δt = +1/d · Δ[D]/Δt
Negative sign for reactants (decreasing), positive for products (increasing).
Units: mol L⁻¹ s⁻¹
Units: mol L⁻¹ s⁻¹
Instantaneous Rate
📐 Instantaneous Rate
Rateinst = limΔt→0 [Δ[A]/Δt] = d[A]/dt
Slope of tangent drawn on concentration-time graph at any point.
🔑 Key Insight
The rate of reaction decreases as the reaction progresses (for most reactions) because the concentration of reactants decreases over time.
Graph – Concentration vs Time
Module 03
Rate Law & Order of Reaction
The rate law (or rate expression) is an experimentally determined equation that relates the rate of reaction to the concentration of reactants raised to certain powers.
📐 Rate Law Expression
Rate = k [A]m [B]n
k = rate constant (specific rate constant)
m = order w.r.t A (from experiment, NOT stoichiometry)
n = order w.r.t B
(m + n) = overall order of reaction
m = order w.r.t A (from experiment, NOT stoichiometry)
n = order w.r.t B
(m + n) = overall order of reaction
Units of Rate Constant (k)
📐 Units of k for nth Order
Units of k = mol1−n · Ln−1 · s−1
Zero order: mol L⁻¹ s⁻¹ | First order: s⁻¹ | Second order: L mol⁻¹ s⁻¹
Order vs Molecularity
| Parameter | Order | Molecularity |
|---|---|---|
| Definition | Sum of powers in rate law | No. of reacting species in elementary step |
| Determined by | Experiment only | Mechanism / balanced equation |
| Value | 0, 1, 2, 3 (can be fractional) | 1, 2, or 3 (always integer) |
| Applicable to | Overall & elementary reactions | Elementary reactions only |
| Example | Rate = k[H₂][I₂] → 2nd order | H₂ + I₂ → 2HI (bimolecular) |
Module 04
Integrated Rate Laws
Integrated rate laws give the concentration as a function of time for different reaction orders.
Zero Order Reaction
📐 Zero Order — Integrated Rate Law
[A]t = [A]0 − kt
Graph: [A] vs t → straight line, slope = −k
Graph: [A] vs t → straight line, slope = −k
Example: Decomposition of HI on gold surface, photochemical reactions
First Order Reaction
📐 First Order — Integrated Rate Law
ln[A]t = ln[A]0 − kt
log([A]0/[A]t) = kt / 2.303
[A]t = [A]0 · e−kt
log([A]0/[A]t) = kt / 2.303
[A]t = [A]0 · e−kt
Example: Radioactive decay (¹⁴C), decomposition of N₂O₅, hydrogenation reactions
Second Order Reaction
📐 Second Order — Integrated Rate Law
1/[A]t = 1/[A]0 + kt
Graph: 1/[A] vs t → straight line, slope = +k
Graph: 1/[A] vs t → straight line, slope = +k
Example: Saponification of ester, 2HI → H₂ + I₂ in gas phase
| Order | Rate Law | Integrated | Graph (linear) | t₁/₂ |
|---|---|---|---|---|
| 0 | r = k | [A] = [A]₀ − kt | [A] vs t | [A]₀ / 2k |
| 1 | r = k[A] | ln[A] = ln[A]₀ − kt | ln[A] vs t | 0.693 / k |
| 2 | r = k[A]² | 1/[A] = 1/[A]₀ + kt | 1/[A] vs t | 1 / k[A]₀ |
Module 05
Half-Life (t₁/₂)
The half-life of a reaction is the time required for the concentration of a reactant to decrease to half its initial value.
📐 Half-Life Formulae
Zero order: t½ = [A]0 / 2k
First order: t½ = 0.693 / k (independent of [A]₀)
Second order: t½ = 1 / (k · [A]0)
First order: t½ = 0.693 / k (independent of [A]₀)
Second order: t½ = 1 / (k · [A]0)
For first-order reactions only, t₁/₂ is constant and independent of initial concentration — this is why radioactive decay always quotes a single half-life value.
💡 Application: Radiocarbon Dating
¹⁴C has t₁/₂ = 5730 years. Since its decay is first order, scientists measure the remaining ¹⁴C activity to date organic materials up to ~50,000 years old.
Module 06
Arrhenius Equation & Activation Energy
The Arrhenius equation quantitatively describes the effect of temperature on the rate constant. Proposed by Svante Arrhenius in 1889.
📐 Arrhenius Equation
k = A · e−Ea/RT
ln k = ln A − Ea / (R · T)
log k = log A − Ea / (2.303 · R · T)
ln k = ln A − Ea / (R · T)
log k = log A − Ea / (2.303 · R · T)
A = frequency factor / pre-exponential factor (orientation + collision)
Eₐ = activation energy (J mol⁻¹)
R = 8.314 J K⁻¹ mol⁻¹ (gas constant) | T = temperature in Kelvin
Eₐ = activation energy (J mol⁻¹)
R = 8.314 J K⁻¹ mol⁻¹ (gas constant) | T = temperature in Kelvin
Two Temperature Form
📐 Comparing k at Two Temperatures
log (k2 / k1) = Ea/2.303R · [1/T1 − 1/T2]
Used to calculate Eₐ experimentally from rate constants at two different temperatures.
Diagram – Potential Energy Profile
⚠️ Temperature & Rate Rule of Thumb
For every 10°C rise in temperature, the rate of reaction approximately doubles (temperature coefficient ≈ 2). This is because more molecules exceed the activation energy Eₐ.
Module 07
Reaction Mechanism
A reaction mechanism is the step-by-step sequence of elementary reactions by which the overall chemical change occurs. The slowest step is the rate-determining step (RDS).
- Elementary Reaction — a single step that occurs exactly as written; molecularity is meaningful.
- Intermediate — species produced in one step and consumed in another; does NOT appear in the overall rate law.
- Rate-Determining Step — the slowest step; controls the overall reaction rate.
- Steady-State Approximation — concentration of intermediates assumed constant (d[I]/dt ≈ 0).
Example: Decomposition of H₂O₂
🔬 Mechanism — Two-Step
Step 1 (slow): H2O2 + I⁻ → H2O + IO⁻
Step 2 (fast): H2O2 + IO⁻ → H2O + O2 + I⁻
Overall: 2H2O2 → 2H2O + O2
Rate = k[H2O2][I⁻] (from slow step)
Step 2 (fast): H2O2 + IO⁻ → H2O + O2 + I⁻
Overall: 2H2O2 → 2H2O + O2
Rate = k[H2O2][I⁻] (from slow step)
I⁻ appears as catalyst (regenerated in step 2). IO⁻ is the reaction intermediate.
Module 08
Factors Affecting Reaction Rate
Concentration
↑ conc → ↑ collisions → ↑ rate. Rate ∝ [A]ᵐ[B]ⁿ
Temperature
↑ T → more molecules exceed Eₐ → ↑ k exponentially
Surface Area
Smaller particle size → larger surface → faster heterogeneous rate
Catalyst
Provides alternate path with lower Eₐ → ↑ rate without being consumed
Light (Radiation)
Photons provide activation energy in photochemical reactions (H₂ + Cl₂)
Collision Theory
📐 Collision Frequency & Effective Collisions
k = p · ZAB · e−Ea/RT
ZAB = collision frequency between A and B molecules
p = steric factor (proper orientation probability; 0 < p ≤ 1)
Only collisions with correct orientation AND energy ≥ Eₐ are effective.
p = steric factor (proper orientation probability; 0 < p ≤ 1)
Only collisions with correct orientation AND energy ≥ Eₐ are effective.
Module 09
Catalysis
A catalyst is a substance that increases the rate of a reaction without being permanently consumed. It provides an alternate reaction path with a lower activation energy.
Types of Catalysis
| Type | Description | Example |
|---|---|---|
| Homogeneous | Catalyst & reactants in same phase | NO (g) catalyses SO₂ → SO₃ |
| Heterogeneous | Catalyst in different phase | Fe(s) in Haber process (N₂+H₂→NH₃) |
| Enzyme (Bio) | Protein catalysts, highly specific | Zymase: glucose → ethanol |
| Autocatalysis | Product acts as catalyst | Mn²⁺ in KMnO₄ + H₂C₂O₄ |
📌 Characteristics of Catalyst
(1) Not consumed in net reaction (2) Alters Eₐ, not ΔH (3) Does not shift equilibrium position — only reaches it faster (4) Specific in action.
Industrial Applications
- Haber Process (NH₃ synthesis) — Fe catalyst with Mo promoter; Eₐ reduced from ~230 to ~80 kJ/mol
- Contact Process (H₂SO₄) — V₂O₅ catalyst for SO₂ → SO₃ oxidation
- Catalytic Converter — Pt/Pd reduces CO, NOₓ from car exhaust
- Enzyme Carbonic Anhydrase — rate enhanced by 10⁷-fold; catalyses CO₂ + H₂O ⇌ H₂CO₃
Test Yourself
Quick Revision Quiz
Test your understanding with these conceptual questions.