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Quick Summary
Chemical kinetics studies how fast a reaction occurs and the factors that control that rate. In TN HSE board exams, the most tested areas are: rate law and order determination from data tables, first-order integrated equations, half-life calculations, Arrhenius equation numericals, and graph-based questions. This guide covers all of those systematically.
1. Core Definitions
| Term | Definition |
|---|---|
| Rate of reaction | Change in concentration of reactant or product per unit time; rate = −d[A]/dt = +d[P]/dt |
| Instantaneous rate | Rate at a specific moment; slope of tangent on concentration–time graph |
| Average rate | Change over a time interval; Δ[A]/Δt |
| Rate constant, k | Proportionality constant in rate law; depends on T and Ea, not concentration |
| Order | Sum of powers of concentration terms in the experimentally derived rate law |
| Molecularity | Number of reacting molecules in an elementary (single-step) reaction |
| Activation energy, Ea | Minimum energy that colliding molecules must have to react |
2. Rate Law and Reaction Order
For a general reaction:
Experimental rate law:
- x = order with respect to A
- y = order with respect to B
- Overall order = x + y
Critical rule: x and y are determined experimentally — never assume x = a or y = b from stoichiometry unless the reaction is elementary.
Determining Order from Data
Method — compare experiments where one concentration changes and the other is held constant.
Example data:
| Experiment | [A] / mol L⁻¹ | [B] / mol L⁻¹ | Rate / mol L⁻¹ s⁻¹ |
|---|---|---|---|
| 1 | 0.10 | 0.10 | 2.0 × 10⁻³ |
| 2 | 0.20 | 0.10 | 4.0 × 10⁻³ |
| 3 | 0.10 | 0.20 | 2.0 × 10⁻³ |
From Exp 1 and 2 ([B] constant, [A] doubles): rate doubles → x = 1 (first order in A) From Exp 1 and 3 ([A] constant, [B] doubles): rate unchanged → y = 0 (zero order in B) Overall order = 1. Rate = k[A].
3. Integrated Rate Equations
Zero-Order Reaction
Rate = k (constant, independent of concentration)
- Plot of [A] vs t is a straight line with slope = −k
- Half-life: t½ = [A]₀ / 2k (depends on initial concentration)
- Units of k: mol L⁻¹ s⁻¹
Example: Decomposition of N₂O on hot platinum surface.
First-Order Reaction
Rate = k[A]
Integration gives:
- Plot of log[A] vs t is a straight line with slope = −k/2.303
- Half-life: t½ = 0.693/k (independent of [A]₀ — this is the hallmark of first order)
- Units of k: s⁻¹ (or min⁻¹, etc.)
Examples: radioactive decay, decomposition of SO₂Cl₂, first-order hydrolysis of esters.
Pseudo First-Order Reactions
When a higher-order reaction has one reactant in large excess (effectively constant concentration), it behaves as first order. The apparent rate constant k' = k[B]_excess is called the pseudo first-order rate constant.
Classic example: Hydrolysis of methyl acetate in dilute HCl — water is in vast excess, so rate depends only on ester concentration.
4. Arrhenius Equation
In logarithmic form:
- A is the frequency factor (pre-exponential factor) — accounts for collision frequency and orientation
- Ea is activation energy in J mol⁻¹ (or kJ mol⁻¹)
- R = 8.314 J mol⁻¹ K⁻¹
- T is temperature in Kelvin
Finding Ea from Two Temperatures
If k doubles for a 10°C rise (T₁ = 300 K, T₂ = 310 K):
5. Collision Theory
For a reaction to occur, molecules must: 1. Collide — sufficient collision frequency 2. Collide with energy ≥ Ea — threshold energy 3. Collide with proper orientation (steric factor p)
where Z is the collision frequency.
Energy distribution (Maxwell-Boltzmann curve):
- Area under the curve beyond Ea represents fraction of effective molecules
- Higher T → peak shifts right → larger fraction exceeds Ea → faster rate
6. Effect of Catalyst
A catalyst provides an alternative reaction pathway with lower activation energy.
- It does NOT change ΔH, ΔG, or the equilibrium constant K
- It increases both forward and reverse rates equally
- It reaches the equilibrium faster — does not shift equilibrium position
- The activated complex is different (lower energy) on the catalysed path
Mechanism of heterogeneous catalysis: 1. Adsorption of reactants on catalyst surface 2. Formation of surface intermediate 3. Reaction between adsorbed species 4. Desorption of products from surface
7. Worked Numericals
Problem 1 — Determining Rate Law from Experimental Data
Data:
| Exp | [NO] / M | [Cl₂] / M | Initial rate / M s⁻¹ |
|---|---|---|---|
| 1 | 0.10 | 0.10 | 1.2 × 10⁻³ |
| 2 | 0.10 | 0.20 | 2.4 × 10⁻³ |
| 3 | 0.20 | 0.10 | 4.8 × 10⁻³ |
Find order w.r.t. each reactant and k.
Problem 2 — First-Order Half-Life and Time for 75% Completion
Find: (a) t½, (b) time for 75% completion
Alternatively, using the formula:
Problem 3 — Arrhenius Equation (Effect of Temperature)
Find: Ratio k₂/k₁
The rate increases by a factor of 1.68 for a 10°C rise when Ea = 40 kJ mol⁻¹.
Problem 4 — Finding Ea from Rate Constants at Two Temperatures
Find: Activation energy Ea
8. Important Board Questions with Model Answers
One-Mark Questions
Q1. Define order of a reaction. Order is the sum of the powers of concentration terms in the experimentally determined rate law equation.
Q2. Write the unit of rate constant for a first-order reaction. s⁻¹ (or min⁻¹). Unit of k for nth order = mol^(1−n) L^(n−1) s⁻¹.
Q3. State one example of a pseudo first-order reaction. Hydrolysis of methyl acetate (ester) in excess dilute HCl — water is in large excess so its concentration is effectively constant.
Q4. What happens to the rate constant when temperature increases? Rate constant k increases exponentially with temperature, as described by the Arrhenius equation k = Ae^(−Ea/RT).
Q5. How does a catalyst increase the rate of a reaction? A catalyst provides an alternate reaction pathway with lower activation energy, so more collisions have sufficient energy to react.
Short-Answer Questions (2–3 marks)
Long-Answer Questions (5 marks)
Common Mistakes
- Assuming order equals stoichiometric coefficient without experimental evidence
- Thinking first-order half-life depends on initial concentration (it does not)
- Mixing ln (natural log) and log (base 10) — the factor 2.303 converts between them
- Stating that a catalyst increases equilibrium yield (it does not — only speeds up reaching equilibrium)
- Using temperature in Celsius instead of Kelvin in the Arrhenius equation
Revision Checklist
- [ ] Rate, rate law, order, and molecularity definitions
- [ ] Determining order from experimental data tables
- [ ] Zero-order and first-order integrated equations
- [ ] First-order half-life derivation and numerical application
- [ ] Pseudo first-order — definition and example
- [ ] Arrhenius equation terms and logarithmic form
- [ ] Finding Ea from two temperature rate constants
- [ ] Collision theory — effective collision criteria
- [ ] Effect of catalyst on activation energy and equilibrium
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