3. Chemical Kinetics
🎯 Learning Outcomes
Candidates should be able to:
- 3.1 Define chemical kinetics.
- 3.2 Explain and use the terms: rate of reaction, rate equation, and rate constant.
- 3.3 Qualitatively explain the factors affecting the rate of reaction.
- 3.4 Use collision theory to explain the influence of temperature, concentration, and particle size on chemical reaction rate.
- 3.5 Define activation energy and activated complex.
- 3.6 Derive and use the integrated rate equations and half-life for zero- and first-order reactions.
- 3.7 Construct and use rate equations, calculating an initial rate using concentration data.
- 3.8 Explain the significance of the Arrhenius equation and solve related problems.
- 3.9 Explain and use the terms catalyst and catalysis (homogeneous, heterogeneous).
- 3.10 Describe enzymes as biological catalysts.
- 3.11 Explain the role of a catalyst in the reaction mechanism.
- 3.12 Solve numerical problems based on rate, rate constant, and order of zero- and first-order reactions.
1 Introduction▾
Have you ever wondered why food spoils faster in summer than in winter? Why does a car engine rust over the years, but a sparkler burns in seconds? Or why do doctors use particular drug dosages? All these phenomena involve the speed of chemical reactions — and that is exactly what Chemical Kinetics is about.
Some reactions occur very rapidly, such as the explosion of fireworks, while others occur very slowly, such as the rusting of iron. Chemical kinetics helps us understand why these rates differ.
Kinetics tells us how fast a reaction happens — not just whether it can happen (thermodynamics).
⚡ Why Does Kinetics Matter?
- Industrial chemistry: Controlling reaction speed maximises product yield and reduces cost.
- Medicine: Drug metabolism rates determine safe dosages and dosing schedules.
- Environment: Understanding rates of atmospheric reactions helps control pollution.
- Food science: Preservative chemistry relies on slowing down decomposition reactions.
- Biology: Every enzyme in your body is a natural kinetics optimiser.
2 Concept of Reaction Rate▾
The rate of a chemical reaction tells us how quickly reactants are consumed or products are formed over time.
Average rate of reaction
It is the rate of reaction measured over a long interval of time. Let us consider a general reaction:
If the initial concentration of reactant at time t₁ is [A₁] and the final concentration at time t₂ is [A₂]. Then, the average rate of reaction in terms of the reactants is:
= − ([A₂] − [A₁]) / (t₂ − t₁) = − ΔA / Δt
Hence, the rate of the reaction in terms of product can be expressed as follows.
Instantaneous rate of reaction
Instantaneous rate of reaction: the rate of reaction measured at any instant of time. It is expressed as follows:
On a concentration vs. time graph, this is the slope of the tangent line at that point.
3 Collision Theory & Activation Energy▾
Collision theory of reaction rate
Ineffective collision: particles just bounce apart unchanged.
Effective collision: leads to product formation.
Proper orientation — the molecules must align correctly for bonds to break and form.
Sufficient energy — enough kinetic energy to overcome the activation energy barrier.
| Ineffective Collision | Effective Collision |
|---|---|
| Particles bounce apart unchanged | Bonds break, and new bonds form → Products are formed |
| Energy < activation energy, OR wrong orientation | Energy ≥ activation energy AND correct orientation |
| No reaction occurs | Reaction occurs successfully |
Concept of activation energy
The Activation Energy (Eₐ) of a reaction is the minimum energy required by colliding particles for a collision to be effective. Reaction pathway diagrams show how the activation energy provides a barrier to reaction.
Activated Complex (Transition State) is the high-energy, unstable arrangement of atoms at the peak of the energy barrier. It exists for an extremely short time before breaking apart into products.
4 Factors Affecting Reaction Rate▾
Nature of Reactants
- Ionic reactions are usually fast.
- Covalent reactions are generally slow because bonds must be broken first.
Surface Area of the reactants
Greater surface area increases the rate of reaction because more particles are exposed for collision. For example, powdered calcium carbonate reacts faster than marble chips.
Concentration
As concentration increases, the frequency of collisions increases, resulting in an increased reaction rate.
Pressure
Similarly, when pressure is increased in a gaseous reaction, the frequency of collisions increases, increasing the reaction rate.
Temperature
At higher temperatures, molecules have more kinetic energy, so a higher percentage of successful collisions occurs between reactant molecules.
Temperature increases the rate of reaction because of two factors:
- The frequency of effective collisions is greater because of the greater kinetic energy of the molecules.
- A greater proportion of the molecules have kinetic energy greater than the activation energy.
The second reason has a far greater effect.
| Factor | Effect | Explanation (Collision Theory) |
|---|---|---|
| Nature of reactants | Ionic reactions are fast; covalent bonds require breaking → slower | Ionic species are already separated; covalent bonds need energy to break |
| Surface area (solid) | More surface area → faster | More particles are exposed to collisions |
| Concentration | Higher concentration → faster rate | More particles per volume → more frequent collisions |
| Pressure (gases) | Higher pressure → faster rate | Particles pushed closer together → collision frequency increases |
| Temperature | Higher temperature → much faster rate | ① Molecules move faster (more collisions) ② Far more important: a larger fraction of molecules have energy ≥ Eₐ |
5 The Arrhenius Equation▾
The Arrhenius equation mathematically shows how temperature affects the rate constant.
- k = the rate constant
- A = pre-exponential factor or Arrhenius factor
- Eₐ = activation energy
- R = universal gas constant
- T = absolute temperature
Even a small increase in temperature causes a large increase in k because of the exponential term.
The rate constant for a reaction is 2.0 × 10⁻³ s⁻¹ at 300 K and 8.0 × 10⁻³ s⁻¹ at 320 K. Calculate the activation energy.
Solution:
log(8.0×10⁻³ / 2.0×10⁻³) = Eₐ / (2.303 × 8.314) × (1/300 − 1/320)
log(4) = Eₐ / 19.14 × (2.083 × 10⁻⁴)
0.602 = Eₐ × 1.088 × 10⁻⁵
Eₐ = 0.602 / 1.088 × 10⁻⁵ ≈ 55,330 J mol⁻¹ ≈ 55.3 kJ mol⁻¹
The activation energy for a reaction is 80 kJ mol⁻¹ and A = 1.0 × 10¹ s⁻¹. Calculate the rate constant at 27 °C.
Solution:
Using k = A × e⁻⁽Eₐ/RT⁾:
Eₐ/RT = 80,000 / (8.314 × 300) = 80,000 / 2,494.2 = 32.08
k = 1.0 × 10⁹ × e⁻³²·⁰⁸
k = 1.0 × 10⁹ × 9.16 × 10⁻¹⁴
k ≈ 9.16 × 10⁻⁵ s⁻¹
6 Catalysis▾
Catalysts provide an alternative reaction pathway with lower activation energy.
Catalysts increase the rate because they make the reaction go by a different reaction pathway (mechanism) that has a lower activation energy than the uncatalysed reaction.
Homogeneous Catalyst
When a catalyst and the reactants are in the same phase.
- Concentrated H₂SO₄ (liquid) catalysing the esterification of an alcohol with a carboxylic acid (both liquids).
- Fe²⁺ ions (aqueous) catalysing the reaction between S₂O₈²⁻ and I⁻ in aqueous solution.
- Acid-catalysed hydrolysis of sucrose in aqueous solution.
Heterogeneous Catalyst
A catalyst that is in a different phase from the reactants.
- Iron (Fe) catalyst in the Haber process — N₂(g) + 3H₂(g) ⇌ 2NH₃(g)
- Nickel in the hydrogenation of vegetable oils (margarine production)
- Vanadium(V) oxide (V₂O₅) in the Contact process for manufacturing H₂SO₄
7 Enzyme Catalysis▾
Inside every living cell, thousands of chemical reactions are occurring every second — made possible by remarkable protein catalysts called enzymes.
Key Features
- Highly specific: One enzyme catalyzes one type of reaction.
Example: Diastase hydrolyzes starch → maltose, but does not hydrolyze cellulose. - Optimum temperature: Maximum activity at a specific temperature (~37 °C for human enzymes). Too high → denatures (loses shape). Too low → too slow.
- Optimum pH: Each enzyme works best at a specific pH.
Example: Pepsin (stomach) works at pH ~2; trypsin (small intestine) works at pH ~8. - Analogy: An enzyme is like a specific key that fits only one lock. Change the lock (different substrate), and the key doesn’t work.
Role of Catalyst in Reaction Mechanism
A catalyst works by providing an alternative mechanism with a lower activation energy for the rate-determining step. This can involve:
- The catalyst forms an intermediate with one of the reactants (homogeneous catalysis).
- Reactants adsorbing onto the catalyst surface, where bonds are weakened (heterogeneous catalysis).
Either way, the energy barrier is reduced, and the reaction proceeds faster.
8 Rate Law, Rate Constant & Order of Reaction▾
Experiments show that the reaction rate depends on the concentration of reactants in a specific mathematical way. This relationship is captured in the rate equation (also called the rate law).
The rate equation for the general reaction P + Q → R + S is:
where k = rate constant, x = order of reaction with respect to reactant P, y = order of reaction with respect to reactant Q, overall order = x + y
The overall order of the reaction is the sum of all the orders in the rate equation. For this reaction, the overall order of reaction would be x + y.
Rate has units of mol L⁻¹ s⁻¹. Concentration has units of mol L⁻¹. The units of the rate constant, k, depend on the overall order of the reaction, and the units can be calculated.
9 Zero-Order & First-Order Reactions▾
Zero-order reaction
A zero-order reaction proceeds at a constant rate, unaffected by the reactant’s concentration.
e.g., Formation of HCl gas from H₂ and Cl₂ gas in the presence of sunlight on the surface of water.
For a zero-order reaction, Rate = k [A]⁰ = k, i.e., rate = k. So, units of k = mol L⁻¹ s⁻¹
Integrated rate law for a zero-order reaction
Consider a general zero-order reaction in which reactant A is converted to a product. Let:
- a = initial concentration of reactant (mol L⁻¹)
- x = amount of reactant converted to product after time t (mol L⁻¹)
- (a − x) = concentration of reactant at time t (mol L⁻¹)
For a zero-order reaction, the rate is independent of the concentration of the reactant. The rate depends on the zeroth power of concentration: Rate ∝ [A]⁰ = constant.
Expressing the rate in terms of the change in x with respect to time:
where k₀ is the zero-order rate constant. Since (a−x)⁰ = 1, the rate equals the rate constant at all times. Equation (i) is the differential rate equation for the zero-order reaction.
Rearranging equation (i) to separate variables and integrating both sides:
∫dx = k₀∫dt
x = k₀t + C … (ii)
At t = 0, x = 0. Substituting into equation (ii): 0 = k₀ × 0 + C ⟹ C = 0.
Substituting C = 0 back into equation (ii): x = k₀t … (iii)
Rearranging for the rate constant: k₀ = x / t … (iv)
Equations (iii) and (iv) are the integrated rate equations for a zero-order reaction. Equation (iii) shows that x varies linearly with time, and equation (iv) gives the rate constant directly from the amount of reactant consumed per unit time.
- The rate is constant and independent of the concentration of the reactant.
- A plot of concentration [A] vs. time t gives a straight line with slope −k₀.
- The rate constant k₀ has units of mol L⁻¹ s⁻¹ (concentration per unit time).
- Common examples include enzyme-catalysed reactions at saturating substrate concentrations, and reactions on solid catalytic surfaces.
Integrated rate law for a first-order reaction
A first-order reaction is a chemical reaction in which the rate depends on the concentration of only one reactant raised to the first power.
Some examples of first-order reactions:
Let us consider a reaction in which reactant A changes into a product. Let a be the initial concentration of reactant A. After a certain time t, x mol of reactant changes into product.
For a first-order reaction, the rate depends on only one concentration term: Rate ∝ [A]¹
dx/dt = k₁(a − x) … (i)
where k₁ is the rate constant (also called the velocity constant or specific rate of reaction). Equation (i) is the differential rate equation for the first-order reaction.
Rearranging equation (i) to separate variables and integrating both sides (using the standard result ∫dx/(ax+b) = ln(ax+b)/a + C):
∫dx / (a − x) = k₁∫dt
−ln(a − x) = k₁t + C … (ii)
At t = 0, x = 0. Substituting into equation (ii): −ln(a − 0) = k₁ × 0 + C ⟹ C = −ln a.
Substituting the value of C back into equation (ii):
ln a − ln(a − x) = k₁t
ln [a / (a − x)] = k₁t … (iii)
- The rate depends linearly on the concentration of a single reactant.
- The integrated rate equation is logarithmic, giving a straight line when ln[A] is plotted against t.
- The rate constant k₁ has units of s⁻¹ (or min⁻¹, h⁻¹, etc.).
Half-life reaction
At t = t½, [A]t = [A]₀/2. Substituting this boundary condition into the zero-order integrated rate law [A]t = [A]₀ − kt:
k·t½ = [A]₀ − [A]₀/2 = [A]₀/2
t½ = [A]₀ / 2k (zero-order half-life)
For a first-order reaction, substituting [A]t = [A]₀/2 into the natural-log integrated rate law:
ln(1/2) = −k·t½ ⟹ ln(2) = k·t½
t½ = ln(2)/k ≈ 0.693/k (first-order half-life)
First-order reactions have a fixed half-life time that is independent of the initial concentration — this is their key distinguishing feature.
| Kinetic Parameter | Zero-Order Reaction | First-Order Reaction |
|---|---|---|
| Differential Rate Law | Rate = k | Rate = k[A] |
| Integrated Rate Law | [A]t = [A]₀ − kt | [A]t = [A]₀ · e−kt |
| Half-Life Expression | t½ = [A]₀ / (2k) | t½ = 0.693 / k |
| Rate Constant (k) Units | mol L⁻¹ s⁻¹ | s⁻¹ |
| Concentration Dependence | Directly proportional to [A]₀ | Completely independent of [A]₀ |
10 Pseudo-Order & Second-Order Reactions▾
Pseudo-order reaction
A pseudo-order reaction is a reaction in which one reactant is present in large excess, so its concentration remains nearly constant during the reaction. As a result, the rate appears to depend only on the concentration of the other reactant.
A pseudo-first-order reaction is actually a second-order reaction that behaves like a first-order reaction.
So Rate ≈ k′[CH₃COOC₂H₅], where k′ = k[H₂O] = pseudo-first-order rate constant.
Second-order reaction
Rate ∝ [reactant]² — if concentration doubles, rate quadruples.
e.g., 2NO₂ → 2NO + O₂
For a second-order reaction, rate = k[A]². So, units of rate constant, k = mol⁻¹ L s⁻¹
| Overall Order | Units of k |
|---|---|
| Zero order | mol L⁻¹ s⁻¹ |
| First order | s⁻¹ |
| Second order | mol⁻¹ L s⁻¹ |
11 Order and Molecularity of Reaction▾
| Feature | Molecularity | Order |
|---|---|---|
| Definition | No. of particles colliding simultaneously in the rate-determining step | Sum of powers of concentrations in the experimental rate equation |
| Values | Whole numbers only: 1, 2, 3 | Can be 0, 1, 2, or even fractional |
| How determined | From the reaction mechanism (theoretical) | From experimental data (empirical) |
| For complex reactions | Refers to the slowest (rate-determining) step | Overall observed value from the experiment |
📌 Chapter Summary
- Chemical kinetics is the study of reaction rates, the factors that affect them, and reaction mechanisms.
- Rate of reaction = Δ[concentration] / Δtime. Units: mol L⁻¹ s⁻¹.
- Collision theory: Effective collisions require (i) energy ≥ Eₐ and (ii) correct orientation.
- Activation energy (Eₐ): minimum energy needed for a reaction; the activated complex forms at the energy peak.
- Factors increasing rate: increased surface area, concentration, pressure (gases), temperature; adding a catalyst.
- Arrhenius equation: k = Ae⁻⁽Eₐ/RT⁾. Temperature has an exponential effect on k.
- Rate equation: Rate = k[A]ˣ[B]ʸ. Order is determined experimentally, NOT from stoichiometric coefficients.
- Zero order: Rate = k; t½ = [A]₀/2k (half-life decreases over time).
- First order: Rate = k[A]; t½ = 0.693/k (constant half-life — key feature).
- Second order: Rate = k[A]²; k units: mol⁻¹ L s⁻¹.
- A catalyst lowers Eₐ by providing an alternative reaction pathway; it is regenerated.
- Homogeneous catalysis: catalyst in the same phase as reactants. Heterogeneous: different phases.
- Enzymes: biological protein catalysts; highly specific; have optimum temperature and pH; follow the lock-and-key model.
📖 Key Terms Glossary
| Term | Definition |
|---|---|
| Activation Energy (Eₐ) | Minimum energy needed for colliding particles to react. |
| Activated Complex | High-energy, unstable arrangement of atoms at the energy peak. |
| Arrhenius Equation | k = Ae⁻⁽Eₐ/RT⁾; mathematically links rate constant to temperature. |
| Catalyst | Substance increasing reaction rate without being consumed; lowers Eₐ. |
| Collision Theory | A theory that explains reactions occur through effective collisions. |
| Enzyme | Biological protein catalyst; highly specific; has optimum T and pH. |
| Half-Life (t½) | Time for the reactant concentration to fall to half its initial value. |
| Molecularity | Number of particles colliding in the rate-determining elementary step. |
| Order of Reaction | Power to which the concentration is raised in the experimental rate equation. |
| Rate Constant (k) | Proportionality constant in the rate equation; depends on T and Eₐ. |
| Rate Equation | Rate = k[A]ˣ[B]ʸ; experimental relationship between rate and concentrations. |
| Rate-Determining Step | Slowest step in a mechanism; controls the overall reaction rate. |
| Reaction Mechanism | A sequence of elementary steps by which reactants form products. |