Unit 3: Chemical Kinetics

The speed of chemical reactions — how fast reactants become products

3.1 Rate of a Chemical Reaction

Chemical kinetics is the study of reaction rates, mechanisms, and the factors that influence them. While thermodynamics tells us if a reaction is feasible, kinetics tells us how fast it proceeds.

        Average rate: r_av = −Δ[R]/Δt = +Δ[P]/Δt

        Instantaneous rate: r_inst = −d[R]/dt = +d[P]/dt

        Units: mol L⁻¹ s⁻¹ (or atm s⁻¹ for gases)

For a reaction aA + bB → cC + dD, the rate is expressed as:

Rate = −(1/a) Δ[A]/Δt = −(1/b) Δ[B]/Δt = +(1/c) Δ[C]/Δt = +(1/d) Δ[D]/Δt

The negative sign for reactants ensures the rate is a positive quantity (concentration decreases). Rate is divided by stoichiometric coefficients to make it independent of which species is measured.

3.2 Rate Law and Order

The rate law expresses how rate depends on reactant concentrations. It must be determined experimentally — it cannot be predicted from the balanced equation alone.

        Rate law: Rate = k [A]ˣ [B]ʸ

        Order: x + y = overall order (experimental quantity, can be 0, fraction, or any number)

        k = rate constant (specific to each reaction at a given temperature)

Example: Determining Order from Experimental Data

For 2NO(g) + O₂(g) → 2NO₂(g):

Exp	[NO] (mol L⁻¹)	[O₂] (mol L⁻¹)	Initial Rate
1	0.30	0.30	0.096
2	0.60	0.30	0.384 (×4 when [NO] ×2)
3	0.30	0.60	0.192 (×2 when [O₂] ×2)

Doubling [NO] quadruples the rate → order = 2 for NO. Doubling [O₂] doubles the rate → order = 1 for O₂.

Rate = k [NO]² [O₂] → Overall order = 3

Molecularity vs Order

Property	Molecularity	Order
Applicable to	Elementary reactions only	Any reaction
Values	1, 2, or 3 (never 0 or fraction)	0, 1, 2, 3, or fraction
Determined by	Number of molecules in balanced equation	Experiment
Meaning	Simultaneous collisions required	Sum of concentration powers in rate law

For complex reactions, the order is determined by the slowest step (rate-determining step). The molecularity of that step equals the overall order.

3.3 Integrated Rate Equations

Zero Order Reaction

Differential Rate Law

−d[R]/dt = k

Integrated Rate Law

[R] = [R]₀ − kt

Half-Life

t½ = [R]₀ / 2k

Zero order reactions are uncommon but occur on saturated metal surfaces and in some enzyme-catalyzed reactions. Example: decomposition of NH₃ on hot platinum.

First Order Reaction

Differential Rate Law

−d[R]/dt = k[R]

Integrated Rate Law

ln[R] = ln[R]₀ − kt
or [R] = [R]₀ e⁻ᵏᵗ

Half-Life

t½ = 0.693 / k

        Key property of first-order reactions: Half-life is constant — independent of initial concentration. This is why first-order kinetics applies to radioactive decay and many natural processes.
    

Pseudo First Order Reactions

When one reactant is in large excess, its concentration barely changes. The reaction appears first order even though it is technically higher order.

CH₃COOC₂H₅ + H₂O → CH₃COOH + C₂H₅OH
Rate = k [CH₃COOC₂H₅] (water in large excess → [H₂O] ≈ constant)

3.4 Temperature Dependence

Most reactions speed up with increasing temperature. For many reactions, the rate approximately doubles for every 10°C rise.

        Arrhenius Equation: k = A e⁻ᴱᵃ/ᴿᵀ

        Linear form: ln k = −(Eₐ/R)(1/T) + ln A

        Two temperatures: log(k₂/k₁) = Eₐ/2.303R × (T₂−T₁)/(T₁T₂)

Effect of Catalyst

A catalyst provides an alternative reaction pathway with lower activation energy. It does not change ΔG, the equilibrium constant, or the thermodynamic feasibility — it only helps the system reach equilibrium faster.

Catalysts lower Eₐ → more molecules have sufficient energy to react → rate increases. The catalyst is regenerated and not consumed in the overall reaction.

3.5 Collision Theory

According to collision theory, reactant molecules must collide with sufficient energy (≥ Eₐ) and proper orientation for a reaction to occur.

        Rate = P × Zₐᵦ × e⁻ᴱᵃ/ᴿᵀ

        P = steric factor (orientation requirement)

        Zₐᵦ = collision frequency

        e⁻ᴱᵃ/ᴿᵀ = fraction of molecules with energy ≥ Eₐ

Collision theory works well for simple molecules but shows deviations for complex molecules where orientation effects (steric factor) become significant.

3.6 Factors Affecting Rate — Summary

Factor	Effect on Rate	Explanation
Concentration	Increases with ↑[reactant]	More collisions per unit time
Temperature	Increases with ↑T	More molecules exceed Eₐ
Catalyst	Increases rate	Lowers Eₐ via alternative path
Surface area	Increases with ↑ area	More exposed particles for collision

Summary

Chemical kinetics studies reaction rates and their dependence on concentration, temperature, and catalysts. The rate law (Rate = k[A]ˣ[B]ʸ) must be determined experimentally. Order is the sum of concentration powers; molecularity applies only to elementary reactions. Integrated rate equations relate concentration to time for zero and first order reactions. The Arrhenius equation (k = Ae⁻ᴱᵃ/ᴿᵀ) describes temperature dependence. Collision theory explains that effective collisions require sufficient energy and proper orientation. Catalysts lower activation energy without being consumed.