Learning Objectives
- Understand rate of reaction and factors affecting it
- Learn about rate laws, order, and molecularity
- Derive and apply integrated rate equations for zero and first order
- Study the Arrhenius equation and activation energy
- Understand collision theory and reaction mechanisms
Key Concepts
Rate of Reaction
For aA + bB → cC + dD:
Rate = -(1/a)(d[A]/dt) = -(1/b)(d[B]/dt) = (1/c)(d[C]/dt) = (1/d)(d[D]/dt)
Average rate: Δ[concentration]/Δt. Instantaneous rate: d[concentration]/dt (slope of concentration-time graph).
Factors Affecting Rate
Concentration, temperature, catalyst, nature of reactants, surface area (for heterogeneous reactions).
Rate Law and Order
Rate law: Rate = k[A]ˣ[B]ʸ (experimentally determined).
Order: x + y = overall order. Determined experimentally (not from stoichiometry).
Molecularity: Number of molecules participating in an elementary step. Always a positive integer (1, 2, or 3). Cannot be zero or fractional.
Order can be zero, fractional, or negative. Molecularity applies only to elementary reactions.
Integrated Rate Equations
Zero Order: Rate = k. [A] = [A]₀ - kt. t₁/₂ = [A]₀/(2k). Linear [A] vs t plot.
First Order: Rate = k[A]. ln[A] = ln[A]₀ - kt. k = (2.303/t) log([A]₀/[A]). t₁/₂ = 0.693/k (independent of concentration).
Pseudo-first order: When one reactant is in large excess. Example: hydrolysis of ethyl acetate in water.
Units of k: Zero order: mol L⁻¹ s⁻¹. First order: s⁻¹. Second order: L mol⁻¹ s⁻¹. General: (mol L⁻¹)^(1-n) s⁻¹.
Temperature Dependence
Arrhenius Equation: k = Ae^(-Ea/RT)
ln k = ln A - Ea/RT. Plot of ln k vs 1/T gives straight line with slope = -Ea/R.
Two-temperature form: log(k₂/k₁) = (Ea/2.303R)(1/T₁ - 1/T₂)
A = pre-exponential factor (frequency factor). Ea = activation energy.
Rule of thumb: rate roughly doubles for every 10°C rise (temperature coefficient ≈ 2-3).
Collision Theory
For reaction to occur: molecules must collide with sufficient energy (≥ Ea) and proper orientation.
Rate = Z_AB × e^(-Ea/RT) × P (P = steric/probability factor).
Activation energy (Ea): Minimum energy above average that reactants must have to react.
Catalyst: Lowers activation energy by providing an alternative pathway. Increases rate without being consumed.
Summary
Chemical kinetics studies reaction rates and mechanisms. Rate laws are determined experimentally and define the order of reaction. Integrated rate equations allow calculation of concentrations at any time and half-life. The Arrhenius equation relates rate constant to temperature through activation energy. Catalysts lower Ea and increase reaction rate.
Important Terms
- Rate Constant (k): Proportionality constant in rate law
- Order: Sum of powers of concentration in rate law
- Molecularity: Number of reacting species in elementary step
- Half-life: Time for concentration to reduce by half
- Activation Energy: Minimum energy barrier for reaction
- Catalyst: Substance that changes rate without being consumed
Quick Revision
- Zero order: [A] = [A]₀ - kt; t₁/₂ = [A]₀/2k
- First order: k = (2.303/t) log([A]₀/[A]); t₁/₂ = 0.693/k
- Arrhenius: k = Ae^(-Ea/RT); ln(k₂/k₁) = (Ea/R)(1/T₁ - 1/T₂)
- Order: experimental; Molecularity: theoretical (elementary only)
- Catalyst lowers Ea; does not change ΔH or equilibrium
- Rate ≈ doubles every 10°C rise