Rate of a Chemical Reaction
Rate = change in concentration per unit time. For A → B: Rate = −d[A]/dt = +d[B]/dt.
Average rate vs instantaneous rate (tangent to concentration-time curve).
Rate Law and Rate Constant
Rate = k[A]ᵐ[B]ⁿ where m, n = order w.r.t. A and B (determined experimentally, not from stoichiometry).
Units of k depend on overall order:
- Zero order: mol L⁻¹ s⁻¹
- First order: s⁻¹
- Second order: L mol⁻¹ s⁻¹
Order vs Molecularity
| Order | Molecularity |
|---|---|
| Experimental | Theoretical (from mechanism) |
| Can be fractional or zero | Always whole number (1, 2, 3) |
| Refers to overall rate law | Refers to elementary step |
Integrated Rate Laws
Zero order: [A] = [A]₀ − kt; t½ = [A]₀/2k
First order: ln[A] = ln[A]₀ − kt; t½ = 0.693/k (independent of concentration)
Second order: 1/[A] = 1/[A]₀ + kt; t½ = 1/(k[A]₀)
Arrhenius Equation
k = A·e^(−Ea/RT)
Taking logarithm: ln k = ln A − Ea/RT
log(k₂/k₁) = (Ea/2.303R) × (1/T₁ − 1/T₂)
A = frequency factor (pre-exponential factor), Ea = activation energy.
Effect of Temperature
Rate doubles/triples for every 10°C rise (thumb rule). More precisely described by Arrhenius equation. A catalyst lowers Ea without being consumed.