1. Postulates of Collision Theory
Formulated by Max Trautz and William Lewis, collision theory accounts for reaction rates based on molecular encounters:
- Collision Frequency ($Z$): Total number of collisions per unit volume per second. Concentration or pressure increases $Z$.
- Energy Factor ($e^{-E_a/RT}$): Fraction of molecules possessing threshold kinetic energy ($E \ge E_a$).
- Orientation Factor ($P$ or steric factor): Spatial configuration during impact must align correctly for bond rearrangement.
Rate = $P \cdot Z_{AB} \cdot e^{-E_a / RT}$
2. Arrhenius Equation & Temperature Dependence
Quantifies how the rate constant ($k$) varies with absolute temperature ($T$) and activation energy ($E_a$):
$k = A \cdot e^{-E_a / RT}$
High-Yield JEE/NEET Points:
- Two-Temperature Form: $\log\left(\frac{k_2}{k_1}\right) = \frac{E_a}{2.303 R} \left(\frac{T_2 - T_1}{T_1 T_2}\right)$
- Temperature Coefficient: Rate constant typically doubles or triples for every 10 K rise due to exponential growth in active molecules.
- Graphical Interpretation: Slope of $\ln k$ versus $1/T$ equals $-E_a/R$, and intercept yields $\ln A$.
3. Catalysts & Activation Energy Barriers
A catalyst alters reaction velocity without being consumed by offering an alternative pathway of lower activation energy.
- Positive Catalyst: Lowers $E_a$, allowing a substantially larger fraction of molecules to successfully react at identical temperatures.
- Equilibrium Constant ($K_c$): Unaffected by catalysts because forward and backward activation barriers are reduced equally; equilibrium is reached faster, not shifted.
$E_a \text{ (catalyzed)} < E_a \text{ (uncatalyzed)}$