Collision Theory of Chemical Reactions — Revision Notes

⚡ 30-Second Revision

Postulates: — Collisions, $E_a$, Proper Orientation.
Rate Constant: — $k = P Z_{AB} e^{-E_a/RT}$
$Z_{AB}$ (Collision Frequency): — Total collisions per unit volume per unit time. $\propto \text{conc.}$, $\propto \sqrt{T}$.
$E_a$ (Activation Energy): — Minimum energy for effective collision.
P (Steric Factor): — Probability of correct orientation ($0 < P \le 1$).
Boltzmann Factor ($e^{-E_a/RT}$): — Fraction of molecules with energy $\ge E_a$.
Arrhenius Relation: — $A = P Z_{AB}$.
Catalyst: — Lowers $E_a$, increases $e^{-E_a/RT}$, speeds up reaction.

2-Minute Revision

Collision theory explains reaction rates based on molecular collisions. For a reaction to occur, reactant molecules must collide. However, only 'effective collisions' lead to product formation. An effective collision requires two conditions: first, the colliding molecules must possess energy equal to or greater than the **activation energy ($E_a$)**, which is the minimum energy barrier.

Second, they must collide with the proper orientation, ensuring reactive sites align. The rate constant ($k$) is given by $k = P Z_{AB} e^{-E_a/RT}$, where $P$ is the steric factor (orientation probability), $Z_{AB}$ is the collision frequency, and $e^{-E_a/RT}$ is the fraction of molecules with sufficient energy.

Increasing temperature increases reaction rate because it boosts both collision frequency and, more significantly, the fraction of energetic molecules. Catalysts accelerate reactions by lowering $E_a$, thereby increasing the number of effective collisions.

Collision theory provides a physical interpretation for the Arrhenius pre-exponential factor ($A = P Z_{AB}$).

5-Minute Revision

Collision theory is a fundamental model explaining chemical reaction rates by considering molecular collisions. It posits three main requirements for a reaction: 1) Reactant molecules must collide. 2) Colliding molecules must possess a minimum energy, called **activation energy ($E_a$)**, to overcome the energy barrier.

3) They must collide with the proper orientation for reactive sites to interact. Collisions meeting both energy and orientation criteria are termed 'effective collisions' and lead to product formation.

The rate constant ($k$) for a bimolecular reaction is expressed as $k = P Z_{AB} e^{-E_a/RT}$. Let's break this down:

$Z_{AB}$ (Collision Frequency): — This is the total number of collisions between reactants A and B per unit volume per unit time. It increases with concentration and temperature (as molecules move faster).
$e^{-E_a/RT}$ (Boltzmann Factor): — This exponential term represents the fraction of molecules that have kinetic energy equal to or greater than $E_a$ at a given temperature $T$. A small increase in temperature leads to a significant increase in this fraction, explaining the strong temperature dependence of reaction rates.
$P$ (Steric Factor): — This dimensionless factor (between 0 and 1) accounts for the proper orientation requirement. For complex molecules, P can be very small, meaning only a few collisions have the correct alignment.

Example: If a reaction has $E_a = 60 \text{ kJ/mol}$ at $300 \text{ K}$, the Boltzmann factor $e^{-E_a/RT} = e^{-60000 / (8.314 \times 300)} \approx e^{-24.06} \approx 3.2 \times 10^{-11}$. If temperature increases to $310 \text{ K}$, $e^{-60000 / (8.314 \times 310)} \approx e^{-23.28} \approx 7.7 \times 10^{-11}$. The fraction of effective molecules more than doubles with just a $10 \text{ K}$ rise.

Collision theory provides a theoretical basis for the empirical Arrhenius equation ($k = A e^{-E_a/RT}$), identifying the Arrhenius pre-exponential factor $A$ with $P Z_{AB}$. Catalysts accelerate reactions by lowering $E_a$, which exponentially increases the fraction of effective collisions, thus speeding up the reaction without affecting equilibrium. Limitations include the hard-sphere model and the empirical nature of P.

Prelims Revision Notes

Collision Theory of Chemical Reactions

1. Basic Postulates:

* Collision: Reactant molecules must collide for a reaction to occur. * **Activation Energy ($E_a$):** Colliding molecules must possess minimum energy ($E_a$) to react. This is the energy barrier. * Proper Orientation (Steric Factor, P): Molecules must collide with the correct spatial orientation for reactive sites to interact.

2. Effective Collisions: Collisions that satisfy both $E_a$ and proper orientation criteria, leading to product formation.

3. Rate Constant Expression: For a bimolecular reaction, the rate constant $k$ is given by:

$$k = P Z_{AB} e^{-E_a/RT}$$

* **$Z_{AB}$ (Collision Frequency):** Total number of collisions per unit volume per unit time.

* Increases with concentration (more molecules, more collisions). * Increases with temperature (molecules move faster, more collisions). $Z_{AB} \propto \sqrt{T}$. * **$e^{-E_a/RT}$ (Boltzmann Factor):** Fraction of molecules with energy $\ge E_a$.

* Increases exponentially with temperature (most significant factor for rate increase). * Decreases exponentially with $E_a$ (higher $E_a$, fewer energetic molecules). * **$P$ (Steric Factor/Probability Factor):** Accounts for proper orientation.

$0 < P \le 1$. * For simple molecules, P is close to 1. * For complex molecules, P can be very small ($<1$), indicating stringent orientation requirements.

4. Relationship with Arrhenius Equation:

* Arrhenius Equation: $k = A e^{-E_a/RT}$ * Comparison: $A = P Z_{AB}$. * The Arrhenius pre-exponential factor (A) represents the frequency of effectively oriented collisions.

5. Effect of Temperature:

* Increased temperature $\implies$ increased $Z_{AB}$ (minor effect). * Increased temperature $\implies$ exponentially increased $e^{-E_a/RT}$ (major effect). * Overall: Reaction rate increases significantly with temperature.

6. Effect of Catalyst:

* Catalyst lowers $E_a$ by providing an alternative reaction pathway. * Lower $E_a$ $\implies$ higher $e^{-E_a/RT}$ $\implies$ more effective collisions $\implies$ faster reaction. * Catalyst does NOT affect $Z_{AB}$ or equilibrium constant.

7. Limitations:

* Treats molecules as hard spheres (simplification). * Cannot theoretically calculate P from first principles (P is often empirical). * Primarily applicable to simple bimolecular reactions.

Key Formulas to Remember:

$k = P Z_{AB} e^{-E_a/RT}$
$A = P Z_{AB}$
$\ln \frac{k_2}{k_1} = \frac{E_a}{R} \left( \frac{1}{T_1} - \frac{1}{T_2} \right)$ (from Arrhenius equation, often used in problems related to collision theory)

Vyyuha Quick Recall

C.E.O. for Reactions:

Collisions must happen. Energy must be sufficient (Activation Energy). Orientation must be correct (Steric Factor).

*Remember: C.E.O. makes the company (reaction) run effectively!*