Collision Theory
Molecular basis of reaction rates
Understanding Collision Theory
Collision theory, developed by Max Trautz and William Lewis in the early 1900s, provides a molecular-level explanation for chemical reaction rates by treating reactions as the result of molecular collisions. This theory revolutionized chemical kinetics by connecting macroscopic observables (reaction rates, activation energies, rate constants) to microscopic events—individual molecule collisions. According to collision theory, for a reaction to occur, reactant molecules must collide with sufficient energy and proper spatial orientation to break existing bonds and form new ones.
The elegance of collision theory lies in its ability to explain temperature and concentration effects on reaction rates through fundamental molecular behavior. Higher temperatures increase molecular speeds, leading to more frequent and more energetic collisions. Higher concentrations place more molecules in a given volume, increasing collision frequency. However, not all collisions result in reactions—only those meeting specific energy and orientation criteria contribute to product formation, making reaction rates far slower than simple collision frequencies would suggest.
While collision theory successfully predicts trends and provides qualitative insights, quantitative predictions often require modifications. The steric factor (p), which accounts for orientation requirements, is difficult to calculate from first principles and must often be determined experimentally. Despite limitations for complex reactions involving multiple steps or large molecules, collision theory remains fundamental to understanding reaction kinetics and forms the conceptual foundation for more sophisticated theories like transition state theory and molecular dynamics simulations.
Rate Expression from Collision Theory
Rate = Z × f × p
Collision frequency × energy fraction × orientation factor
Z = collision frequency
Collisions per second per unit volume
f = e^(-Ea/RT)
Fraction with E ≥ Ea
p = steric factor
Proper orientation probability (0 < p ≤ 1)
Key Insights:
- Z depends on molecular speeds (∠√T) and concentrations ([A][B])
- f is the Boltzmann factor from Maxwell-Boltzmann energy distribution
- p accounts for molecular geometry; p ≈ 1 for atoms, p << 1 for large molecules
- Rate Law emerges: Rate = k[A][B] where k = Z × p × e^(-Ea/RT)
- Explains Arrhenius equation: A (pre-exponential factor) = Z × p
Three Requirements for Successful Reaction
1. Molecules Must Collide
Reactant molecules must physically encounter each other. Collision frequency Z depends on:
- Concentration: Z ∠[A][B] (more molecules → more collisions)
- Temperature: Z ∠√T (faster molecules → more frequent collisions)
- Molecular size: Larger collision cross-sections increase Z
Example: At room temperature, gas molecules at 1 atm collide ~10²⹠times per second per liter. If all collisions reacted, reactions would be instantaneous!
2. Sufficient Energy (E ≥ Ea)
Collisions must provide enough energy to overcome the activation energy barrier. The fraction of molecules with sufficient energy is:
f = e^(-Ea/RT)
- Derived from Maxwell-Boltzmann distribution of molecular energies
- For Ea = 50 kJ/mol at 298 K: f ≈ 10â»â¹ (only 1 in a billion collisions!)
- Temperature effect: Increasing T by 10°C roughly doubles f (rule of thumb)
- Lower Ea → larger f → faster reaction (catalysts work by lowering Ea)
3. Proper Orientation (Steric Factor p)
Reactive sites must align correctly during collision. The steric factor quantifies this geometric requirement:
- p ≈ 1: Spherical atoms (H• + I• → HI) have no orientation restriction
- p ~ 0.01-0.1: Small molecules (Hâ‚‚ + Iâ‚‚) need moderate alignment
- p ~ 10â»â¶: Large complex molecules (enzymes, polymers) have strict geometry
Example: For CH₃Br + OH⻠→ CH₃OH + Brâ», hydroxide must attack from the backside (SN2 mechanism), giving p ~ 0.001. Frontal or side collisions don't react.
Detailed Example: Calculating Reaction Rate
Problem: For H₂(g) + I₂(g) → 2HI(g) at 700 K, estimate the rate given:
Given Data:
- [Hâ‚‚] = [Iâ‚‚] = 0.01 M
- Collision frequency Z = 10¹ⰠL·molâ»Â¹Â·sâ»Â¹ (typical for gases)
- Activation energy Ea = 165 kJ/mol
- Steric factor p ≈ 0.16
- R = 8.314 J·molâ»Â¹Â·Kâ»Â¹
Step 1: Calculate f (energy fraction)
f = e^(-Ea/RT) = exp(-165,000 J·molâ»Â¹ / (8.314 × 700))
f = exp(-28.3) = 5.1 × 10â»Â¹Â³
Only 0.000000000051% of collisions have sufficient energy!
Step 2: Calculate rate constant k
k = Z × p × f = (10¹â°) × (0.16) × (5.1 × 10â»Â¹Â³) L·molâ»Â¹Â·sâ»Â¹
k = 8.2 × 10â»â´ L·molâ»Â¹Â·sâ»Â¹
Step 3: Calculate reaction rate
Rate = k[Hâ‚‚][Iâ‚‚] = (8.2 × 10â»â´) × (0.01) × (0.01)
Rate = 8.2 × 10â»â¸ M/s
Interpretation:
Despite ~10²⹠collisions/second, only tiny fraction (f × p ≈ 10â»Â¹Â³) are successful. This explains why reactions with high activation energies are slow even with many collisions occurring!
Temperature Effect on Reaction Rate
Increasing temperature affects both Z and f, but the energy fraction f dominates:
Effect on Z (Small)
Z ∠√T. Increasing from 300 K to 310 K (10°C rise):
Z increases by √(310/300) ≈ 1.017 (1.7% increase)
Effect on f (Large)
f = e^(-Ea/RT). For Ea = 50 kJ/mol, increasing 300 K → 310 K:
f increases by factor of ~1.9 (90% increase!)
Rule of Thumb:
For many reactions near room temperature, rate doubles for every 10°C temperature increase. This \"rate doubling\" rule comes primarily from the exponential sensitivity of f to temperature, not from collision frequency changes.
Connection to Arrhenius Equation
Collision theory provides molecular interpretation of the empirical Arrhenius equation:
k = A e^(-Ea/RT)
Pre-exponential factor A: A = Z × p (collision frequency × steric factor)
Exponential term: e^(-Ea/RT) = f (energy fraction)
Typical A values: 10â¸-10¹ⴠL·molâ»Â¹Â·sâ»Â¹ depending on molecular complexity
Physical meaning: A represents the maximum possible rate constant if all collisions had sufficient energy (f = 1)
This connection validates collision theory: experimentally measured A values from Arrhenius plots generally agree with Z × p estimates, confirming the molecular collision model.
Applications & Real-World Significance
1. Catalysis Explanation
Catalysts lower Ea, dramatically increasing f without changing Z or p. A 20 kJ/mol reduction in Ea at 300 K increases f by factor of ~3000, explaining why catalysts accelerate reactions millions of times.
2. Food Preservation
Refrigeration slows spoilage by reducing f. At 4°C vs 25°C, spoilage reactions (Ea ~ 50 kJ/mol) proceed ~4× slower, extending shelf life proportionally.
3. Atmospheric Chemistry
Ozone depletion by CFCs requires specific collision geometries (small p ~10â»â¶) and moderate Ea (~20 kJ/mol). Collision theory predicts reaction rates at stratospheric temperatures (220 K), crucial for environmental modeling.
4. Enzyme Kinetics
Enzyme-substrate binding has extremely low p (~10â»â¹) due to precise active site geometry. Collision theory explains why enzyme concentrations must be carefully controlled in biochemical pathways.
Limitations & Important Notes
Works Best for Simple Reactions
Collision theory gives reasonable predictions for elementary gas-phase reactions (atoms, small molecules). For complex multi-step reactions or solution-phase chemistry, more sophisticated models (transition state theory, Marcus theory) are needed.
Steric Factor p is Hard to Predict
Calculating p from molecular structure alone is nearly impossible without detailed computational chemistry. p is usually determined by comparing experimental k values with calculated Z × f, making it a semi-empirical parameter.
Ignores Quantum Effects
Collision theory treats molecules as classical particles. Quantum tunneling can allow reactions even when E < Ea, particularly for light atoms like hydrogen. At very low temperatures, quantum effects dominate and collision theory fails.
Pro Tip: Order-of-Magnitude Estimates
Use collision theory for quick estimates: Z ~ 10¹ⰠL·molâ»Â¹Â·sâ»Â¹, calculate f from Ea, assume p ~ 0.1 for simple molecules, p ~ 10â»â´ for complex ones. This gives k within 2-3 orders of magnitude—useful for feasibility assessments!