Collision Theory Calculator

Collision theory explains why not every molecular collision leads to a chemical reaction. Two requirements must both be met: the collision must have enough energy (at least the activation energy Ea), and the molecules must be oriented correctly (the steric requirement).

The reaction rate per unit volume is:

r = p · Z · e^(-Ea/RT)

where:

• Z = collision frequency (collisions per m³ per second, from kinetic molecular theory)
• p = steric factor (fraction of collisions with correct geometry, typically 0.01 to 1)
• e^(-Ea/RT) = Boltzmann factor (fraction of collisions with sufficient energy)
• R = 8.314 J/(mol·K), T = temperature in Kelvin

The Boltzmann factor e^(-Ea/RT) is the key temperature-dependent term. At 298 K with Ea = 50 kJ/mol: exp(-50000 / (8.314 × 298)) ≈ exp(-20.2) ≈ 1.7×10⁻⁹. This means only about 1 in 600 million collisions has enough energy to react — even for a relatively modest activation barrier.

Raising temperature from 298 K to 308 K (a 10-degree increase) roughly doubles the rate for many reactions. This is because the exponential term changes more steeply at lower temperatures.

The steric factor p accounts for the fact that molecules must collide in the right orientation. Linear molecules like CO₂ reacting end-on have p ≈ 0.001. Spherical atoms reacting have p close to 1. For complex organic reactions, p can be as low as 10⁻⁸.

The collision frequency Z comes from kinetic theory: Z = σ·(8kT/πμ)^(1/2)·nA·nB, where σ is the collision cross-section, μ is the reduced mass, and nA, nB are number densities. For simplicity, enter Z directly here or use a typical value from your data.