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. Only about 1 collision in 600 million carries enough energy to react, and 50 kJ/mol is a modest barrier by the standards of real chemistry.

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.

The chart plots the rate against temperature so the shape of that exponential is visible rather than asserted. Notice how flat it is at low temperature and how sharply it turns: that curve is the whole reason a reaction can be untouchably slow at room temperature and run away at 400 K.