OPOpenPithMake curiosity visibleChemistry lab / Microscopic world

About this lab

One reaction box, six topics: how molecules collide their way into a reaction.

A reaction happens at the moment molecules collide. The hit must be hard enough: the energy along the line of centres must clear the activation energy. It must also be aimed: the reactive ends must face each other. Temperature decides how many molecules hit hard enough; concentration and pressure decide how often they meet. In a reversible reaction both directions run all the time.

The particles in the box come from a two-dimensional hard-disc simulation with a fixed seed; readings, curves and flashes all come from the same model. How catalysts lower the activation energy is in the Catalyst lab.

Six findings

Six findings

  • Effective collisions: the activation energy for HI decomposition is about 184 kJ/mol. With 250 kJ/mol of relative energy and an aim offset of 0.6, only 160 kJ/mol lies along the line of centres, so the molecules bounce. With H facing I they never react, however hard they hit.
  • Temperature: with Ea = 8 kJ/mol, about 4.0 % of molecules are activated at 300 K and 20.1 % at 600 K. Heating mainly fattens the tail of the distribution; it does not speed up every molecule.
  • Concentration and pressure: halving the volume at constant temperature at least doubles the collision rate; the share of energetic collisions stays the same, about 9 %.
  • Reaching equilibrium: at 298 K with 40 mmol/L counted as NO₂, either starting side ends at [NO₂] = 9.5 mmol/L and [N₂O₄] = 15.2 mmol/L, Kc ≈ 169 L/mol. At equilibrium the forward and reverse rates are equal and neither is zero.
  • Shifting equilibrium: halving the volume sends [NO₂] from 9.5 straight to 19.0 mmol/L, then down to 14.0 mmol/L; heating to 348 K raises it to 28.4 mmol/L; cooling to 273 K lowers it to 3.8 mmol/L.
  • Chain reaction: no HCl forms in the dark. Each initiation makes about 24.5 HCl in weak light and about 5.1 in strong light. Every mole of HCl releases 92.3 kJ.

Model and sources

Model and sources

  • Particles: equal-mass hard discs in two dimensions, fixed seed and fixed step (1/240 s); a frame is stored every 1/30 s and seeking only interpolates. Speeds are slowed enormously for display.
  • Reaction rule: the relative kinetic energy along the line of centres, ½μu², exceeds Ea and the reactive end of A faces B (P = ½). In two dimensions the share of collisions above Ea is exactly e^(−Ea/RT); collision theory and the particle count are checked against each other.
  • The box uses Ea = 8 kJ/mol (a teaching assumption): real activation energies are often 50–200 kJ/mol and would need hundreds of millions of collisions per reaction. The HI collision topic uses the real 184 kJ/mol.
  • Equilibrium: standard enthalpies and Gibbs energies of NO₂ and N₂O₄ from the NBS tables; Kp extrapolated with van ’t Hoff (ΔH taken as constant); k_r follows Arrhenius with Ea = 54 kJ/mol, and the time scale is compressed about 10⁶ times (teaching assumption). Events in the box are drawn by stochastic simulation with a fixed seed.
  • Chain reaction: the rate constants of the five elementary steps are teaching assumptions that keep only the real ordering; one visible molecule stands for 1/60 mol. The visible count is not a threshold for a real explosion.

check:kinetics recomputes every reading and every number in these findings from the model.

Back to chemistry ↑