A reaction can only happen where a reactant molecule physically touches exposed catalyst surface. Splitting a fixed total mass into many small spheres keeps the volume (and mass) the same but multiplies the exposed surface enormously, because surface-to-volume scales as 1/radius:
Total surface area = 3 · V_total / r
(one big block: small SA — many nanoparticles: same V_total, tiny r, huge SA)
- Bulk block — the whole catalyst mass as one solid sphere. Only its outer shell is ever in contact with reactant.
- Nanoparticles — the identical mass divided into many tiny spheres scattered through the chamber, exposing far more total surface for the same material.
- Both scenarios run simultaneously in the background with the same reactant count and the same per-contact reaction chance — only the amount of exposed surface differs.
Industrially this means the same throughput for far less (often expensive, scarce) catalyst material — or dramatically faster reactions for the same catalyst mass.