The correct expression of the rate of the reaction according to the collision theory is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(PZ_{AB} e^{-Ea/RT}\)
The collision theory treats molecules as hard spheres that react only when they collide. Three things decide the rate of a bimolecular reaction \( \ce{A + B -> products} \):
the collision frequency \( Z_{AB} \), the number of collisions per second per unit volume;
the fraction of collisions with energy equal to or greater than the activation energy, \( e^{-E_a/RT} \);
the steric factor P, for proper orientation.
Putting the three together:
\( \displaystyle \text{Rate} = P\,Z_{AB}\,e^{-E_a/RT} \)
Why the other options are incorrect
Option (1) \(Z_{AB} e^{-Ea/RT}\) — Incorrect. This counts every sufficiently energetic collision as effective and ignores orientation. It works for atoms and simple molecules but overestimates the rate for complex molecules.
Option (3) \(\frac{-Ea}{RT}\) — Incorrect. This is only the exponent, a pure number; it is not a rate.
Option (4) \(Pe^{-Ea/RT}\) — Incorrect. This leaves out the collision frequency; without collisions there is no reaction, so \( Z_{AB} \) must appear.
NCERT (2026-27 edition):
Collision Theory of Chemical Reactions – …
