Q.ix. What fraction of molecules in a gas at 300 K collide with an energy equal to activation energy of 50 kJ/mol ? (2 $\times$ 10$^{-9}$)

Collision theory explains reaction rates at the molecular level: reactant molecules must collide to react, but the total collision rate in a gas is vastly (many powers of ten) larger than the observed reaction rate, so most collisions fail. Two conditions must BOTH be met for a collision to succeed: (1) the colliding molecules must together possess kinetic energy equal to or greater than the activation energy $E_a$ -- the fraction that qualify is $f=e^{-E_a/RT}$, e.g. only about $7\times10^{-14}$ of collisions at 298 K with $E_a=75$ kJ/mol; and (2) beyond the simplest molecules, the colliding species must also be correctly ORIENTED relative to each other so the react …