Explain briefly the collision theory of bimolecular reactions.

Explanation

(i) Collision theory is based on the kinetic theory of gases. According to this theory, chemical reaction occurs as a result of collisions between the reacting molecules.
(ii) Let us understand this theory by considering the following reaction.
`A_(2)(g)+B_(2)(g)rarr 2AB(g)`

(iii) If we consider that, the reaction between `A_(2)` and `B_(2)` molecules proceeds through collisions between them, then the rate would be proportional to the number of collisions per second.
(iv) Rate `prop` number of molecules colliding per litre per second (collision rate).
(v) The number of collisions is directly proportional to the concentraction of both `A_(2)` and `B_(2)`.
Collision rate `prop [A_(2)][B_(2)]`
Collision rate `= Z [A_(2)][B_(2)]`
(vi) Where, Z is a constant
The collision rate in gases can be calculated from kinetic theory of gases.
(vii) For a gas at room temperature (298 K) and 1 atm pressure, each molecule undergoes approximately `10^(9)` collisions per second, 1 collision in `10^(-9)` second.
(viii) Thus, if every collision resulted in reaction, the reaction would be complete in `10^(-9)` second. In actual practice this does not happen.
(ix) It implies that all collisions are not effective to lead to the reaction. In order to react, the colliding molecules must possess a minimum energy called activation energy.
(x) The molecules that collide with remain intact and no reaction occurs.
(xi) Fraction of effective collisions (f) is given by the following expression
`f=e^((-E_(2))/(RT))`
(xii) To understand the magnitude of collision factor (f), Let us calculate the collision factor (f) for a reaction having activation energy of `100 "kJ mol"^(-1)` at 300 K.
`-((100xx10^(3)"J mol"^(-1))/(8.314 "J K"^(-1)mol^(-1)xx300 K))`
f = e
`f=e^(-40)~~ 4xx10^(-18)`
(xiii) Thus, out of `10^(18)` collisions only four collisions are sufficiently energetic to convert reactants to products.
(xiv) This fraction of collisions is further reduced due to orientation factor i.e., even if the reactant collide with sufficient energy, they will not reactunless the orientation of the reactant molecules is suitable for the formation of the transition state.
(xv) The figure illustrates the importance of proper alignment of molecules which leads to reaction.

(xvi) The fraction of effective collisions (f) having proper orientation is given by the steric factor p.
`rArr "Rate " = p xx e^((-Ea)/(RT))xx Z[A_(2)][B_(2)]" "` ....(1)
As per the rate law,
Rate `= k [A_(2)][B_(2)] " "` ....(2)
Where k is the rate constant
On comparing equation (1) and (2), the rate constant k is
`k=p Z e^((-Ea)/(RT))`