Q.(a) Describe the salient features of the collision theory of reaction rates of bimolecular reactions.

Collision theory explains reaction rates in terms of the fraction of molecular collisions that are both energetic and correctly oriented enough to react; Kohlrausch's law states that ions migrate and contribute to conductivity independently of each other at infinite dilution.

(a) Collision theory of reaction rates (for bimolecular reactions):

Collision theory, developed by Max Trautz and William Lewis, explains the rate of a bimolecular reaction based on the kinetic theory of gases. Its salient features are:

1. For a reaction to occur, reactant molecules must collide with each other. The rate of reaction is proportional to the frequency of collisions (Z) between the reacting species.

2. However, not every collision leads to a reaction — only a small fraction of collisions, called effective collisions, actually result in product formation.

3. A collision is effective only if the colliding molecules possess energy equal to or greater than a certain minimum energy called the threshold energy (i.e., they must have kinetic energy ≥ the activation energy, Ea). The fraction of molecules having this energy is given by the Boltzmann factor $e^{-E_a/RT}$.

4. In addition to sufficient energy, the molecules must also collide with the proper orientation, so that the old bonds can break and new bonds can form correctly. This is accounted for by a steric/probability factor, P.

Combining these factors, the rate of a bimolecular reaction is given by:

$Rate = P \cdot Z_{AB} \cdot e^{-E_a/RT}$

where $Z_{AB}$ is the collision frequency of reactants A and B, $e^{-E_a/RT}$ is the fraction of collisions with sufficient energy, and $P$ is the orientation/steric factor (0 < P ≤ 1).

Thus, effective collisions = (total collisions) × (fraction with enough energy) × (fraction with correct orientation).

(b) Kohlrausch's Law of Independent Migration of Ions:

This law states: "At infinite dilution, when dissociation of the electrolyte is complete, each ion makes a definite contribution towards the molar conductivity of the electrolyte, irrespective of the nature of the other ion with which it is associated, and the molar conductivity at infinite dilution for any electrolyte is the sum of the individual contributions of its constituent ions."

Mathematically, for an electrolyte that dissociates to give $\nu_+$ cations and $\nu_-$ anions:

$\Lambda_m^{\circ} = u_+ \lambda_+^{\circ} + u_- \lambda_-^{\circ}$

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