Q.(a) Describe the salient features of the Collision Theory of reaction rates of bimolecular reactions.

(a) Collision theory explains reaction rate in terms of the frequency of effective collisions (sufficient energy plus proper orientation) between reacting molecules. (b) Kohlrausch's law states that the limiting molar conductivity of an electrolyte is the sum of the independent contributions of its constituent ions, and it lets us calculate Lambda-infinity for weak electrolytes.

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

Collision theory, developed by Max Trautz and William Lewis, states that:

1. For a chemical reaction to occur, reactant molecules/atoms/ions must collide with one another.
2. However, not all collisions lead to a reaction — only a fraction of the total collisions, called effective collisions, result in product formation.
3. A collision is effective only if it satisfies TWO conditions simultaneously:
   • The colliding molecules must possess energy equal to or greater than a certain minimum energy called the threshold energy; equivalently, the molecules must have kinetic energy at least equal to the activation energy (Ea) needed to break existing bonds.
   • The molecules must collide with the proper orientation, so that the reacting atoms are correctly aligned to form new bonds (this is captured by the steric/probability factor, P).

For a simple bimolecular reaction A + B -> Products, the rate is expressed as:

Rate = P x Z(AB) x e^(-Ea/RT)

where Z(AB) is the collision frequency (number of collisions per unit time per unit volume) of A and B, e^(-Ea/RT) is the fraction of collisions having energy equal to or greater than Ea (from the Boltzmann/Arrhenius distribution), and P is the steric/probability factor accounting for orientation requirements.

This theory correctly predicts that reaction rate increases with temperature (more molecules exceed Ea) and explains why the Arrhenius equation, k = A e^(-Ea/RT), holds, with A related to P x Z(AB).

(b) Kohlrausch's Law of independent migration of ions:

Kohlrausch's law states that at infinite dilution, when dissociation of the electrolyte is complete, each ion migrates independently of its co-ion and makes its own definite contribution to the total molar conductivity of the electrolyte, regardless of the nature of the other ion it is associated with.

Mathematically, for an electrolyte that dissociates to give ν+ cations and ν- anions:

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