Find the rate of reaction

Question: KI in acetone undergoes SN² reaction with each of P, Q, R and S. The rates of reaction vary as:

a)    P > Q > R > S

b)   S > P > R > Q

c)    P > R > Q > S

d)   R > P > S > Q

Solution: P,Q, R and S are alkyl halide. When any of them reacts with KI in the presence of acetone, alkyl iodide is formed. This is also known as Finkelstein reaction.

 In this reaction (I-) which is a nucleophile, replaces (Cl-), thus it is known as a nucleophilic substitution reaction. Since, in the reaction one bond is broken and one bond is formed in one step, it is called SN2 reaction (substitution nucleophilic bimolecular reaction).

The rate of SN2 reaction involves an interaction between nucleophile and the organic substrate. It can be described as:

rate = k [Nu][R-LG]. 

Where, Nu is nucleophile which is I- while [R-LG] is RX which are P, Q, R and S.

The relative reactivity for SN2 reaction in the given structure is:

According to this the correct option is (b).