Which of the following statement(s) is (are) not associated with \(S_N1\) reaction:

(A) Rearrangement is possible.

(B) The rate is affected by solvent polarity.

(C) The strength of nucleophile is involved in rate determining step.

(D) The reaction order of alkyl halides is tertiary > secondary > primary.

(E) Proceeds with complete inversion of configuration.

Choose the correct answer from the options given below:

(C), (E) Only

The correct answer is option 4. (C), (E) Only.

Let us analyze each statement in relation to \(S_N1\) (Substitution Nucleophilic Unimolecular) reactions:

(A) Rearrangement is possible. This statement is associated with \(S_N1\) reactions. In \(S_N1\) reactions, the leaving group leaves first, forming a carbocation intermediate. Rearrangements can occur in the carbocation intermediate, leading to the formation of more stable carbocations through hydride or alkyl shifts.

(B) The rate is affected by solvent polarity. This statement is associated with \(S_N1\) reactions. \(S_N1\) reactions are typically favored in polar protic solvents because these solvents stabilize the carbocation intermediate through solvation. Therefore, solvent polarity affects the rate of \(S_N1\) reactions.

(C) The strength of the nucleophile is involved in the rate-determining step.This statement is not associated with \(S_N1\) reactions. In \(S_N1\) reactions, the rate-determining step involves the formation of the carbocation intermediate, not the nucleophilic attack. Since the nucleophile attacks after the formation of the carbocation, its strength does not affect the rate of the reaction.

(D) The reaction order of alkyl halides is tertiary > secondary > primary. This statement is associated with \(S_N1\) reactions. \(S_N1\) reactions proceed via the formation of a carbocation intermediate. Tertiary alkyl halides form more stable carbocations than secondary alkyl halides, which, in turn, form more stable carbocations than primary alkyl halides. Therefore, the reactivity order in \(S_N1\) reactions is tertiary > secondary > primary alkyl halides.

(E) Proceeds with complete inversion of configuration. This statement is not associated with \(S_N1\)reactions. \(S_N1\) reactions proceed with racemization or retention of configuration, depending on the reaction conditions and the structure of the starting material. Complete inversion of configuration is a characteristic of \(S_N2\) reactions, not \(S_N1\) reactions.

Based on the analysis:

The statement(s) not associated with \(S_N1\) reaction is/are: (C) The strength of the nucleophile is involved in the rate-determining step, and (E) Proceeds with complete inversion of configuration.

So, the correct answer is: (4) (C), (E) Only.