For the reaction

The correct statement is

The given reaction is the Finkelstein reaction, which proceeds through an $$S_N2$$ (bimolecular nucleophilic substitution) mechanism.

In this reaction, an alkyl bromide ($RCH_2Br$) reacts with an iodide ion ($I^-$) in the presence of acetone to form an alkyl iodide ($RCH_2I$).

Consider each statement individually.

For option (C):

Initially, the reactants consist of a neutral alkyl halide and a localized iodide ion ($I^-$), where the entire negative charge resides on a single iodine atom.

During the $$S_N2$$ reaction, the nucleophile attacks the carbon atom while the leaving group departs simultaneously, producing the transition state

$$[I^{\delta-}\cdots CH_2(R)\cdots Br^{\delta-}]^{\ddagger}.$$

In this transition state, the negative charge is distributed over the incoming iodine atom, the central carbon atom, and the leaving bromine atom rather than being localized on a single atom.

As a result, the transition state has a lower charge density and is therefore less polar than the isolated iodide ion.

Hence, statement (C) is correct.

For option (A):

In the Finkelstein reaction, acetone dissolves sodium iodide but not sodium bromide.

As the reaction proceeds,

$$NaBr$$

precipitates out of the solution, removing $$Br^-$$ ions from the reaction mixture.

Therefore, $$Br^-$$ cannot effectively act as a competing nucleophile.

Hence, statement (A) is incorrect.

For option (B):

Acetic acid is a polar protic solvent.

Polar protic solvents strongly solvate nucleophilic anions such as $$I^-$$ through hydrogen bonding, significantly reducing their nucleophilicity and slowing the $$S_N2$$ reaction.

The Finkelstein reaction requires a polar aprotic solvent such as acetone.

Hence, statement (B) is incorrect.

For option (D):

Acetone is a polar aprotic solvent and does not strongly solvate anions because it cannot form hydrogen bonds with them.

Moreover, the rate-determining step involves a transition state rather than freely solvated ions.

Therefore, the statement that the solvent solvates the ions formed in the rate-determining step is incorrect.

Hence, statement (D) is incorrect.

Therefore, the only correct statement is

(C) The transition state is less polar than the iodide ion.