Question

Which one is an INCORRECT statement with regard to the following reaction?

• A. The reaction rate decreases upon changing the solvent from ethyl alcohol to 1:1 mixture of ethyl alcohol and water.
• B. The reaction rate does not change upon increasing the concentration of hydroxide ion.
• C. The rate determining step is the dissociation of tert-butylbromide.
• D. The reaction rate is proportional to the concentration of tert-butylbromide.

Hint:

For $\text{S}_{\text{N}}1$ reactions:
Rate $\propto$ solvent polarity. More polar solvent = Faster ionization = Higher rate!
For $\text{S}_{\text{N}}2$ reactions:
Polar aprotic solvents (like acetone, DMSO) are preferred because they do not solvate and "cage" the nucleophile.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The reaction involves tert-butyl bromide (a tertiary alkyl halide) and a hydroxide ion in a polar protic solvent.
Tertiary alkyl halides undergo nucleophilic substitution via the $S_{N1$ mechanism} (unimolecular) because they form highly stable tertiary carbocations.
Key Formula or Approach:
For an $S_{N}1$ reaction:
1. Rate Law: \( \text{Rate} = k[\text{Substrate}] \).
2. Rate depends on the stability of the carbocation intermediate.
3. Polar protic solvents stabilize the transition state and the ionic intermediates through solvation.

Step 2: Detailed Explanation:
$\bullet$ Statement (B): In $S_{N}1$, the nucleophile (OH$^{-}$) is not involved in the rate-determining step. Increasing its concentration has no effect. This is a correct statement.
$\bullet$ Statement (C): The first step is the slow ionization of the C-Br bond to form the carbocation. This is the rate-determining step (RDS). This is a correct statement.
$\bullet$ Statement (D): Since it is a first-order reaction, the rate is directly proportional to the substrate concentration. This is a correct statement.
$\bullet$ Statement (A): Water is significantly more polar than ethanol (dielectric constant $\approx 80$ vs $24.5$). Adding water to the solvent increases the overall polarity, which enhances the stabilization of the carbocation and increases the reaction rate. Statement (A) says the rate decreases, making it incorrect.

Step 3: Final Answer:
The incorrect statement is (A).