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 Question:
This question asks us to identify the incorrect statement regarding the nucleophilic substitution reaction of tert-butyl bromide with hydroxide ion in ethanol solvent.

Step 2: Key Formula or Approach:
Analyze the mechanism of the reaction:
- The substrate is a tertiary alkyl halide (tert-butyl bromide).
- The reaction is carried out in a polar protic solvent (ethanol) with a nucleophile ($\text{OH}^-$).
- This reaction proceeds via the $\text{S_{\text{N}}1$ mechanism} (unimolecular nucleophilic substitution) because the tertiary substrate forms a highly stable tertiary carbocation ($\text{t-Bu}^+$).

Step 3: Detailed Explanation:
Let's evaluate each statement under the rules of the $\text{S}_{\text{N}}1$ pathway:

• Why Statement (B) is correct:
- For an $\text{S}_{\text{N}}1$ reaction, the rate law depends only on the substrate concentration:
\[ \text{Rate} = k[\text{t-BuBr}] \] - It is a first-order process that is independent of the concentration and strength of the nucleophile ($\text{OH}^-$). Thus, increasing $[\text{OH}^-]$ will not change the reaction rate.

• Why Statement (C) is correct:
- The rate-determining step (RDS) is the slow, initial step where the carbon-bromine bond polarizes and dissociates to form the carbocation intermediate:
\[ \text{t-BuBr} \rightarrow \text{t-Bu}^+ + \text{Br}^- \quad \text{(Slow, RDS)} \]
• Why Statement (D) is correct:
- Since the rate law is $\text{Rate} = k[\text{t-BuBr}]$, the reaction rate is directly proportional to the concentration of the alkyl halide.

• Why Statement (A) is incorrect:
- In the rate-determining step of an $\text{S}_{\text{N}}1$ reaction, neutral reactant molecules form charged transition states and ionic intermediates (carbocation and leaving group).
- Polar protic solvents stabilize this transition state and the resulting ions via strong solvation (hydrogen bonding and dipole-dipole interactions), reducing the activation energy.
- Water ($\text{H}_2\text{O}$) is much more polar (dielectric constant $\approx 80$) than pure ethanol (dielectric constant $\approx 24.5$).
- Therefore, adding water to the ethanol solvent (creating a 1:1 mixture) increases the polarity of the medium. This enhances carbocation stabilization and dramatically increases (not decreases) the reaction rate.

Step 4: Final Answer:
Since statement (A) asserts that the rate decreases in a more polar solvent mixture, it is incorrect and is the desired answer.