In the mechanism for the reaction of HBr with t - butyl alcohol, pick out the correct statement .

Options

A. Formation of protonated alcohol in a slow step
B. Formation of `(CH_3)_3C^(+)` is a slow step
C. Formation of `(CH_3)_3CBr` from `(CH_3)_3C^+` is a slow step
D. Formation of `(CH_3)_3C^+` is a fast step

Answer

To solve the question regarding the mechanism of the reaction between HBr and tert-butyl alcohol, we will analyze the steps involved in the reaction mechanism and identify the correct statement.

### Step-by-Step Solution:

1. **Identify the Reactants**:
- The reactants in this reaction are HBr (hydrobromic acid) and tert-butyl alcohol (t-butanol).
- The structure of tert-butyl alcohol is:
\[ \text{(CH}_3\text{)}_3\text{COH} \]

2. **Initiation Step**:
- The first step involves the protonation of the alcohol by HBr.
- The oxygen atom in tert-butyl alcohol has lone pairs and can act as a base to accept a proton (H⁺) from HBr.
- This leads to the formation of a protonated alcohol:
\[ \text{(CH}_3\text{)}_3\text{C-OH}_2^+ \]
- This step is fast because acid-base reactions typically occur quickly.

3. **Carbocation Formation**:
- The next step involves the loss of water (H₂O) from the protonated alcohol, leading to the formation of a tert-butyl carbocation:
\[ \text{(CH}_3\text{)}_3\text{C}^+ \]
- This step is slow and is the rate-determining step of the mechanism.

4. **Nucleophilic Attack**:
- In the final step, the bromide ion (Br⁻) from HBr acts as a nucleophile and attacks the carbocation to form tert-butyl bromide:
\[ \text{(CH}_3\text{)}_3\text{C-Br} \]
- This step is fast as it involves the reaction between a nucleophile and an electrophile.

5. **Conclusion**:
- The correct statement regarding the mechanism is that the formation of the tert-butyl cation is the slowest step, while the formation of the protonated alcohol is fast, and the nucleophilic attack is also fast.

### Final Answer:
The correct statement is: **The formation of tert-butyl cation is the slowest step.**