Which among the following is not true for the hydrolysis of t - butyl bromide with aqueous NaOH ?

Options

A. Reaction occurs through the `S_N1` mechanism.
B. The intermediate formed is a carbocation.
C. Rate of the reaction doubles when concentration of alkali is doubled.
D. Rate of the reaction doubles when the concentration of t - butyl bromide is doubled.

Answer

To solve the question regarding the hydrolysis of t-butyl bromide with aqueous NaOH, we will analyze the statements related to the reaction mechanism and the properties of the reactants involved.

### Step-by-Step Solution:

1. **Identify the Reaction Type**:
- The hydrolysis of t-butyl bromide (tert-butyl bromide) involves a tertiary alkyl halide.
- Tertiary alkyl halides typically undergo an SN1 reaction mechanism due to the stability of the carbocation formed during the reaction.

**Hint**: Remember that the stability of carbocations increases with the degree of substitution; tertiary carbocations are the most stable.

2. **Formation of Carbocation**:
- In the SN1 mechanism, the first step is the formation of a carbocation after the leaving group (Br-) departs.
- The reaction can be represented as:
\[ (CH_3)_3CBr \rightarrow (CH_3)_3C^+ + Br^- \]

**Hint**: Focus on the stability of the carbocation; tertiary carbocations are stabilized by hyperconjugation and inductive effects.

3. **Nucleophilic Attack**:
- Once the carbocation is formed, the nucleophile (OH-) from NaOH attacks the positively charged carbon center.
- This results in the formation of t-butyl alcohol:
\[ (CH_3)_3C^+ + OH^- \rightarrow (CH_3)_3COH \]

**Hint**: The nucleophile attacks the carbocation, leading to the final product.

4. **Rate of Reaction**:
- In an SN1 reaction, the rate of reaction depends only on the concentration of the alkyl halide (t-butyl bromide) and not on the concentration of the nucleophile (NaOH).
- Thus, if the concentration of t-butyl bromide is doubled, the rate of reaction will also double.

**Hint**: Recall that in SN1 reactions, the rate law is first-order with respect to the substrate.

5. **Evaluate Statements**:
- Now we need to evaluate the statements given in the question to find which one is not true:
- **A**: The reaction occurs through the SN1 mechanism. (True)
- **B**: The rate of reaction depends on the concentration of the nucleophile. (Not True)
- **C**: The intermediate formed is a carbocation. (True)
- **D**: The rate of reaction doubles when the concentration of t-butyl bromide is doubled. (True)

**Hint**: Carefully analyze each statement against the principles of SN1 reactions.

6. **Conclusion**:
- The statement that is not true is **B**, as the rate of reaction does not depend on the concentration of the nucleophile in an SN1 mechanism.

### Final Answer:
The statement that is not true for the hydrolysis of t-butyl bromide with aqueous NaOH is **B**: "The rate of reaction depends on the concentration of the nucleophile."