Complete the missing links .
`A overset(CH_(3) MgBr)(to) B overset(H_(3)O^(+))(to) C`

Options

A. `CH_3COCH_3 (CH_3)_3COMgBr, (CH_3)_3COH`
B. `CH_3COOH, (CH_3)CHOMgBr, CH_3CH_2OH`
C. `(CH_3COO)_2Ca, CH_3CH_2OMgBr, CH_2underset(OH)underset(|)"CH"-CH_3`
D. `CH_3COOCH_3, (CH_3)_3COMgBr,CH_3-underset(OH)underset(|)"CH"-CH_3`

Explanation

To solve the question, we need to identify the compounds A, B, and C based on the reaction with Grignard's reagent (CH₃MgBr) and subsequent hydrolysis.

### Step-by-Step Solution:

1. **Identify Compound A:**
- The question states that compound A reacts with Grignard's reagent. Given the context, we can deduce that compound A is likely a type of ether.
- In this case, we can identify A as **dimethyl ether (CH₃OCH₃)**.

2. **Reaction with Grignard's Reagent:**
- When dimethyl ether (A) reacts with Grignard's reagent (CH₃MgBr), the Grignard reagent acts as a nucleophile and attacks the ether.
- This reaction leads to the formation of a new compound, which we can denote as B. The reaction can be represented as follows:
\[ \text{CH}_3\text{OCH}_3 + \text{CH}_3\text{MgBr} \rightarrow \text{CH}_3\text{C(OMgBr)(CH}_3\text{)} \]
- Here, B is a magnesium alkoxide, specifically **(CH₃)₂C(OMgBr)**.

3. **Hydrolysis of Compound B:**
- The next step involves the hydrolysis of compound B in the presence of water (H₃O⁺).
- During hydrolysis, the alkoxide reacts with water, leading to the formation of an alcohol. The hydrolysis can be represented as follows:
\[ \text{(CH}_3\text{)}_2\text{C(OMgBr)} + \text{H}_3\text{O}^+ \rightarrow \text{(CH}_3\text{)}_2\text{C(OH)} + \text{MgBrOH} \]
- The resulting compound C is a tertiary alcohol, specifically **tert-butyl alcohol (C(CH₃)₃OH)**.

4. **Final Summary:**
- Therefore, the complete reaction sequence is:
- A: Dimethyl ether (CH₃OCH₃)
- B: (CH₃)₂C(OMgBr)
- C: Tert-butyl alcohol (C(CH₃)₃OH)

### Final Answer:
- A: Dimethyl ether (CH₃OCH₃)
- B: (CH₃)₂C(OMgBr)
- C: Tert-butyl alcohol (C(CH₃)₃OH)