Which of the following are the starting materials for the Grignard synthesis of tert-butanol? 

CH₃MgBr  + CH₃COCH₃

The correct answer is option 1. \(CH_3MgBr + CH_3COCH_3\).

The Grignard synthesis involves the reaction of a Grignard reagent with a carbonyl compound to form an alcohol. For tert-butanol, which is a tertiary alcohol (2-methyl-2-propanol), we need the appropriate starting materials to create the structure.

Let us look at the options in detail:

1. \(CH_3MgBr + CH_3COCH_3\)

\(CH_3MgBr\) (methyl magnesium bromide) is the Grignard reagent.

\(CH_3COCH_3\) (acetone) is the carbonyl compound (a ketone).

When the Grignard reagent reacts with the ketone, the carbon of the \(CH_3MgBr\) attacks the carbonyl carbon of acetone. The result after the reaction and hydrolysis is the formation of tert-butanol:

\(CH_3MgBr + CH_3COCH_3 \rightarrow (CH_3)_3COH\)

This forms tert-butanol (2-methyl-2-propanol).

2. \(CH_3CH_2MgBr + CH_3COCH_3\)

\(CH_3CH_2MgBr\) (ethyl magnesium bromide) is the Grignard reagent.

\(CH_3COCH_3\) (acetone) is the carbonyl compound.

The reaction would be:

\(CH_3CH_2MgBr + CH_3COCH_3 \rightarrow CH_3CH_2C(CH_3)_2OH\)

This forms a different alcohol (3-pentanol), not tert-butanol.

3. \(CH_3MgBr + CH_3CH(OH)CH_3\)

\(CH_3MgBr\) (methyl magnesium bromide) is the Grignard reagent.

\(CH_3CH(OH)CH_3\) (isopropanol) is an alcohol, not a ketone or aldehyde.

This combination is not appropriate because isopropanol is already an alcohol and will not react in the same way as a carbonyl compound to form a tertiary alcohol.

4. \(CH_3MgBr + (CH_3)_3CH_3\)

The chemical formula \((CH_3)_3CH_3\) is incorrect and does not represent a ketone or aldehyde. Therefore, it cannot be used for the Grignard synthesis.

Given these explanations, the correct option for synthesizing tert-butanol using the Grignard reaction is:

\(CH_3MgBr + CH_3COCH_3\)

This reaction results in the formation of tert-butanol because the Grignard reagent \((CH_3MgBr)\) reacts with acetone \((CH_3COCH_3)\) to form the desired tertiary alcohol (tert-butanol).