In which of the following, Mg reacts best with alkyl bromide.

\(C_2H_5OC_2H_5\)

The answer is (3) \(C_2H_5OC_2H_5\).

Grignard reagents are prepared by reacting an alkyl halide with magnesium metal in an anhydrous ether solvent. The ether solvent is important because it prevents the magnesium metal from reacting with oxygen or water.

The three solvents listed in the question are all ether solvents, but they have different properties. \(C_2H_5OC_2H_5\), also known as diethyl ether, is the most inert of the three solvents. This means that it is less likely to react with the magnesium metal, which results in a higher yield of the Grignard reagent.

The other two solvents, \(C_6H_5OCH_3\) , also known as methyl anisole, and \(C_6H_5N(CH_3)_2\), also known as N, N-dimethylaniline, are more reactive than diethyl ether. This means that they are more likely to react with the magnesium metal, which results in a lower yield of the Grignard reagent.

Therefore, the best solvent for preparing Grignard reagents is \(C_2H_5OC_2H_5\).

The other options are incorrect. Option (1) \(C_6H_5OCH_3\) , is a less inert solvent than diethyl ether, so it will result in a lower yield of the Grignard reagent. Option (2) \(C_6H_5N(CH_3)_2\), is even more reactive than \(C_6H_5OCH_3\) , so it will result in an even lower yield of the Grignard reagent. Option (4) equally in all the three, is incorrect because the three solvents have different properties, as explained above.