using 1-bromobutane and any necessary organic or inorganic reagent, suggest efficient syntheses of each of the following alcohols:

1) 1-pentanol

2) 2-hexanol

3) 1-phenyl-1-hexanol

4) 3-methyl-3-heptanol

5) 1-butylcyclobutanol

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To synthesize each of the given alcohols using 1-bromobutane as a starting material, we can apply various organic reactions. Below are efficient syntheses for each alcohol:

1) 1-Pentanol:
Using 1-bromobutane (primary alkyl halide), we can perform a nucleophilic substitution reaction with potassium cyanide (KCN) in the presence of ethanol as a solvent. This reaction is known as the SN2 reaction or the cyanide substitution reaction. The reaction proceeds as follows:
1-bromobutane + KCN → 1-pentyl cyanide
The obtained 1-pentyl cyanide can then undergo a hydrolysis reaction, either acidic or basic, to yield 1-pentanol.

2) 2-Hexanol:
A similar procedure can be followed to synthesize 2-hexanol. Starting with 1-bromobutane, we can perform an SN2 reaction with sodium azide (NaN3) to obtain 2-hexyl azide. The reaction is as follows:
1-bromobutane + NaN3 → 2-hexyl azide
Then, the obtained 2-hexyl azide can be subjected to a reduction reaction, such as the Staudinger reaction, using triphenylphosphine (PPh3) as a reducing agent in the presence of anhydrous solvents like ether. This yields 2-hexanol.

3) 1-Phenyl-1-hexanol:
To synthesize this alcohol, we need an extra step compared to the previous cases. Starting with 1-bromobutane, we can perform an SN2 reaction with sodium cyanide (NaCN) to obtain 1-phenyl-1-hexyl nitrile. The reaction is as follows:
1-bromobutane + NaCN → 1-phenyl-1-hexyl nitrile
Next, the nitrile group can be reduced by using either lithium aluminum hydride (LiAlH4) or diisobutylaluminium hydride (DIBAL-H) to yield the desired alcohol, 1-phenyl-1-hexanol.

4) 3-Methyl-3-heptanol:
Using 1-bromobutane, we can perform an SN2 reaction with methylmagnesium bromide (CH3MgBr), also known as Grignard reagent, to obtain 3-methyl-3-heptylmagnesium bromide. The reaction is as follows:
1-bromobutane + CH3MgBr → 3-methyl-3-heptylmagnesium bromide
Subsequently, the obtained Grignard reagent can be treated with water (H2O) or dilute acid to hydrolyze it and produce 3-methyl-3-heptanol.

5) 1-Butylcyclobutanol:
In this synthesis, we need to introduce a cyclic structure. Starting with 1-bromobutane, we can perform an SN2 reaction with sodium ethoxide (NaOEt) in ethanol or another suitable solvent to obtain 1-butyl ethyl ether. The reaction is as follows:
1-bromobutane + NaOEt → 1-butyl ethyl ether
Next, the obtained 1-butyl ethyl ether can undergo a ring-closing reaction through an acid-catalyzed intramolecular condensation reaction, converting it into 1-butylcyclobutanol.

Note: Safety precautions should be followed when working with organic reagents and reaction conditions.