Q.Consider the reaction, CH₃CH₂CH₂Br + NaCN → CH₃CH₂CH₂CN + NaBr. This reaction will be the fastest in a) ethanol b) methanol c) DMF (N,N'-dimethylformamide) d) water

Acetonitrile (CH$_3$CN, 2 carbons) is made by heating methyl chloride with alcoholic KCN.

Acetonitrile is $CH_3-C\equiv N$, which has only 2 carbon atoms (one from the original methyl group, one from the CN group). It is prepared by heating a haloalkane with alcoholic potassium cyanide (KCN), which provides the nucleophilic CN$^-$ ion (via the more covalent, less ionic KCN reacting through carbon to give the nitrile, C-substitution product):

$CH_3Cl + KCN \xrightarrow{alc.} CH_3CN + KCl$

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CH3-CHCl2 (ethylidene chloride, a gem-dihalide) hydrolyses with aqueous KOH to give acetaldehyde (CH3CHO), because the intermediate gem-diol is unstable and loses water to form a carbonyl group.

Ethylidene chloride is 1,1-dichloroethane, CH3-CHCl2 — both chlorines sit on the SAME carbon (a geminal dihalide), unlike ethylene dichloride (CH2Cl-CH2Cl), which has one chlorine on each carbon.

When a gem-dihalide is treated with aqueous KOH, nucleophilic substitution (OH- replacing Cl-, twice) first gives a geminal diol:

CH3-CHCl2 + 2KOH -> CH3-CH(OH)2 + 2KCl

A carbon bearing two -OH groups on the same carbon (a gem-diol) is unstable and spontaneously eliminates a molecule of water to form a carbonyl (C=O) group:

CH3-CH(OH)2 -> CH3-CHO + H2O

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AgCN attacks through N (covalent Ag–C bond), giving ethyl isocyanide, $CH_3CH_2NC$, not the nitrile.

$AgCN$ is predominantly covalent (Ag–C bond has significant covalent character), so the more electronegative nitrogen atom of the cyanide ion is the one that attacks the alkyl halide's electrophilic carbon (as opposed to $KCN$, which is ionic and reacts through carbon). This gives the isocyanide …

Alkyl halides with silver nitrite give nitroalkanes as the major product.

Silver nitrite ($AgNO_2$) is largely covalent, and in the nitrite ion the nitrogen atom (rather than oxygen) is the stronger nucleophile that attacks the electrophilic carbon of the alkyl halide (SN2), so the major product is the nitroalkane (C-bonded), with the metal halide as byproduct:

$R-X + AgNO_2 \rightarrow R-NO_2\ (nitroalkane) + AgX\downarrow$ …