The most efficient method for synthesizing a carboxylic acid from an alkyl halide is through a two-step process: first, the nucleophilic substitution of the alkyl halide with a cyanide ion CN- to form a nitrile, followed by hydrolysis of the nitrile to form the carboxylic acid. Here is a detailed mechanism, including all reagents and reaction conditions involved:Step 1: Nucleophilic substitution of the alkyl halide with a cyanide ionReagents: Sodium cyanide NaCN or potassium cyanide KCN Solvent: Dimethyl sulfoxide DMSO or another polar aprotic solventReaction conditions: Room temperature or slightly elevated temperature 50-60C , under an inert atmosphere e.g., nitrogen or argon Mechanism:1. The cyanide ion CN- acts as a nucleophile and attacks the electrophilic carbon atom of the alkyl halide R-X, where R is an alkyl group and X is a halogen .2. The bond between the carbon and the halogen breaks, with the halogen leaving as a halide ion X- .3. The nitrile R-CN is formed as the product.Step 2: Hydrolysis of the nitrile to form the carboxylic acidReagents: Aqueous acid e.g., H2SO4, HCl or base e.g., NaOH, KOH Solvent: WaterReaction conditions: Reflux heating under continuous condensation at 100-110C for several hoursMechanism under acidic conditions :1. The carbonyl carbon of the nitrile R-CN is protonated by the acid H+ , forming an iminium ion R-CNH+ .2. A water molecule attacks the electrophilic carbonyl carbon, forming a tetrahedral intermediate.3. The iminium ion is deprotonated, resulting in the formation of an amide R-CONH2 .4. The amide nitrogen is protonated by the acid H+ , forming a protonated amide R-CONH3+ .5. A water molecule attacks the electrophilic carbonyl carbon, forming a second tetrahedral intermediate.6. The tetrahedral intermediate collapses, releasing a water molecule and forming a protonated carboxylic acid R-COOH2+ .7. The protonated carboxylic acid is deprotonated, yielding the final carboxylic acid product R-COOH .Mechanism under basic conditions :1. The cyanide ion CN- is attacked by a hydroxide ion OH- , forming a metal cyanate intermediate R-CNO- .2. The metal cyanate intermediate rearranges to form an amide R-CONH2 .3. The amide is attacked by a hydroxide ion OH- , forming a tetrahedral intermediate.4. The tetrahedral intermediate collapses, releasing an amine NH2- and forming a carboxylate ion R-COO- .5. The carboxylate ion is protonated by water, yielding the final carboxylic acid product R-COOH .In summary, the most efficient method for synthesizing a carboxylic acid from an alkyl halide involves a two-step process: nucleophilic substitution with a cyanide ion to form a nitrile, followed by hydrolysis of the nitrile to form the carboxylic acid.