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Explain the following with one example:
(a) Williamson’s synthesis
(b) Kolbe’s reaction
(c) Hell-volhard-zelinsky $\left( {HVZ} \right)$ reaction.
(d) Aldol reaction.

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Hint: In organic reactions covalent bonds break and some new covalent bonds are formed . This making and breaking of covalent bonds usually occur in a number of steps before they are finally turned into products ; the sequential description of all the steps of the transformation into product is called the mechanism of a reaction.

Complete step by step answer:
(a) Williamson’s synthesis: It is the method used for the production of ethers . It occurs by an $S{N^2}$ reaction in which a metal alkoxide displaces a halide ion from an alkyl halide. The alkoxide ion is prepared by the reaction of an alcohol with a strong base such as sodium Hydride
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(b) Kolbe’s reaction: It is a chemical reaction that begins by first heating sodium phenoxide(the sodium salt of phenol) with carbon dioxide under pressure $\left( {100\;{\text{atm}},{{125}^ \circ }C} \right)$ , then the product is treated with sulphuric acid. The final product is an aromatic hydroxy acid which is also known as salicylic acid.
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(c) Hell-volhard-zelinsky $\left( {HVZ} \right)$ reaction: When carboxylic acid reacts with chlorine or bromine using red phosphorus then halo atom is substituted at the Alpha carbon and the product obtained is mono $\alpha $ -halogenated acids. This is known as the $HVZ$ reaction.
$C{H_3}C{H_2}COOH + B{r_2}\xrightarrow{{{\text{Red}}\;{\text{P}}}}C{H_3}CHBrCOOH + HBr$
(d) Aldol reaction:  The word aldol means product having both aldehyde and alcoholic group
Aldehyde having $\alpha $ -hydrogen(s) undergoes self condensation on warning with dilute or mild base to give $\beta - $ hydroxy aldehyde, called aldol (aldehyde $ + $ alcohol). This reaction is known as aldol condensation.

Note:The mechanism of a reaction is a very important part because initially we think the reactants will produce something but when we look at the mechanism we find out that actually the product is something else .