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Write the names of process to obtain compound (y) and compound (z) from compound (x) in the above nucleophilic reaction (i) and (ii)?
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Answer
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Hint: \[{S_N}2\] reaction mechanism allows the attack of nucleophiles from the back side of the carbon atom and thus the product takes a stereochemical position opposite to the leaving group originally occupied i.e. inversion of configuration. Whereas applying \[{S_N}2\] twice will result in retention of original configuration.

Complete step by step answer:
The \[{S_N}2\] reaction is a very good example of stereospecific reaction. Stereospecific reactions are those in which different stereoisomers react to give different stereoisomers of the product. Also, \[{S_N}2\] reaction is the common example of Walden inversion in which an asymmetric carbon atom undergoes inversion of configuration.
The \[{S_N}2\] reaction is a nucleophilic substitution reaction in which a bond is broken and another bond is formed synchronously. The rate determining step of the reaction involves two reactant molecules. Since these reactions are second-order reactions, the rate-determining step depends on the concentration of the nucleophile as well as the substrate. The term \[{S_N}2\] means Substitution Nucleophilic Bimolecular reaction, also called as associative substitution and interchange mechanism.
The mechanism proceeds through a backside attack of the nucleophile on the substrate. The nucleophile approaches the substrate at an angle of 180-deg to the bond of the carbon-leaving group. This forms the carbon-nucleophile bond and simultaneously breaks the carbon-leaving group bond via a transition state.
We observe that the leaving group is pushed out of the transition state on the opposite side of the carbon-nucleophile bond, forming the desired product which has an inversion of the tetrahedral geometry at the atom in the centre.
From these points, we can now conclude that double \[{S_N}2\] mechanism takes place when product ‘y’ is formed as one \[{S_N}2\] will lead to inversion and when followed by another \[{S_N}2\] process, inversion of inversion results in retention of configuration. Whereas when product ‘z’ is obtained, a single \[{S_N}2\] process occurs that gives us the product with inversion of original ‘x’ configuration.
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Hence, we can say that double \[{S_N}2\] and single \[{S_N}2\] process takes place so as to obtain compound (y) and compound (z) from compound (x) in the above nucleophilic reaction (i) and (ii).

Note:
\[{S_N}2\] reactions are stereospecific i.e. not the same as stereoselective. A stereospecific mechanism specifies the stereochemical output of a reactant, whereas a stereoselective reaction selects products from those which are available by the same non-specific process acting on a given reactant.