Which alkyl halide from the following pairs would you expect to react more rapidly by `S_(N)2` mechanism ? Explain your answer.
`CH_(3)CH_(2)CH_(2)CH_(2) " or " CH_(3)CH_(2) - underset(Br)underset(|)CH - CH_(3)`
(ii) `CH_(3)CH_(2)underset(Br)underset(|)CHCH_(3)" or " H_(3)C - underset(CH_(3))underset(|)overset(CH_(3))overset(|)C-Br`
(iii) `CH_(3)underset(CH_(3))underset(|)CHCH_(2)CH_(2) Br " or " CH_(3)CH_(2)underset(CH_(3))underset(|)CHCH_(2)Br`

Explanation

(i) `CH_(3)CH_(2)CH_(2)Br " is a " 1^(@) " alkyl halide while " CH_(3)CH_(2) - CHBr - CH_(3) " is a " 2^(@) ` alkyl halide .
There will be more steric hindrance in `2^(@)` alkyl halides than in `1^(@) ` alkyl halides. Therefore, `CH_(3), CH_(2)CH_(2) Br` will react faster than `CH_(3)CH_(2) - CHBr - CH_(3) " in " S_(N) 2` reaction .
(ii) `CH_(3)CH_(2) - CHBr - CH_(3) " is " 2^(@) ` alkyl halide while `(CH_(3))_(3)C - Br " is " 3^(@) ` alkyl halide . Due to lesser steric hindrance, `2^(@) ` alkyl halides react faster than `3^(@)` alkyl halides. Therefore, `CH_(3)CH_(2) - CHBr - CH_(3) ` will reacter than `(CH_(3))_(3)CBr " in " S_(N) 2` reaction .
(iii) `overset(4)CH_(3) - underset(I)underset(CH_(3))underset(|)overset(3)(CH) - overset(2)CH_(2)overset(1)CH_(2)Br " " overset(4)CH_(3)overset(3)CH_(2)- underset(II)underset(CH_(3))underset(|)overset(2)(CH) - overset(1)CH_(2)Br`
Both I and II are `1^(@) ` alkyl halides . But in alkyl halide (II) , the `CH_(3) " group at " C_(2) `is closer to the Br atom while in alkyl halide (I) , the `CH_(3)" group at " C_(3)` is little away from the Br atom.
As a result , alkyl halide (II) will suffer greater steric hindrance than alkyl halide (I) . Therefore , `(CH_(3))_(2) CHCH_(2)CH_(2) Br` will react faster than `CH_(3)CH_(2)CH(CH_(3))Br " in " S_(N)2` reaction .