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Q. The $ {{S}_{N}}1 $ reactivity of the following halides will be in the order
(i) $ (CH_3)_3CBr $
(ii) $ (C_6H_5)_2CHBr $
(iii) $ (C_6H_5)_2C(CH_3)Br $
(iv) $ (CH_3)_2CHBr $
(v) $ C_2H_5Br $

KEAMKEAM 2007Haloalkanes and Haloarenes

Solution:

$ {{S}_{N}}1 $ (Unimolecular nucleophilic substitution reactions)
$ Rate\propto (substrate) $
Rate of determining step in the formation of carbocation depends on the stability of carbocation formed. The stability of carbocations follow the order-
$ {{({{C}_{6}}{{H}_{5}})}_{2}}{{C}^{+}}(C{{H}_{3}})>{{({{C}_{6}}{{H}_{5}})}_{2}}\overset{+}{\mathop{C}}\,H> $
$ {{(C{{H}_{3}})}_{2}}\overset{+}{\mathop{C}}\,H>C{{H}_{3}}CH_{2}^{+} $
$ \because $ Order of $ {{S}_{N}}1 $ reactivity is $ {{({{C}_{6}}{{H}_{5}})}_{2}}C(C{{H}_{3}})Br>{{({{C}_{6}}{{H}_{5}})}_{2}}CHBr> $
$ {{(C{{H}_{3}})}_{3}}CBr>{{(C{{H}_{3}})}_{2}}\overset{+}{\mathop{C}}\,HBr>{{C}_{2}}{{H}_{5}}Br $ ie,
$ iii>ii>i>iv>v $